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Title: The Energy System of Matter
A Deduction from Terrestrial Energy Phenomena
Author: James Weir
Release Date: December 20, 2011 [EBook #38348]
Language: English
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THE ENERGY SYSTEM OF MATTER
THE ENERGY SYSTEM OF MATTER
A DEDUCTION FROM TERRESTRIAL
ENERGY PHENOMENA
BY
JAMES WEIR
_WITH 12 DIAGRAMS_
LONGMANS, GREEN AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK BOMBAY, AND CALCUTTA
1912
All rights reserved
PREFACE
An intimate study of natural phenomena and a lengthened experience in
physical research have resulted in the formation of certain
generalisations and deductions which I now present in this volume. I
have reached the conclusion that every physical phenomenon is due to the
operation of energy transformations or energy transmissions embodied in
material, and takes place under the action or influence of incepting
energy fields. In any instance the precise nature of the phenomena is
dependent on the peculiar form of energy actively engaged, on the nature
of the material to which this energy is applied, and on the nature of
the incepting field which influences the process. In the course of the
work several concrete cases are discussed, in which these features of
energy are illustrated and explained by the use of simple experimental
apparatus. It is hoped that, by this means, the distinctive differences
which exist in the manifestations of energy, in its transformation, in
its transmission, and in its incepting forms will be rendered clear to
the reader. I have to express my indebtedness to Mr. James Affleck,
B.Sc., for his assistance in the preparation of this work for
publication.
JAMES WEIR.
OVER COURANCE,
LOCKERBIE, SCOTLAND.
CONTENTS
PAGE
INTRODUCTION 1
PART I
GENERAL STATEMENT
1. ADVANTAGES OF GENERAL VIEW OF NATURAL OPERATIONS 7
2. SEPARATE MASS IN SPACE 8
3. ADVENT OF ENERGY--DISTORTIONAL EFFECTS 9
4. THE GRAVITATION FIELD 11
5. LIMITS OF ROTATIONAL ENERGY--DISRUPTIONAL
PHENOMENA 13
6. PASSIVE FUNCTION AND GENERAL NATURE OF GRAVITATION
FIELD 17
7. LIMIT OF GRAVITATION TRANSFORMATION 18
8. INTERACTIONS OF TWO PLANETARY BODIES--EQUILIBRIUM
PHENOMENA 19
9. AXIAL ENERGY--SECONDARY PROCESSES 22
10. MECHANISM OF ENERGY RETURN 27
11. REVIEW OF COSMICAL SYSTEM--GENERAL FUNCTION OF
ENERGY 29
12. REVIEW OF COSMICAL SYSTEM--NATURAL CONDITIONS 31
PART II
PRINCIPLES OF INCEPTION
13. ILLUSTRATIVE SECONDARY PROCESSES 34
14. INCEPTING ENERGY INFLUENCES 40
15. COHESION AS AN INCEPTING INFLUENCE 45
16. TERRESTRIAL GRAVITATION AS AN INCEPTING INFLUENCE 48
17. THE GRAVITATION FIELD 51
18. THE THERMAL FIELD 54
19. THE LUMINOUS FIELD 58
20. TRANSFORMATIONS--UPWARD MOVEMENT OF A MASS
AGAINST GRAVITY 62
21. TRANSFORMATIONS--THE SIMPLE PENDULUM 67
22. STATICAL ENERGY CONDITIONS 68
23. TRANSFORMATIONS OF THE MOVING PENDULUM--ENERGY
OF MOTION TO ENERGY OF POSITION AND VICE VERSA 72
24. TRANSFORMATIONS OF THE MOVING PENDULUM--FRICTIONAL
TRANSFORMATION AT THE BEARING SURFACES 77
25. STABILITY OF ENERGY SYSTEMS 79
26. THE PENDULUM AS A CONSERVATIVE SYSTEM 81
27. SOME PHENOMENA OF TRANSMISSION PROCESSES--TRANSMISSION
OF HEAT ENERGY BY SOLID MATERIAL 84
28. SOME PHENOMENA OF TRANSMISSION PROCESSES--TRANSMISSION
BY FLEXIBLE BAND OR CORD 89
29. SOME PHENOMENA OF TRANSMISSION PROCESSES--TRANSMISSION
OF ENERGY TO AIR MASSES 92
30. ENERGY MACHINES AND ENERGY TRANSMISSION 95
31. IDENTIFICATION OF FORMS OF ENERGY 107
32. COMPLETE SECONDARY CYCLICAL OPERATION 114
PART III
TERRESTRIAL CONDITIONS
33. GASEOUS EXPANSION 118
34. GRAVITATIONAL EQUILIBRIUM OF GASES 124
35. TOTAL ENERGY OF GASEOUS SUBSTANCES 131
36. COMPARATIVE ALTITUDES OF PLANETARY ATMOSPHERES 135
37. REACTIONS OF COMPOSITE ATMOSPHERE 139
38. DESCRIPTION OF TERRESTRIAL CASE 143
39. RELATIVE PHYSICAL CONDITIONS OF ATMOSPHERIC
CONSTITUENTS 150
40. TRANSMISSION OF ENERGY FROM AQUEOUS VAPOUR TO
AIR MASSES 153
41. TERRESTRIAL ENERGY RETURN 160
42. EXPERIMENTAL ANALOGY AND DEMONSTRATION OF THE
GENERAL MECHANISM OF ENERGY TRANSFORMATION
AND RETURN IN THE ATMOSPHERIC CYCLE 170
43. APPLICATION OF PENDULUM PRINCIPLES 181
44. EXTENSION OF PENDULUM PRINCIPLES TO TERRESTRIAL
PHENOMENA 188
45. CONCLUDING REVIEW OF TERRESTRIAL CONDITIONS--EFFECTS
OF INFLUX OF ENERGY 192
THE ENERGY SYSTEM OF MATTER
INTRODUCTION
The main principles on which the present work is founded were broadly
outlined in the author's _Terrestrial Energy_ in 1883, and also in a
later paper in 1892.
The views then expressed have since been amply verified by the course of
events. In the march of progress, the forward strides of science have
been of gigantic proportions. Its triumphs, however, have been in the
realm, not of speculation or faith, but of experiment and fact. While,
on the one hand, the careful and systematic examination and
co-ordination of experimental facts has ever been leading to results of
real practical value, on the other, the task of the theorists, in their
efforts to explain phenomena on speculative grounds, has become
increasingly severe, and the results obtained have been decreasingly
satisfactory. Day by day it becomes more evident that not one of the
many existing theories is adequate to the explanation of the known
phenomena: but, in spite of this obvious fact, attempts are still
constantly being made, even by most eminent men, to rule the results of
experimental science into line with this or that accepted theory. The
contradictions are many and glaring, but speculative methods are still
rampant. They have become the fashion, or rather the fetish, of modern
science. It would seem that no experimental result can be of any value
until it is deductively accommodated to some preconceived hypothesis,
until it is embodied and under the sway of what is practically
scientific dogma. These methods have permeated all branches of science
more or less, but in no sphere has the tendency to indulge in
speculation been more pronounced than in that which deals with
energetics. In no sphere, also, have the consequences of such indulgence
been more disastrous. For the most part, the current conceptions of
energy processes are crude, fanciful, and inconsistent with Nature. They
require for their support--in fact, for their very existence--the
acceptance of equally fantastic conceptions of mythical substances or
ethereal media of whose real existence there is absolutely no
experimental evidence. On the assumed properties or motions of such
media are based the many inconsistent and useless attempts to explain
phenomena. But, as already pointed out, Nature has unmistakably
indicated the true path of progress to be that of experimental
investigation. In the use of this method only phenomena can be employed,
and any hypothesis which may be formulated as the result of research on
these lines is of scientific value only in so far as it is the correct
expression of the actual facts observed. By this method of holding close
to Nature reliable working hypotheses can, if necessary, be formed, and
real progress made. It is undeniably the method of true science.
In recent years much attention has been devoted to certain speculative
theories with respect to the origin and ultimate nature of matter and
energy. Such hypotheses, emanating as they do from prominent workers,
and fostered by the inherent imaginative tendency of the human mind,
have gained considerable standing. But it is surely unnecessary to point
out that all questions relating to origins are essentially outside the
pale of true science. Any hypotheses which may be thus formulated have
not the support of experimental facts in their conclusions; they belong
rather to the realm of speculative philosophy than to that of science.
In the total absence of confirmatory phenomena, such theories can, at
best, only be regarded as plausible speculations, to be accepted, it may
be, without argument, and ranking in interest in the order of their
plausibility.
Of modern research into the ultimate constitution of matter little
requires to be said. It is largely founded on certain radio-active and
electrical phenomena which, in themselves, contribute little
information. But aided by speculative methods and the use of
preconceived ethereal hypotheses, various elaborate theories have been
formulated, explaining matter and its properties entirely in terms of
ethereal motions. Such conceptions in their proper sphere--namely, that
of metaphysics--would be no doubt of interest, but when advanced as a
scientific proposition or solution they border on the ridiculous. In the
absence of phenomena bearing on the subject, it would seem that the last
resort of the modern scientist lies in terminology. To the average
seeker after truth, however, the term "matter," as applied to the
material world, will still convey as much meaning as the more elaborate
scientific definitions.
It is not the purpose of this work to add another thread to the already
tangled skein of scientific theory. It is written, rather, with the
conviction, that it is impossible ever to get really behind or beyond
phenomena; in the belief that the complete description of any natural
process is simply the complete description of the associated phenomena,
which may always be observed and co-ordinated but never ultimately
explained. Phenomena must ever be accepted simply as phenomena--as the
inscrutable manifestations of Nature. By induction from phenomena it is
indeed possible to rise to working hypotheses, and thence, it may be, to
general conceptions of Nature's order, and as already pointed out, it is
to this method, of accepting phenomena, and of reasoning only from
experimental facts, that all the advances of modern science are due. On
the other hand, it is the neglect of this method--the departure, as it
were, from Nature--which has led to the introduction into the scientific
thought of the day of the various ethereal media with their extreme and
contradictory properties. The use of such devices really amounts to an
admission of direct ignorance of phenomena. They are, in reality, an
attempt to explain natural operations by a highly artificial method,
and, having no basis in fact, their whole tendency is to proceed, in
ever-increasing degree, from one absurdity to another.
It is quite possible to gain a perfectly true and an absolutely reliable
knowledge of the properties of matter and energy, and the part which
each plays, without resorting to speculative aids. All that is required
is simply accurate and complete observation at first hand. The field of
research is wide; all Nature forms the laboratory. By this method every
result achieved may be tested and verified, not by its concurrence with
any approved theory, however plausible, but by direct reference to
phenomena. The verdict of Nature will be the final judgment on every
scheme.
It is on these principles, allied with the great generalisations with
respect to the conservation of matter and energy, that this work is
founded. As the result of a long, varied, and intimate acquaintance with
Nature, and much experimental research in many spheres, the author has
reached the conclusion, already foreshadowed in _Terrestrial Energy_,
that the great principle of energy conservation is true, not only in the
universal and generally accepted sense, but also in a particular sense
with respect to all really separate bodies, such as planetary masses in
space. Each of these bodies, therefore, forms within itself a completely
conservative energy system. This conclusion obviously involves the
complete denial of the transmission of energy in any form across
interplanetary space, and the author, in this volume, now seeks to
verify the conclusion by the direct experimental evidence of terrestrial
phenomena.
Under present-day conditions in science, the acceptance of the ordinary
doctrine of transmission across space involves likewise the acceptance
of the existence of an ethereal substance which pervades all space and
forms the medium by which such transmission is carried out. The
properties of this medium are, of course, precisely adapted to its
assumed function of transmission. These properties it is not necessary
to discuss, for when the existence of the transmission itself has been
finally disproved, the necessity for the transmitting medium clearly
vanishes.
PART I
GENERAL STATEMENT
1. _Advantages of General View of Natural Operations_
The object of this statement is to outline and illustrate, in simple
fashion, a broad and general conception of the operation and interaction
of matter and energy in natural phenomena.
Such a conception may be of value to the student of Nature, in several
ways. In modern times the general tendency of scientific work is ever
towards specialisation, with its corresponding narrowness of view. A
broad outlook on Nature is thus eminently desirable. It enables the
observer to perceive to some extent the links uniting the apparently
most insignificant of natural processes to those of seemingly greater
magnitude and importance. In this way a valuable idea of the natural
world as a whole may be gained, which will, in turn, tend generally to
clarify the aspect of particular operations. A broad general view of
Nature also leads to the appreciation of the full significance of the
great doctrines of the conservation of matter and energy. By its means
the complete verification of these doctrines, which appears to be beyond
human experiment, may be traced on the face of Nature throughout the
endless chain of natural processes. Such a view also leads to a firm
grasp of the essential nature and qualities of energy itself so far as
they are revealed by its general function in phenomena.
2. _Separate Mass in Space_
In the scheme now to be outlined, matter and energy are postulated at
the commencement without reference to their ultimate origin or inherent
nature. They are accepted, in their diverse forms, precisely as they are
familiar from ordinary terrestrial experience and phenomena.
For the purpose of general illustration the reader is asked to conceive
a mass of heterogeneous matter, concentrated round a given point in
space, forming a single body. This mass is assumed to be assembled and
to obtain its coherent form in virtue of that universal and inherent
property of matter, namely, gravitative or central attraction. This
property is independent of precise energy conditions, its outward
manifestation being found simply in the persistent tendency of matter on
all occasions to press or force itself into the least possible space. In
the absence of all disturbing influences, therefore, the configuration
of this mass of matter, assumed assembled round the given point, would
naturally, under the influence of this gravitative tendency, resolve
itself into that of a perfect sphere. The precise magnitude or
dimensions of the spherical body thus constituted are of little moment
in the discussion, but, for illustrative purposes, it may, in the
meantime, be assumed that in mass it is equivalent to our known solar
system. It is also assumed to be completely devoid of energy, and as a
mass to be under the influence of no external constraint. Under these
conditions, the spherical body may obviously be assumed as stationary in
space, or otherwise as moving with perfectly uniform velocity along a
precisely linear path. Either conception is justifiable. The body has no
relative motion, and since it is absolutely unconstrained no force could
be applied to it and no energy expenditure would be required for its
linear movement.
3. _Advent of Energy--Distortional Effects_
Nature, however, does not furnish us with any celestial or other body
fulfilling such conditions. Absolutely linear motion is unknown, and
matter is never found divorced from energy. To complete the system,
therefore, the latter factor is required, and, with the advent of energy
to the mass, its prototype may be found in the natural world.
This energy is assumed to be communicated in that form which we shall
term "work" energy (§§ 13, 31) and which, as a form of energy, will be
fully dealt with later. This "work" energy is assumed to be manifested,
in the first place, as energy of motion. As already pointed out, no
expenditure of energy can be associated with a linear motion of the
mass, since that motion is under no restraint, but in virtue of the
initial central attraction or gravitative strain, the form of energy
first communicated may be that of kinetic energy of rotation. Its
transmission to the mass will cause the latter to revolve about some
axis of symmetry within itself. Each particle of the mass thus pursues a
circular path with reference to that axis, and has a velocity directly
proportional to its radial displacement from it.
This energised rotating spherical mass is thus the primal conception of
the energy scheme now to be outlined. It will be readily seen that, as a
primal conception, it is essentially and entirely natural; so much so,
indeed, that any one familiar with rotatory motion might readily predict
from ordinary experience the resulting phenomena on which the scheme is,
more or less, based.
When energy is applied to the mass, the first phenomenon of note will be
that, as the mass rotates, it departs from its originally spherical
shape. By the action of what is usually termed centrifugal force, the
rotating body will be distorted; it will be flattened at the polar or
regions of lowest velocity situated at the extremities of the axis of
rotation, and it will be correspondingly distended at the equatorial or
regions of highest velocity. The spherical body will, in fact, assume a
more or less discoidal form according to the amount of energy applied to
it; there will be a redistribution of the original spherical matter;
certain portions of the mass will be forced into new positions more
remote from the central axis of rotation.
4. _The Gravitation Field_
These phenomena of motion are the outward evidence of certain energy
processes. The distortional movement of the material is carried out
against the action and within the field of certain forces which exist in
the mass of material in virtue of its gravitative or cohesive qualities.
It is carried out also in virtue of the application of energy to the
sphere, which energy has been, as it were, transformed or worked down,
in the distortional movement, against the restraining action of this
gravitation field or influence. The outward displacement of the material
from the central axis is thus coincident with a gain of energy to the
mass, this gain of energy being, of course, at the expense of, and by
the direct transformation of, the originally applied energy. It is
stored in the distorted material as energy of position, potential
energy, or energy of displacement relative to the central axis. But, in
the distortive movement, the mass will also gain energy in other forms.
The movement of one portion of its material relative to another will
give rise (since it is carried out under the gravitational influence) to
a fractional process in which, as we know from terrestrial experience,
heat and electrical energy will make their appearance. These forms of
energy will give rise, in their turn, to all the phenomena usually
attendant on their application to material. As already pointed out also,
the whole mass gains, in varying degree, energy of motion or kinetic
energy. It would appear, then, that although energy was nominally
applied to the mass in one form only, yet by its characteristic property
of transformation it has in reality manifested itself in several
entirely different forms. It is important to note the part played in
these transformation processes by the gravitation field or influence.
Its action really reveals one of the vital working principles of
energetics. This principle may be generally stated thus:--
EVERY TRANSFORMATION OF ENERGY IS CARRIED OUT BY THE ACTION OF
ENERGISED MATTER IN THE LINES OR FIELD OF AN INCEPTING ENERGY
INFLUENCE.
In the particular case we have just considered, the incepting field is
simply the inherent gravitative property of the energised mass. This
property is manifested as an attractive force between portions of
matter. This, however, is not of necessity the only aspect of an
incepting influence. In the course of this work various instances of
transformation will be presented in which the incepting influence
functions in a guise entirely different. It is important to note that
the incepting influence itself is in no way changed, altered, or
transformed during the process of transformation which it influences.
5. _Limits of Rotational Energy. Disruptional Phenomena_
It is clear that the material at different parts of the rotating
spheroid will be energised to varying degrees. Since the linear velocity
of the material in the equatorial regions of the spheroid is greater
than that of the material about the poles, the energy of motion of the
former will exceed that of the latter, the difference becoming greater
as the mass is increasingly energised and assumes more and more the
discoidal form.
The question now arises as to how far this process of energising the
material mass may be carried. What are its limits? The capacity of the
rotating body for energy clearly depends on the amount of work which
may be spent on its material in distorting it against the influence of
the gravitative attraction. The amount is again dependent on the
strength of this attraction. But the value of the gravitative attraction
or gravitation field is, by the law of gravitation, in direct proportion
to the quantity of material or matter present, and hence the capacity of
the body for energy depends on its mass or on the quantity of matter
which composes it.
Now if energy be impressed on this mass beyond its capacity a new order
of phenomena appears. Distortion will be followed by disruption and
disintegration. By the action of the disruptive forces a portion of the
primary material will be projected into space as a planetary body. The
manner of formation of such a secondary body is perhaps best illustrated
by reference to the commonplace yet beautiful and suggestive phenomenon
of the separation of a drop of water or other viscous fluid under the
action of gravitation. In this process, during the first downward
movement of the drop, it is united to its source by a portion of
attenuated material which is finally ruptured, one part moving downwards
and being embodied in the drop whilst the remainder springs upwards
towards the source. In the process of formation of the planetary body we
are confronted with an order of phenomena of somewhat the same nature.
The planetary orb which is hurled into space is formed in a manner
similar to the drop of viscous fluid, and under the action of forces of
the same general nature. One of these forces is the bond of gravitative
attraction between planet and primary which is never severed, and when
complete separation of the two masses finally occurs, the incessant
combination of this force with the tangential force of disruption acting
on the planet will compel it into a fixed orbit, which it will pursue
around the central axis. When all material links have thus been severed,
the two bodies will then be absolutely separate masses in space. The
term "separate" is here used in its most rigid and absolute sense. No
material connection of any kind whatever exists, either directly or
indirectly, between the two masses. Each one is completely isolated from
the other by interplanetary space, and in reality, so far as material
connection is concerned, each one might be the sole occupant of that
space. This conception of separate masses in space is of great
importance to the author's scheme, but, at the same time, the condition
is one which cannot be illustrated by any terrestrial experimental
contrivance. It will be obvious that such a device, as might naturally
be conceived, of isolating two bodies by placing them in an exhausted
vessel or vacuous space, by no means complies with the full conditions
of true separation portrayed above, because some material connection
must always exist between the enclosed bodies and the containing
vessel. This aspect is more fully treated later (§ 30). The condition of
truly separate masses is, in fact, purely a celestial one. No means
whatever are existent whereby such a condition may be faithfully
reproduced in a terrestrial environment.
In their separate condition the primary and planetary mass will each
possess a definite and unvarying amount of energy. It is to be noted
also, that since the original mass of the primary body has been
diminished by the mass of the planet cast off, the capacity for energy
of the primary will now be diminished in a corresponding degree. Any
further increment of energy to the primary in any form has now, however,
no direct influence on the energy of the planet, which must maintain its
position of complete isolation in its orbit. But although thus separate
and distinct from the primal mass in every material respect, the planet
is ever linked to it by the invisible bond of gravitation, and every
movement made by the planet in approaching or receding from the primary
is made in the field or influence of this attraction. In accordance,
therefore, with the general principle already enunciated (§ 4), these
actions or movements of the energised planetary mass, being made in the
field of the incepting gravitative influence, will be accompanied by
transformations, and thus the energy of the planet, although unvarying
in its totality, may vary in its form or distribution with the inward or
outward movement of the planet in its orbital path. As the planet
recedes from the primary it gains energy of position, but this gain is
obtained solely at the expense, and by the direct transformation of its
own orbital energy of motion. Its velocity in its orbit must, therefore,
decrease as it recedes from the central axis of the system, and increase
as it approaches that axis. Thus from energy considerations alone it is
clear that, if the planetary orbit is not precisely circular, the
velocity of the planet must vary at different points of its path.
6. _Passive Function and General Nature of Gravitation Field_
From the phenomena described above, it will be observed that, in the
energy processes of transformation occurring in both primary and planet,
the function of the gravitation field or influence is entirely passive
in nature. The field is, in truth, the persistent moving or directing
power behind the energy processes, the incepting energy influence or
agency which determines the nature of the transformation in each case
without being, in any way, actively engaged in it. In accelerating or
retarding the transformation process it has thus absolutely no effect.
These features are controlled by other factors. Neither does this
incepting agency affect, in any way, the limits of the transformation
process, these limits being prescribed by the physical or energy
qualities of the acting materials. In general nature the gravitation
field appears to be simply an energy influence--a peculiar manifestation
of certain passive qualities of energy. This aspect will, however,
become clearer to the reader when the properties of gravitation are
studied in conjunction with those of other incepting energy influences
(§§ 17, 18, 19).
7. _Limit of Gravitation Transformation_
In the case of a planetary body, there is a real limit to the extent of
the transformation of its orbital energy of motion under the influence
of the gravitation field. As the orbit of the planet widens, and its
mean distance from the primary becomes greater, its velocity in its
orbital path must correspondingly decrease. As already pointed out (§
5), this decrease is simply the result of the orbital energy of motion
being transformed or worked down into energy of position. But since this
orbital energy is strictly limited in amount, a point must ultimately be
reached where it would be transformed in its entirety into energy of
position. When this limiting condition is attained, the planet clearly
could have no orbital motion; it would be instantaneously at rest in
somewhat the same way as a projectile from the earth's surface is at
rest at the summit of its flight in virtue of the complete
transformation of its energy of motion into energy of position. In this
limiting condition, also, the energy of position of the planet would be
the maximum possible, and its orbital energy zero. The scope of the
planetary orbital path is thus rigidly determined by the planetary
energy properties. Assuming the reduction of gravity with distance to
follow the usual law of inverse squares, the value of the displacement
of the planet from the central axis when in this stationary or limiting
position may be readily calculated if the various constants are known.
In any given case it is obvious that this limiting displacement must be
a finite quantity, since the planetary orbital energy which is being
worked down is itself finite in amount.
8. _Interactions of Two Planetary Bodies--Equilibrium Phenomena_
Up to the present point, the cosmical system has been assumed to be
composed of one planetary body only in addition to the primary mass. It
is clear, however, that by repetition of the process already described,
the system could readily evolve more than one planet; it might, in fact,
have several planetary masses originating in the same primary, each
endowed with a definite modicum of energy, and each pursuing a
persistent orbit round the central axis of the system. Since the mass of
the primary decreases as each successive planet is cast off, its
gravitative attractive powers will also decrease, and with every such
decline in the central restraining force the orbits of the previously
constituted planets will naturally widen. By the formation in this way
of a series of planetary masses, the material of the original primary
body would be as it were distributed over a larger area or space, and
this separation would be accompanied by a corresponding decrease in the
gravitative attraction between the several masses. If the distributive
or disruptive process were carried to its limit by the continuous
application of rotatory energy to each separate unit of the system, this
limit would be dependent on the capacity of the system for energy. As is
shown later (§ 20), this capacity would be determined by the mass of the
system.
For simplicity, let us consider the case in which there are two
planetary bodies only in the system in addition to the primary. In
virtue of the gravitative attraction or gravitation field between the
two, they will mutually attract one another in their motion, and each
will, in consequence, be deflected more or less out of that orbital path
which it would normally pursue in the absence of the other. This
attraction will naturally be greatest when the planets are in the
closest proximity; the planet having the widest orbit will then be drawn
inwards towards the central axis, the other will be drawn outwards. The
distance moved in this way by each will depend on its mass, and on the
forces brought to bear on it by the combined action of the two remaining
masses of the system. Moving thus in different directions, the motion of
each planet is carried out in the lines of the gravitation field between
the two. One planet, therefore, gains and the other loses energy of
position with respect to the central axis of the system. The one planet
can thus influence, to some extent, the energy properties of the other,
although there is absolutely no direct energy communication between the
two; as shown hereafter, the whole action and the energy change will be
due simply to the motion carried out in the field of the incepting
gravitation influence.
It is clear, however, that this influence is exerted on the distribution
of the energy, on the form in which it is manifested, and in no way
affects the energy totality of either planet. Each, as before, remains a
separate system with conservative energy properties. That planet which
loses energy of position gains energy of motion, and is correspondingly
accelerated in its orbital path; the other, in gaining energy of
position, does so at the expense of its own energy of motion, and is
retarded accordingly. The action is really very simple in nature when
viewed from a purely energy standpoint. It has been dealt with in some
detail in order to emphasise the fact that there is absolutely nothing
in the nature of a transmission of energy between one planet and the
other. Taking a superficial view of the operation, it might be inferred
that, as the planets approach one another, energy of motion (or energy
of position) is transmitted from one to the other, causing one to retard
and the other to accelerate its movement, but a real knowledge of the
energy conditions shows that the phenomenon is rather one of a simple
restoration of equilibrium, a redistribution or transformation of the
intrinsic energy of each to suit these altering conditions. Each planet
is, in the truest sense, a separate mass in space.
9. _Axial Energy--Secondary Processes_
Passing now to another aspect of the energy condition of a planetary
body, let the planet be assumed to be endowed with axial energy or
energy of rotation, so that, while pursuing its orbital path in space,
it also rotates with uniform angular velocity about an axis within
itself. What will be the effect of the primary mass on the planet under
these new energy conditions? We conceive that the effect is again purely
one of transformation. In this process the primary mass functions once
more as an entirely passive or incepting agent, which, while exerting a
continuous transforming influence on the planet, does not affect in any
way the inherent energy properties of the latter. Up to the present
point we have only dealt with one incepting influence in transformation
processes, namely, that of gravitation, which has always been
manifested as an attractive force. It is not to be supposed, however,
that this is the only aspect in which incepting influences may be
presented. Although attractive force is certainly an aspect of some
incepting influences, it is not a distinctive feature of incepting
influences generally. In many cases, the aspect of force, in the sense
of attraction or repulsion, is entirely awanting. In the new order of
transformations which come into play in virtue of the rotatory motion of
a planetary mass in the field of its primary, we shall find other
incepting influences in action entirely different in nature from the
gravitation influence, but, nevertheless, arising from the same primary
mass in a similar way. Now the application of energy to the planet,
causing it to rotate in the lines or under the influence of these
incepting fields of the primary, brings into existence on the planet an
entirely new order of phenomena. So long as the planet had no axial
motion of rotation, some of the incepting influences of the primary were
compelled, as it were, to inaction; but with the advent of axial energy
the conditions are at once favourable to their action, and to the
detection of their transforming effects. In accordance with the general
principle already enunciated (§ 4), the action of the planetary
energised material in the lines of the various incepting fields of the
primary is productive of energy transformations. The active energy of
these transformations is the axial or rotatory energy of the planet
itself, and, in virtue of these transformations, certain other forms of
energy will be manifested on the planet and associated with the various
forms of planetary material. These manifestations of energy, in fact,
constitute planetary phenomena. Since the action or movement of the
rotating material of the planet through the incepting fields of the
primary is most pronounced in the equatorial or regions of highest
linear velocity, and least in the regions of low velocity adjoining the
poles of rotation, the transforming effect may naturally be expected to
decrease in intensity from equator to poles. Planetary energy phenomena
will thus vary according to the location of the acting material. It will
be clear, also, that each incepting agency or influence associated with
the primary mass will give rise to its own peculiar transformations of
axial energy on the planetary surface. These leading or primary
transformations of axial energy, in which the incepting influence is
associated with the primary mass only, we term primary processes. But it
is evident that the various forms of energy thus set free on the planet
as a result of the primary processes will be communicated to, and will
operate on, the different forms of planetary material, and will give
rise to further or secondary transformations of energy, in which the
incepting agency is embodied in or associated with planetary material
only. The exact nature of these secondary transformations will vary
according to the circumstances in which they take place. Each of them,
however, as indicated above, will be, in itself, carried out in virtue
of some action of the energised planetary material in the lines or field
of what we might term a secondary incepting influence. The latter,
however, must not be confused with the influences of the primary. It is
essentially a planetary phenomenon, an aspect of planetary energy; it is
associated with the physical or material machine by means of which the
secondary process of transformation is carried out. The nature of this
secondary influence will determine the nature of the secondary
transformation in each case. Its precise extent may be limited by other
considerations (§ 15).
As an example, assume a portion of the axial energy to be primarily
transformed into heat in virtue of the planet's rotation in the field of
an independent thermal incepting influence exerted by the primary. To
the action of this agency, which we might term the thermal field, we
assume are due all primary heating phenomena of planetary material. Now
the secondary transformations will take place when the heat energy thus
manifested is applied to some form of matter. It is obvious, however,
that this application might be carried out in various ways. Heat may be
devoted to the expansion of a solid against its cohesive forces. It may
be expended against the elastic forces of a gas, or it may be worked
down against chemical or electrical forces. In every case a
transformation of energy will result, varying in nature according to the
peculiar conditions under which it is carried out. In this or a similar
fashion each primary incepting influence may give rise to a series of
secondary actions more or less complex in nature. These secondary
transformation processes, allied with other processes of transmission,
will, in fact, constitute the visible phenomena of the planet, and in
their variety will exactly correspond to these phenomena.
With regard to the gravitation field, its general influence on the
rotating mass may be readily predicted. The material on that part of the
planetary surface which is nearest to or happens to face the primary in
rotation is, during the short time it occupies that position, subjected
to a greater attractive influence than the remainder which is more
remote from the primary. It will, in consequence, tend to be more or
less distorted or elevated above its normal position on the planetary
surface. This distorting effect will vary in degree according to the
nature of the material, whether solid, liquid, or gaseous, but the
general effect of the distortional movement, combined with the rotatory
motion of the planet, will be to produce a tidal action or a periodical
rise and fall of the more fluid material distributed over the planetary
surface. The distortion will, of course, be accompanied by energy
processes in which axial energy will be transformed into heat and other
forms, which will finally operate in the secondary processes exactly as
in previous cases.
10. _Mechanism of Energy Return_
But the question now arises, as to how this continuous transformation of
the axial energy can be consistent with that condition of uniformity of
rotation of the planet which was originally assumed. If the total energy
of the planetary mass is limited, and if it can receive no increment of
energy from any external source, it is clear that the axial energy
transformed must, by some process, be continuously returned to its
original form. Some process or mechanism is evidently necessary to carry
out this operation. This mechanism we conceive to be provided by certain
portions of the material of the planet, principally the gaseous matter
which resides on its surface, completely enveloping it, and extending
outwards into space (§ 38). In other words, the atmosphere of the planet
forms the machine or material agency by which this return of the
transformed axial energy is carried out. It has already been pointed out
(§ 9) how the working energy of every secondary transformation is
derived from the original axial energy of the planet itself. Each of
these secondary transformations, however, forms but one link of one
cyclical chain of secondary transformations, in which a definite
quantity of energy, initially in the axial form, passes, in these
secondary operations, through various other forms, by different
processes and through the medium of different material machines, until
it is eventually absorbed into the atmosphere of the planet. These
complete series of cyclical operations, by which the various portions of
axial energy are carried to the atmosphere, may in some cases be of a
very simple nature, and may be continuously repeated over very short
intervals of time; in other cases, the cycle may seem obscure and
complicated, and its complete operation spread over very long periods,
but in all cases the final result is the same. The axial energy
abstracted, sooner or later, recurs to the atmospheric machine. By its
action in this machine, great masses of gaseous material are elevated
from the surface of the planet against the attractive force of
gravitation; the energy will thus now appear in the form of potential
energy or energy of position. By a subsequent movement of these gaseous
masses over the surface of the planet from the regions of high velocity
towards the poles, combined with a movement of descent to lower levels,
the energy of position with which they were endowed is returned once
more in the original axial form.
This, roughly, constitutes the working of the planetary atmospheric
machine, which, while in itself completely reversible and
self-contained, forms also at the same time the source and the sink of
all the energy working in the secondary transformations. In the
ceaseless rounds of these transformations which form planetary phenomena
it links together the initial and concluding stages of each series by a
reversible process. Energy is thus stored and restored continuously. The
planet thus neither gains nor loses energy of axial motion; so far as
its energy properties are concerned, it is entirely independent of every
external influence. Its uniformity of rotation is absolutely maintained.
Each planet of the system will, in the same way, be an independent and
conservative unit.
11. _Review of Cosmical System--General Function of Energy_
Reviewing the system as a whole, the important part played by energy in
its constitution is readily perceived. The source of the energy which
operates in all parts of the system is found in that energy originally
applied (§ 3). When the system is finally constituted, this energy is
found distributed amongst the planets, each of which has received its
share, and each of which is thereby linked to the primary by its
influence. It is part of this same energy which undergoes transformation
in virtue of the orbital movements of the planets in the field of the
gravitative influence. Again, it is found in the form of planetary
axial energy, and thence, under the influence of various incepting
agencies, it passes in various forms through the whole gamut of
planetary phenomena, and finally functions in the atmospheric machine.
Every phenomenon of the system, great or small, is, in fact, but the
external evidence either of the transformation or of the transmission of
this energy--the outward manifestation of its changed or changing forms.
Its presence, which always implies its transformation (§ 4), is the
simple primary condition attached to every operation. The primal mass
originally responded to the application of energy by the presentation of
phenomena. Every material portion of the system will similarly respond
according to circumstances. Energy is, in fact, the working spirit of
the whole cosmical scheme. It is the influence linking every operation
of the system to the original transformations at the central axis, so
that all may be combined into one complete and consistent whole. It is
to be noted, however, that although they have a common origin the
orbital energy of each planetary mass is entirely distinct from its
energy of axial rotation, and is not interchangeable therewith. The
transformation of the one form of energy in no way affects the totality
of the other.
The disruption of the primary mass furnishes a view of what is virtually
the birth of gravitation as it is conceived to exist between separate
bodies. It may now be pointed out that the attractive influence of
gravitation is, in reality, but one of the many manifestations of energy
of the system. It is not, however, an active manifestation of the
working energy, but rather an aspect of energy as it is related to the
properties of matter. We have absolutely no experimental experience of
matter devoid of energy. Gravitation might readily be termed an energy
property of matter, entirely passive in nature, and requiring the advent
of some other form in order that it may exercise its function as an
incepting agency.
From a general consideration of the features of this system, in which
every phenomenon is an energy phenomenon, it seems feasible to conclude
also that every property of matter is likewise an energy property. It is
certain, indeed, that no reasonable or natural concept of either matter
or energy is possible if the two be dissociated. The system also
presents a direct and clear illustration of the principles of
conservation in the working of the whole, and also in each planetary
unit.
12. _Natural Conditions_
It will be noted that, up to the present point, the cosmical system has
been discussed from a purely abstract point of view. This method has
been adopted for a definite reason. Although able, at all points, to
bring more or less direct evidence from Nature, the author has no desire
that his scheme should be regarded in any way as an attempt to originate
or describe a system of creation. The object has been, by general
reasoning from already accepted properties of matter and energy, to
arrive at a true conception of a possible natural order of phenomena. It
is obvious, however, that the solar system forms the prototype of the
system described above. The motion of the earth and other planets is
continuously occurring under the influence of gravitation, thermal,
luminous, and other incepting fields which link them to the central
mass, the sun. As a result of the action of such fields, energy
transformations arise which form the visible phenomena of the system in
all its parts, each transformation, whether associated with animate or
inanimate matter, being carried out through the medium of some
arrangement of matter hereafter referred to as a material machine. The
conditions are precisely as laid down above. The system is dominated, in
its separate units, and as a whole, by the great principle of the
conservation of energy. Each planetary mass, as it revolves in space,
is, so far as its energy properties are concerned, an absolutely
conservative unit of that system. At the same time, however, each
planetary mass remains absolutely dependent on the primary for those
great controlling or incepting influences which determine the
transformation of its inherent energy.
In the special case of the earth, which will be dealt with in some
detail, it is the object of this work to show that its property of
complete energy conservation is amply verified by terrestrial phenomena.
The extension of the principle from the earth to the whole planetary
system has been made on precisely the same grounds as Newton extended
the observed phenomena to his famous generalisation with respect to
gravitation.
PART II
PRINCIPLES OF INCEPTION
13. _Illustrative Secondary Processes_
In this part of the work, an attempt will be made to place before the
reader some of the purely terrestrial and other evidential phenomena on
which the conclusions of the preceding General Statement are founded.
The complete and absolute verification of that Statement is obviously
beyond experimental device. Bound, as we are, within the confines of one
planet, and unable to communicate with the others, we can have no direct
experimental acquaintance with really separate bodies (§ 5) in space.
But, if from purely terrestrial experience we can have no direct proofs
on such matters, we have strong evidential conclusions which cannot be
gainsayed. If the same kind of energy operates throughout the solar
system, the experimental knowledge of its properties gained in one field
of research is valuable, and may be readily utilised in another. The
phenomena which are available to us for study are, of course, simply the
ordinary energy processes of the earth--those operations which in the
foregoing Statement have been described as secondary energy processes.
Their variety is infinite, and the author has accordingly selected
merely a few typical examples to illustrate the salient points of the
scheme. The energy acting in these secondary processes is, in every
case, derived, either directly or indirectly, from the energy of
rotation or axial energy of the earth. In themselves, the processes may
be either energy transformations or energy transmissions or a
combination of both these operations. When the action involves the
bodily movement of material mass in space, the dynamical energy thus
manifested, and which may be transmitted by the movement of this
material, is termed mechanical or "work" energy (§ 31); when the energy
active in the process is manifested as heat, chemical, or electrical
energy, we apply to it the term "molecular" energy. The significance of
these terms is readily seen. The operation of mechanical or "work"
energy on a mass of material may readily proceed without any permanent
alteration in the internal arrangement or general structure of that
mass. Mechanical or "work" energy is dissociated from any molecular
action. On the other hand, the application of such forms of energy as
heat or electrical energy to material leads to distinctly molecular or
internal effects, in which some alteration in the constitution of the
body affected may ensue. Hence the use of the terms, which of course is
completely arbitrary.
The principal object of this part of the work is to illustrate clearly
the general nature, the working, and the limits of secondary processes.
For this purpose, the author has found it best to refer to certain more
or less mechanical contrivances. The apparatus made use of is merely
that utilised in everyday work for experimental or other useful
purposes. It is essentially of a very simple nature; no originality is
claimed for it, and no apology is offered for the apparent simplicity of
the particular energy operations chosen for discussion. In fact, this
feature has rather led to their selection. In scientific circles to-day,
familiarity with the more common instances of energy operations is apt
to engender the belief that these processes are completely understood.
There is no greater fallacy. In many cases, no doubt, the superficial
phenomena are well known, but in even the simplest instances the
mechanism or ultimate nature of the process remains unknown. A free and
somewhat loose method of applying scientific terms is frequently the
cloak which hides the ignorance of the observer. No attempt will here be
made to go beyond the simple phenomena. The object in view is simply to
describe such phenomena, to emphasise and explain certain aspects of
already well-known facts, which, up to the present, have been neglected.
In some of the operations now to be described, mechanical or "work"
energy is the active agent, and material masses are thereby caused to
execute various movements in the lines or field of restraining
influences. For ordinary experimental convenience, the material thus
moved must of necessity be matter in the solid form. The illustrative
value of our experimental devices, however, will be very distinctly
improved if it be borne in mind that the operations of mechanical energy
are not restricted to solids only, but that the various processes of
transformation and transmission here illustrated by the motions of solid
bodies may, in other circumstances, be carried out in a precisely
similar fashion by the movements of liquids or even of gases. The
restrictions imposed in the method of illustration are simply those due
to the limitations of human experimental contrivance. Natural operations
exhibit apparatus of a different type. By the movements of solid
materials a convenient means of illustration is provided, but it is to
be emphasised that, so far as the operations of mechanical energy are
concerned, the precise form or nature of the material moved, whether it
be solid, liquid, or gaseous, is of no consequence. To raise one pound
of lead through a given distance against the gravitative attraction of
the earth requires no greater expenditure of energy than to raise one
pound of hydrogen gas through the same distance. The same principle
holds in all operations involving mechanical energy.
Another point of some importance which will be revealed by the study of
secondary operations is that every energy process has in some manner
definite energy limits imposed upon it. In the workings of mechanical or
"work" energy it is the mass value of the moving material which, in this
respect, is important. The mass, in fact, is the real governing factor
of the whole process (§ 20). It determines the maximum amount of energy
which can be applied to the material, and thus controls the extent of
the energy operation.
But in actions involving the molecular energies, the operation may be
limited by other considerations altogether. For example, the application
of heat to a solid body gives rise to certain energy processes (§ 27).
These processes may proceed to a certain degree with increase of
temperature, but a point will finally be attained where change of state
of the heated material takes place. This is the limiting point of this
particular operation. When change of state occurs, the phenomena will
assume an entirely different aspect. The first set of energy processes
will now be replaced by a set of operations absolutely different in
nature, themselves limited in extent, but by entirely different causes.
The first operation must thus terminate when the new order appears. In
this manner each process in which the applied energy is worked will be
confined within certain limiting boundaries. In any chain of energy
operations each link will thus have, as it were, a definite length. In
chemical reactions, the limits may be imposed in various ways according
to the precise nature of the action. Chemical combination, and chemical
disruption, must be looked on as operations which involve not only the
transformation of energy but also the transformation of matter. In most
cases, chemical reactions result in the appearance of matter in an
entirely new form--in the appearance, in fact, of actually different
material, with physical and energy properties absolutely distinct from
those of the reacting constituents. This appearance of matter in the new
form is usually the evidence of the termination, not only of the
particular chemical process, but also of the energy process associated
with it. Transformation of energy may thus be limited by transformation
of matter.
Examples of the limiting features of energy operations could readily be
multiplied. Even a cursory examination of most natural operations will
reveal the existence of such limits. In no case do we find in Nature any
body, or any energy system, to which energy may be applied in unlimited
amount, but in every case, rigid energy limits are imposed, and, if
these limits are exceeded, the whole energy character of the body or
system is completely changed.
14. _Incepting Energy Influences_
In experimental and in physical work generally, it has been customary,
in describing any simple process of energy transformation, to take
account only of those energies or those forms of energy which play an
active part in the process--the energy in its initial or applied form
and the energy in its transformed or final form. This method, however,
requires enlarging so as to include another feature of energy
transformation, a feature hitherto completely overlooked, namely, that
of incepting energy. Now, this conception of incepting energy, or of
energy as an incepting influence, is of such vital importance to the
author's scheme, that it is necessary here, at the very outset, to deal
with it in some detail. To obtain some idea of the general nature of
these influences, it will be necessary to describe and review a few
simple instances of energy transformation. One of the most illuminating
for this purpose is perhaps the familiar process of dynamo-electric
transformation.
A spherical mass A (Fig. 1) of copper is caused to rotate about its
central axis in the magnetic field in the neighbourhood of a long and
powerful electro-magnet. In such circumstances, certain well-known
transformations of energy will take place. The energy transformed is
that dynamical or "work" energy which is being applied to the spherical
mass by the external prime mover causing it to rotate. As a result of
this motion in the magnetic field, an electrical action takes place;
eddy currents are generated in the spherical mass, and the energy
originally applied is, through the medium of the electrical process,
finally converted into heat and other energy forms. The external
evidence of the process will be the rise in temperature and
corresponding expansion of the rotating mass.
[Illustration: FIG. 1]
Such is the energy transformation. Let us now review the conditions
under which it takes place. Passing over the features of the "work"
energy applied and the energy produced in the transformation, it is
evident that the primary and essential condition of the whole process is
the presence of the magnetic field. In the absence of this influence,
every other condition of this particular energy operation might have
been fulfilled without result. The magnetic field is, in reality, the
determining agency of the process. But this field of magnetic force is
itself an energy influence. Its existence implies the presence of
energy; it is the external manifestation of that energy (usually
described as stored in the field) which is returned, as shown by the
spark, when the exciting circuit of the electro-magnet is broken. The
transformation of the dynamical or "work" energy (§ 31) applied to the
rotating sphere is thus carried out by the direct agency, under the
power, or within the field of this magnetic energy influence, to which,
accordingly, we apply the expression, incepting energy influence, or
incepting energy.
There are several points to be noted with regard to these phenomena of
inception. In the first place, it is clear that the energy which thus
constitutes the magnetic field plays no active part in the main process
of transformation: during the operation it neither varies in value nor
in nature: it is entirely a passive agent. Neither is any continuous
expenditure of energy required for the maintenance of this incepting
influence. It is true that the magnetic field is primarily due to a
circulatory current in the coils or winding of the electro-magnet, but
after the initial expenditure of energy in establishing that field is
incurred, the continuous expenditure of energy during the flow of the
current is devoted to simply heating the coils. A continuous heat
transformation is thus in progress. The magnetic energy influence,
although closely associated with this heat transformation, yet
represents in itself a distinct and separate energy feature. This last
point is, perhaps, made more clear if it be assumed that, without
altering the system in any way, the electro-magnet is replaced by a
permanent magnet of precisely the same dimensions and magnetic power.
There would then be no energy expenditure whatever for excitation, but
nevertheless, the main transformation would take place in precisely the
same manner and to exactly the same degree as before. The incepting
energy influence is found in the residual magnetism.
If an iron ball or sphere were substituted, in the experiment, for the
copper one, the phenomena observed on its rotation would be of an
exactly similar nature to those described above. There is, however, one
point of difference. Since the iron is magnetic, the magnet pole will
now exert an attractive force on the iron mass, and if the latter were
in close proximity to the pole (Fig. 1), a considerable expenditure of
energy might be required to separate the two. It is evident, then, that
in the case of iron and the magnetic metals, this magnetic influence is
such that an expenditure of energy is required, not only to cause these
materials to move in rotation so as to cut the lines of the field of the
magnetic influence, but also to cause them to move outwards from the
seat of the influence _along_ the lines of the field. The movements,
indeed, involve transformations of energy totally different in nature.
Assuming the energy to be obtained, in both cases, from the same
external source, it is, in the first instance, converted by rotatory
motion in the field into electrical and heat energy, whereas, in the
second case, by the outward motion of displacement from the pole, it is
transformed and associated with the mass in the form of energy of
position or energy of displacement relative to the pole. Since the
attractive force between the iron mass and the pole may be assumed to
diminish according to a well-known law, the energy transformation per
unit displacement will also diminish at the same rate. The precise
nature and extent of the influence of the incepting agent thus depend on
the essential qualities of the energised material under its power. In
this case, the magnetic metals, such as iron, provide phenomena of
attraction which are notably absent in the case of the dia-magnetic
metals such as copper. Other substances, such as wood, appear to be
absolutely unaffected by any movement in the magnetic field. The precise
energy condition of the materials in the field of the incepting
influence is also an important point. The incepting energy might be
regarded as acting, not on the material itself, but rather on the energy
associated with that material. From the phenomena already considered, it
is clear that before the incepting influence of magnetism can act on the
copper ball, the latter must be endowed with energy of rotation. It is
on this energy, then, that the incepting influence exerts its
transforming power. It would be useless to energise the copper ball, say
by raising it to a high temperature, and then place it at rest in the
magnetic field; the magnetic energy influence would not operate on the
heat energy, and consequently, no transformation would ensue.
It is easy to conceive, also, that in the course of an energy
transformation, the material may attain an energy condition in which the
incepting influence no longer affects it. Take once more the case of the
iron ball. It is well known that, at a high temperature, iron becomes
non-magnetic. It would follow, then, that if the rotational
transformation in the magnetic field could be carried out to the
requisite degree, so that, by the continuous application of that heat
energy which is the final product of the process, the ball had attained
this temperature, then the other transformation consequent on the
displacement of the ball from the attracting pole could not take place.
No change has really occurred in the incepting energy conditions. They
are still continuous and persistent, but the energy changes in the
material itself have carried it, to a certain degree, beyond the
influence of these conditions.
15. _Cohesion as an Incepting Influence_
Other aspects of incepting energy may be derived from the examples cited
above. Returning to the case of the rotating copper sphere, let it be
assumed that in consequence of its rotation in the magnetic field it is
raised from a low to a high temperature. Due to the heating effect
alone, the mass will expand or increase in volume. This increase is the
evidence of a definite energy process by which certain particles or
portions of the mass have in distortion gained energy of
position--energy of separation--or potential energy relative to the
centre of the sphere. In fact, if the mass were allowed to cool back to
its normal condition, this energy might by a suitable arrangement be
made available for some form of external work. It is obvious, however,
that this new energy of position or separation which has accrued to the
mass in its heated condition has in reality been obtained by the
transformation of the "work" energy originally applied. The abnormal
displacement of certain particles or portions of the mass from the
centre of the sphere is simply the external evidence of their increased
energy. Now this displacement, or strain, due to the heat expansion, is
carried out against the action of certain cohesive forces or stresses
existing between the particles throughout the mass. These cohesive
forces are, in fact, the agency which determines this transformation of
heat into energy of position. Their existence is essential to the
process. But these cohesive forces are simply the external manifestation
of that energy by virtue of which the mass tends to maintain its
coherent form. They are the symbol of that energy which might be termed
the cohesion energy of the mass--they are, in fact, the symbol of the
incepting energy influence of the transformation. This incepting energy
influence of cohesion is one which holds sway throughout all solid
material. It is, therefore, found in action in every movement involving
the internal displacement or distortion of matter. It is a property of
matter, and accordingly it is found to vary not only with the material,
but also with the precise physical condition or the energy state of the
material with which it is associated. In this respect, it differs
entirely from the preceding magnetic influence. The latter, we have
seen, has no direct association with the copper ball, or with the
material which is the actual venue of the transformation. As an energy
influence, it is itself persistent, and unaffected by the energy state
of that material. On the other hand, the cohesion energy, being purely a
property of the material which is the habitat of the energy process, is
directly affected by its energy state. This point will be clearer by
reference to the actual phenomena of the heat transformation. As the
process proceeds, the temperature of the mass as the expansion increases
will rise higher and higher, until, at a certain point, the solid
material is so energised that change of state ensues. At this, the
melting-point of the material, liquefaction takes place, and its
cohesive properties almost vanish. In this fashion, then, a limit is
clearly imposed on the process of heat transformation in the solid
body--a limit defined by the cohesive or physical properties of the
particular material. In this limiting power lies the difference between
cohesion and magnetism as incepting influences. Looking at the whole
dynamo-electric transformation in a general way, it will be clear that
the magnetic influence in no way limits or affects the amount of
dynamical or "work" energy which may be applied to the rotating sphere.
This amount is limited simply by the cohesive properties of the material
mass in rotation. The magnetic influence might, in fact, be regarded as
the primary or inducing factor in the system, and the cohesion influence
as the secondary or limiting factor.
16. _Terrestrial Gravitation as an Incepting Influence_
The attractive influence of gravitation appears as an incepting agency
in terrestrial as well as in celestial phenomena. In fact, of all the
agencies which incept energy transformations on the earth, gravitation,
in one form or another, is the most universal and the most important.
Gravitation being a property of all matter, no mundane body, animate or
inanimate, is exempt from its all-pervading influence, and every
movement of energised matter within the field of that influence leads
inevitably to energy transformation.
Let us take a concrete illustration. A block of solid material is
supported on a horizontal table. By means of a cord attached, energy is
applied to the block from an external source, so that it slides over the
surface of the table. As a result of this motion and the associated
frictional process, heat energy will make its appearance at the sliding
surfaces of contact. This heat energy is obviously obtained by the
transformation of that energy originally applied to the block from the
external source. What is the incepting influence in this process of
transformation? The incepting influence is clearly the gravitative
attraction of the earth operating between the moving block and the
table. The frictional process, it is well known, is dependent in extent
or degree on the pressure between the surfaces in contact. This pressure
is, of course, due to the gravitative attraction of the earth on the
mass of the block. If it be removed, say by supporting the block from
above, the heat-transformation process at the surfaces at once
terminates. Gravity, then, is the primary incepting influence of the
process. The effect of gravitation in transformation has apparently been
eliminated by supporting the block from above and removing the pressure
between block and table. It is not really so, however, because the
pressure due to the gravitative attraction of the earth on the block has
in reality only been transferred to this new point of support, and if a
movement of the block is carried out it will be found that the heat
transformation has been also transferred to that point. But there are
also other influences at work in the process. The extent of the heat
transformation depends, not only on the pressure, but also on the nature
of the surfaces in contact. It is evident, that in the sliding movement
the materials in the neighbourhood of the surfaces in contact will be
more or less strained or distorted. This distortion is carried out in
the lines of the cohesive forces of the materials, and is the real
mechanism of the transformation of the applied work energy into heat. It
is obvious that the nature of the surfaces in contact must influence the
degree of distortion, that is, whether they are rough or smooth; the
cohesive qualities of the materials in contact will depend also on the
nature of these materials, and the extent of the heat transformation
will be limited by these cohesive properties in precisely the same way
as described for other examples (§ 15). The function of gravitation in
this transformation is, obviously, again quite passive in nature, and is
in no way influenced by the extent of the process. Gravitation is, as it
were, only the agency whereby the acting energy is brought into
communication with the cohesive forces of the sliding materials.
A little reflection will convey to the reader the vast extent of this
influence of gravitation in frictional phenomena, and the important
place occupied by such phenomena in the economy of Nature. From the
leaf which falls from the tree to the mighty tidal motions of air,
earth, and sea due to the gravitative effects of the sun and moon, all
movements of terrestrial material are alike subject to the influence of
terrestrial gravitation, and will give rise to corresponding heat
processes. These heat processes are continually in evidence in natural
phenomena; the effect of their action is seen alike on the earth's
surface and in its interior (internal heating). Of the energy operating
in them we do not propose to say anything further at this stage, except
that it is largely communicated to the atmospheric air masses.
17. _The Gravitation Field_
The foregoing examples of transformation serve to place before the
reader some idea of the general nature and function of an incepting
energy influence. But for the broadest aspects of the latter agencies it
is necessary to revert once more to celestial phenomena. As already
indicated in the General Statement, the primary transformations of
planetary axial energy are stimulated by certain agencies inherent to,
and arising from, the central mass of the system. These energy agencies
or effects operate through space, and are entirely passive in nature.
They are in no way associated with energy transmission; they are merely
the determining causes of the energy-transforming processes which they
induce, and do not in the least affect the conservative energy
properties of the planetary masses over which their influence is cast.
Of the precise number and nature of such influences thus exerted by the
primary mass we can say nothing. The energy transformations which are
the direct result of their action are so extensive and so varied in
character that we would hesitate to place any limit on the number of the
influences at work. Some of these influences, however, being associated
with the phenomena of everyday experience, are more readily detected in
action than others and more accessible to study. It is to these that we
naturally turn in order to gain general ideas for application to more
obscure cases.
Of the many incepting influences, therefore, which may emanate from the
primary mass there are three only which will be dealt with here. Each
exerts a profound action on the planetary system, and each may be
readily studied and its working verified by the observation of common
phenomena. These influences are respectively the gravitation, the
thermal, and the luminous fields.
The general nature and properties of the gravitation field have to some
extent been already foreshadowed (§§ 4, 6, 16). Other examples will be
dealt with later, and it is unnecessary to go into further detail here.
The different aspects, however, in which the influence has been
presented may be pointed out. Firstly, in the separate body in space, as
an inherent property of matter (§ 2); secondly, as an attractive
influence exerted across space between primary and planet, both
absolutely separate bodies (§ 5); and thirdly, as a purely planetary or
secondary incepting influence (§ 16). In every case alike we find its
function to be of an entirely passive nature. Its most powerful effect
on planetary material is perhaps manifested in the tidal actions (§ 9).
With respect to these movements, it may be pointed out that the
planetary material periodically raised from the surface is itself
elevated against the inherent planetary gravitative forces, and also, to
a certain extent, against the cohesive forces of planetary material.
Each of these resisting influences functions as an incepting agency, and
thus the elevation of the mass involves a transformation of energy (§
4). The source of the energy thus transformed is the axial energy of the
planet, and the new forms in which it is manifested are energy of
position or potential energy relative to the planetary surface, and heat
energy. On the return of the material to its normal position, its energy
of position, due to its elevation, will be returned in its original form
of axial energy. In the case of the heat transformation, however, it is
to be noted that this process will take place both as the material is
elevated and also as it sinks once more to its normal position. The
heat transformation thus operates continuously throughout the entire
movement. The upraising of the material in the tidal action is brought
about entirely at the expense of inherent planetary axial energy. The
gravitative and cohesive properties of the planetary material make such
a transformation process possible. It is in virtue of these properties
that energy may be applied to or expended on the material in this way.
The tidal action on the planetary surface is, in fact, simply a huge
secondary process in which axial energy is converted into heat. The
primary incepting power is clearly gravitation.
Of the aspect of gravitation as a purely planetary influence (§ 16)
little requires to be said. The phenomena are so prominent and familiar
that the reader may be left to multiply instances for himself.
18. _The Thermal Field_
The thermal field which is induced by and emanates from the primary mass
differs from the gravitation field in that, so far as we know, it is
unaccompanied by any manifestation of force, attractive or otherwise.
Its action on the rotating planetary mass may be compared to that of the
electro-magnet on the rotating copper sphere (§ 14); the electro-magnet
exerts no force on the sphere, but an energy expenditure is,
nevertheless, required to rotate the latter through the field of the
magnetic influence.
To this thermal field, then, in which the planets rotate, we ascribe all
primary planetary heating phenomena. The mode of action of the thermal
field appears to be similar to that of other incepting influences. By
its agency the energy of axial rotation of planetary material is
directly converted into the heat form. As already shown (§ 17), heat
energy may be developed in planetary material as a result of the action
of other incepting agencies, such as gravitation. These processes are,
however, more or less indirect in nature. But the operation due to the
thermal field is a direct one. The heat energy is derived from the
direct transformation of planetary axial energy of rotation without
passing through any intermediate forms. In common parlance, the thermal
field is the agency whereby the primary mass heats the planetary system.
No idea of transmission, however, is here implied in such phraseology;
the heating effect produced on any planetary mass is entirely the result
of the transformation of its own energy; the thermal field is purely and
simply the incepting influence of the process. Now, in virtue of the
configuration of the rotating planetary masses, their material in
equatorial regions is much more highly energised than the material in
the neighbourhood of the poles, and will, accordingly, move with much
greater linear velocity through the thermal field. The heat
transformation will vary accordingly. It will be much more pronounced at
the equator than at the poles, and a wide difference in temperature will
be maintained between the two regions. The thermal field, also, does not
necessarily produce the same heating effect on all planetary material
alike. Some materials appear to be peculiarly susceptible--others much
less so. This we may verify from terrestrial experience. Investigation
shows the opaque substances to be generally most susceptible, and the
transparent materials, such as glass, rock-salt, tourmaline, &c. almost
insusceptible, to the heating effect of the sun. The influence of the
thermal field can, in fact, operate through the latter materials. A
still more striking and important phenomenon may be observed in the
varying action of the thermal field on matter in its different forms. It
has been already pointed out that, in the course of transformation in
the field of an incepting influence, a material may attain a certain
energy state in which it is no longer susceptible to that influence.
This has been exemplified in the case of the iron ball (§ 14) and a
phenomenon of the same general nature is revealed in the celestial
transformation. A piece of solid material of low melting-point is
brought from the polar regions of the earth to the equator. Due to the
more rapid movement across the sun's thermal field, and the consequent
increased action of that field, a transformation of the axial energy of
rotation of the body takes place, whereby it is heated and finally
liquefied. In the liquid state the material is still susceptible to the
thermal field, and the transformation process accordingly proceeds until
the material finally assumes the gaseous form. At this point, however,
it is found that the operation is suspended; the material, in assuming
the gaseous state, has now attained a condition (§ 15) in which the
thermal field has no further incepting or transforming influence upon
it. No transformation of its axial energy into the heat form is now
possible by this means; indeed, so far as the _direct_ heating effect of
the sun is concerned, the free gaseous material on the planetary surface
is entirely unaffected. All the evidence of Nature points to the
conclusion that all gaseous material is absolutely transparent to the
_direct_ thermal influence of the sun. Matter in the gaseous form
reaches, as it were, an ultimate or limiting condition in this respect.
This fact, that energised material in the gaseous form is not
susceptible to the thermal field, is of very great importance in the
general economy of Nature. It is, in reality, the means whereby the
great primary process of the transformation of the axial energy of the
earth into the heat form is limited in extent. As will be explained
later, it is the device whereby the planetary energy stability is
conserved. It will be apparent, of course, that heat energy may be
readily applied to gaseous masses by other means, such as conduction or
radiation from purely terrestrial sources. The point which we wish here
to emphasise is, simply, that gaseous material endowed with axial energy
on the planetary surface cannot have this axial energy directly
transformed into heat through the instrumentality of the thermal field
of the primary.
19. _The Luminous Field_
The planetary bodies are indebted to the primary mass not only for heat
phenomena, but also for the phenomena of light. These light phenomena
are due to a separate and distinct energy influence (or influences)
which we term the luminous field.
The mode of action of the luminous field is similar to that of other
incepting influences. It operates from the primary, and is entirely
passive in nature. Like the thermal field, it does not appear to be
accompanied by any manifestation of physical stress or force, except,
indeed, the experimental demonstrations of the "pressure of light" can
be regarded as such. In any case, this in no way affects the general
action of light as an incepting agency. Its action on energised
planetary material gives rise to certain transformations of energy,
transformations exclusive and peculiar to its own influence. We will
refer to terrestrial phenomena for illustrations of its working.
Perhaps the commonest example of transformation in which the luminous
field appears as the incepting agency is seen in the growth of plant
life on the surface of the earth. The growth and development of
vegetation and plants generally is the outward evidence of certain
energy transformations. The processes of growth, however, are of such a
complex nature that it is impossible to state the governing energy
conditions in their entirety, but, considering them merely in general
fashion, it may be said that energy in various forms (potential,
chemical, &c.) is stored in the tissues of the growing material. Now the
source of this energy is the axial energy of the earth, and, as stated
above, the luminous field is an incepting factor (there may be others)
in the process of transformation, a factor whereby this axial energy is
converted into certain new forms. It is well known that, amongst the
factors which influence the growth of vegetation, one of the most potent
is that of light. The presence of sunlight is one of the essential
conditions for the successful working of certain transformations of
plant life, and these transformations vary not only in degree but in
nature, according to the variation of the imposed light in intensity and
quality. Some of the processes of growth are no doubt chemical in
nature. Here, again, light may be readily conceived to have a direct
determining influence upon them, exactly as in the cases of its
well-known action in chemical phenomena--for instance, as in
photography. Other examples will readily occur to the reader. One of the
most interesting is the action of light on the eye itself. It may be
pointed out indeed that light is, first and foremost, a phenomenon of
vision. Whatever may be its intrinsic nature, it is primarily an
influence affecting the eye. But the action of seeing, like all other
forms of human activity, involves a certain expenditure of bodily
energy. This energy is, of course, primarily derived from the axial
energy of the earth through the medium of plant and animal life and the
physico-chemical processes of the body itself. Its presence in one form
or another is, in fact, essential to all the phenomena of life. The
action of seeing accordingly involves the transformation of a certain
modicum of this energy, and the influence which incepts this
transformation is the luminous field which originates in and emanates
from the central mass of the system, the sun. In a similar way,
planetary material under certain conditions may become the source of an
incepting luminous field. It is this light influence or luminous field
which, in common parlance, is said to enter the eye. In that organ,
then, is found the mechanism or machine (§ 30), a complicated one, no
doubt, whereby this process of transformation is carried out which makes
the light influence perceptible to the senses. Of the precise nature of
the action little can be said. The theme is rather one for a treatise on
physiology. It may be pointed out, however, with regard to the process
of transformation, that Dewar has already demonstrated the fact that
when light falls on the retina of the eye, an electric current is set up
in the optic nerve. The energy associated with this current is, of
course, obtained at the expense of the bodily energy of the observer,
and this energy, after passing, it may be, through a large number of
transformation processes, will finally be returned to the source from
which it was originally derived, namely, the axial energy of the earth.
The luminous field, also, like the thermal field, has no transforming
effect whatever on the energy of certain substances. It may pass
completely through some and be reflected by others without any sign of
energy transformation. Its properties are, in fact, simply the
properties of light, and must be accepted simply as phenomena. Now, it
is very important, in studying matters of this kind, to realise that it
is impossible ever to get beyond or behind phenomena. It may be pointed
out that in no sphere of physics has the influence of so-called
explanatory mechanical hypotheses been stronger than in that dealing
with the properties of light. New theories are being expounded almost
daily in attempts to explain or dissect simple phenomena. But it may be
asked, In what does our really useful knowledge of light consist?
Simply in our knowledge of phenomena. Beyond this, one cannot go. We may
attempt to explain phenomena, but to create for this purpose elastic
ethereal media or substances without direct evidential phenomena in
support is not to advance real knowledge. There are certain properties
peculiar to the luminous as to all other incepting fields, certain
conditions under which each respectively will act, and the true method
of gaining real insight into these agencies is by the study of these
actual properties (or phenomena) and conditions, and not by attempts to
ultimately explain them. It will be evident that in most cases of
natural energy operations there is more than one energy influence in
action. As a rule there are several. In a growing plant, for example, we
have the thermal, luminous, gravitation, and cohesive influences all in
operation at the same time, each performing its peculiar function in
transformation, each contributing its own peculiar energy phenomena to
the whole. This feature adds somewhat to the complexity of natural
operations and to the difficulties in the precise description of the
various phenomena with which they are associated.
20. _Transformations--Upward Movement of a Mass against Gravity_
When the significance of energy inception and the characteristic
properties of the various agencies have been grasped, it becomes much
easier to deal with certain other aspects of energy processes. To
illustrate these aspects it is, therefore, now proposed to discuss a few
simple secondary operations embodied in experimental apparatus. A few
examples of the operations of transformation and transmission of energy
will be considered. The object in view is to show the general nature of
these processes, and more especially the limits imposed upon them by the
various factors or properties of the material machines in which they are
of necessity embodied. The reader is asked to bear in mind also the
observations already made (§ 13) with respect to experimental apparatus
generally.
The first operation for discussion is that of the upward movement of a
mass of material against the gravitative attraction of the earth. This
movement involves one of the most simple and at the same time one of the
most important of secondary energy processes. As a concrete
illustration, consider the case of a body projected vertically upwards
with great velocity from the surface of the earth. The phenomena of its
motion will be somewhat as follows:--As the body recedes from the
earth's surface in its upward flight, its velocity suffers a continuous
decrease, and an altitude is finally attained where this velocity
becomes zero. The projectile, at this point, is instantaneously at rest.
Its motion then changes; it commences to fall, and to proceed once more
towards the starting-point with continuously increasing velocity.
Neglecting the effect of the air (§ 29) and the rotational movement of
the earth, it may be assumed that the retardation of the projectile in
its upward flight is numerically equal to its acceleration in its
downward flight, and that it finally returns to the starting-point with
velocity numerically equal to the initial velocity of projection. The
process then obviously involves a complete transformation and return of
energy. At the earth's surface, where its flight commences and
terminates, the body is possessed of energy of motion to a very high
degree. At the highest point of flight, this form of energy has entirely
vanished; the body is at rest. Its energy properties are then
represented by its position of displacement from the earth's surface;
its energy of motion in disappearing has assumed this form of energy of
position, energy of separation, or potential energy. The moving body has
thus been the mechanism of an energy transformation. At each stage of
its upward progress, a definite modicum of its original energy of motion
is converted into energy of position. Between the extreme points of its
flight, the energy of the body is compounded of these two forms, one of
which is increasing at the expense of the other. When the summit of
flight is reached the conversion into energy of position is complete. In
the downward motion, the action is completely reversed, and when the
body reaches the starting-point its energy of position has again been
completely transformed into energy of motion. It might be well to draw
attention here to the fact, often overlooked, that this energy of
position gained by the rising mass is, in reality, a form of energy,
separate and distinct, brought into existence by the transformation and
disappearance of the energy of the moving mass. Energy of position is as
truly a form of energy as heat or kinetic energy.
The transformation here depicted is clearly a simple process, yet we
know absolutely nothing of its ultimate nature, of the why or wherefore
of the operation. Our knowledge is confined to the circumstances and
conditions under which it takes place. Let us now, therefore, deal with
these conditions. The transformation is clearly carried out in virtue of
the movement of the body in the lines or field of an incepting
influence. This influence is that of gravitation, which links the body
continually to the earth. Now the function of gravitation in this
process, as in others already described, is that of a completely passive
incepting agent. The active energy which suffers change in the process
is clearly the original work energy (§ 31) communicated to the projected
body. The whole process is, in fact, a purely mechanical operation, and
as in the case of other processes involving mechanical energy, it is
limited by the mass value of the moving material. It is clear that the
greater the amount of energy communicated to the projectile at the
starting-point, the greater will be the altitude it will attain in its
flight. The amount of energy, however, which can thus be communicated is
dependent on the maximum force which can be applied to the projectile.
But the maximum force which can be applied to any body depends entirely
on the resistance offered by that body, and in this case the resisting
force is the gravitative attraction of the earth on the projectile,
which attraction is again a direct function of its mass. The greater the
mass, the greater the gravitative force, and the greater the possibility
of transformation. The ultimate limit of the process would be reached if
the projected mass were so great as to equal half the mass of the earth.
In such circumstances, the earth being assumed to be divided into two
equal masses, the maximum limiting value of the gravitative attraction
would clearly be attained. Any increase of the one mass over the other
would again lead, however, to a diminution in the attractive force and a
corresponding decrease in the energy limit for transformation. The
precise manner in which the operations of mechanical energy are limited
by the mass will now be clear. The principle is quite general, and
applicable to all moving bodies. Mass is ever a direct measure of energy
capacity. A graphical method of representing energy transformations of
this kind, by a system of co-ordinates, would enable the reader to
appreciate more fully the quantitative relations of the forms of energy
involved and also their various limits.
21. _The Simple Pendulum_
The remaining operations of transformation for discussion are embodied
in the following simple apparatus. A spherical metallic mass M (Fig. 2)
is supported by a rod P which is rigidly connected to a horizontal
spindle HS as shown.
[Illustration: FIG. 2]
The spindle is supported and free to revolve in the bearings B{1} and
B{2} which form part of the supporting framework V resting on the
ground; the bearing surfaces at B{1} and B{2} are lubricated, and the
mass M is free to perform, in a vertical plane, complete revolutions
about the axis through the centre of the spindle. In carrying out this
motion its path will be circular, as shown at DCFE; the whole
arrangement is merely an adaptation of the simple pendulum. As
constituted, the apparatus may form the seat of certain energy
operations. Some of these will only take place with the application of
energy of motion to the pendulum from an external source, thereby
causing it to vibrate or to rotate: others, again, might be said to be
inherent to the apparatus, since they arise naturally from its
construction and configuration. We shall deal with the latter first.
22. _Statical Energy Conditions_
The pendulum with its spindle has a definite mass value, and, assuming
it to be at rest in the bearings B{1} and B{2}, it is acted upon by
gravitation, or in other words, it is under the influence or within the
field of the gravitative attraction of the earth's mass upon it. The
effect of this field is directly proportional to the mass of the
pendulum and spindle, and to its action is due that bearing pressure
which is transmitted through the lubricant to the bearing surfaces and
thence to the supporting arms N{1} and N{2} of the framework. Bearings
and columns alike are thus subjected to a downward thrust or pressure.
Being of elastic material, they will be more or less distorted. This
distortion will proceed until the downward forces are balanced by the
upward or reactive forces called into play in virtue of the cohesive
properties of the strained material. Corresponding to a slight downward
movement of the pendulum and spindle in thus straining or compressing
them, the supporting columns will be decreased in length. This downward
movement is the external evidence of certain energy operations. In
virtue of their elevation above the earth's surface, the pendulum and
spindle possess, to a certain degree, energy of position, and any free
downward movement would lead to the transformation of this energy into
energy of motion (§ 20). But the downward motion of pendulum and spindle
is not free. It is made against the resistance of the material of the
supporting columns, and the energy of position, instead of assuming the
form of energy of motion, is simply worked down or transformed against
the opposing cohesive forces of the supporting materials. This energy,
therefore, now resides in these materials in the form of energy of
strain or distortion. In general nature, this strain energy is akin to
energy of position (§ 20). Certain portions of the material of the
columns have been forced into new positions against the internal forces
of cohesion which are ever tending to preserve the original
configuration of the columns. This movement of material in the field of
the cohesive influence involves the transformation of energy (§ 4), and
the external evidence of the energy process is simply the strained or
distorted condition of the material. If the latter be released, and
allowed to resume its natural form once more, this stored energy of
strain would be entirely given up. In reality, the material can be said
to play the part of a machine or mechanism for the energy process of
storage and restoration. No energy process, in fact, ever takes place
unless associated with matter in some form. The supporting arms, in this
case, form the material factor or agency in the energy operation. All
such energy machines, also, are limited in the extent of their
operation, by the qualities of the material factors. In this particular
case, the energy compass of the machine is restricted by certain
physical properties of the material, by the maximum value of these
cohesive or elastic forces called into play in distortion. These forces
are themselves the evidence of energy, of that energy by virtue of which
the material possesses and maintains its coherent form. In this case
this energy is also the factor controlling the transformation, and
appears as a separate and distinct incepting agency. If the process is
to be a reversible one, so that the energy originally stored in the
material as strain energy or energy of distortion may be completely
returned, the material must not be stressed beyond a certain point. Only
a limited amount of work can be applied to it, only a limited amount of
energy can be stored in it. Too much energy applied--too great a weight
on the supporting columns--gives rise to permanent distortion or
crushing, and an entirely new order of phenomena. This energy limit for
reversibility is then imposed by the cohesive properties of the material
or by its elastic limits. Up to this point energy stored in the material
may be returned--the process is reversible in nature--but above this
elastic limit any energy applied must operate in an entirely different
manner.
A little consideration will show also, that the state of distortion, or
energy strain, is not confined to the material of the supporting columns
alone. Action and reaction are equal. The same stresses are applied to
the spindle through the medium of bearings and lubricant. In fact, every
material substance of which the pendulum machine is built up is thus,
more or less, strained against internal forces; all possess, more or
less, cohesion or strain energy. It will be evident, also, that this
condition is not peculiar to this or any other form of apparatus. It is
the energy state or condition of every structure, either natural or
artificial, which is built up of ordinary material, and which, on the
earth's surface, is subjected to the influence of the gravitation field.
This cohesion or strain energy is one of the forms in which energy is
most widely distributed throughout material.
In reviewing the statical condition of the above apparatus, the pendulum
itself has been assumed to be hanging vertically at rest under the
influence of gravitation. If energy be now applied to the system from
some external source so that the pendulum is caused to vibrate, or to
rotate about the axis of suspension, a new set of energy processes make
their appearance. The movement of the pendulum mass, in its circular
path around the central axis, is productive of certain energy reactions,
as follows:--
_a._ A transformation of energy of motion into energy of position
and vice versa.
_b._ A frictional transformation at the bearing surfaces.
These processes will each be in continuous operation so long as the
motion of the pendulum is maintained. Their general nature is quite
independent of the extent of that motion, whether it be merely vibratory
through a small arc, or completely rotatory about the central axis. In
the articles which immediately follow, the processes will be treated
separately.
23. _Transformations of the Moving Pendulum--a. Energy of Motion to
Energy of Position and Vice Versa_
In this simple transformation the motion of the pendulum about the axis
of suspension may be either vibratory or circular, according to the
amount of energy externally applied. In each case, every periodic
movement of the apparatus illustrates the whole energy operation. The
general conditions of the process are almost identical with those in the
case of the upward movement of a mass against gravity (§ 20).
Gravitation is the incepting energy influence of the operation. If the
pendulum simply vibrates through a small arc, then, at the highest
points of its flight, it is instantaneously at rest. Its energy of
motion is here, therefore, zero; its energy of position is a maximum. At
the lowest point of its flight, the conditions are exactly reversed.
Here its energy of motion is a maximum, while its energy of position
passes through a minimum value. The same general conditions hold when
the pendulum performs complete revolutions about the central axis. If
the energy of motion applied is just sufficient to raise it to the
highest point E (Fig. 2), the mass will there again be instantaneously
at rest with maximum energy of position. As the mass falls downwards in
completing the circular movement, its energy of position once more
assumes the kinetic form, and reaches its maximum value at C (Fig. 2),
the lowest position. The moving pendulum mass, so far as its energy
properties are concerned, behaves in precisely the same manner as a body
vertically projected in the field of the gravitative attraction (§ 20).
This simple energy operation of the pendulum is perhaps one of the most
familiar of energy processes. By its means, however, it is possible to
illustrate certain general features of energy reactions of great
importance to the author's scheme.
The energy processes of the pendulum system are carried out through the
medium of the material pendulum machine, and are limited, both in nature
and degree, by the properties of that machine. As the pendulum vibrates,
the transformation of energy of motion to energy of position or vice
versa is an example of a reversible energy operation. The energy active
in this operation continually alternates between two forms of energy:
transformation is continually followed by a corresponding return.
Neglecting in the meantime all frictional and other effects, we will
assume complete reversibility, or that the energy of motion of the
pendulum, after passing completely into the form of energy of position
at the highest point, is again completely returned, in its original
form, in the descent. Now, for any given pendulum, the amount of energy
which can thus operate in the system depends on two factors, namely, the
mass of the pendulum and the vertical height through which it rises in
vibration. If the mass is fixed, then the maximum amount of energy will
be operating in the reversible cycle when the pendulum is performing
complete revolutions round its axis of suspension. The maximum height
through which the pendulum can rise, or the maximum amount of energy of
position which the system can acquire, is thus dependent on the length
of the pendulum arm. These two factors, then, the mass and the length of
the pendulum arm, are simply properties of this pendulum machine,
properties by which its energy compass is restricted. Let us now
examine these limiting factors more minutely.
It is obvious that energy could readily be applied to the pendulum
system in such a degree as to cause it to rotate with considerable
angular velocity about the axis of suspension. Now the motion of the
pendulum mass in the lines of the gravitation field, although productive
of the same transformation process, differs from that of a body moving
vertically upward in that, while the latter has a linear movement, the
former is constrained into a circular path. This restraint is imposed in
virtue of the cohesive properties of the material of the pendulum arm,
and it is the presence of this restraining influence that really
distinguishes the pendulum machine from the machine in which the moving
mass is constrained by gravity alone (§ 20). It has been shown that the
energy capacity of a body projected vertically against gravity is
limited by its mass only; the energy capacity of the pendulum machine
may be likewise limited by its mass, but the additional restraining
factor of cohesion also imposes another limit. In the course of
rotation, energy is stored in the material of the pendulum against the
internal forces of cohesion. The action is simply that of what is
usually termed centrifugal force. As the velocity increases, the
pendulum arm lengthens correspondingly until the elastic limit of the
material in tension is reached. At this point, the pendulum may be said
to have reached the maximum length at which it can operate in that
reversible process of transformation in which energy of motion is
converted into energy of position. The amount of energy which would now
be working in that process may be termed the limiting energy for
reversibility. This limiting energy is the absolute maximum amount of
energy which can operate in the reversible cycle. It is coincident with
the maximum length of the pendulum arm in distortion. When the stress in
the material of that arm reaches the elastic limit, it is clear that the
transformation against cohesion will also have attained its limiting
value for reversibility. This transformation, if the velocity of the
pendulum is constant, is of the nature of a storage of energy. So long
as the velocity is constant the energy stored is constant. If the
elastic limiting stress of the material has not been exceeded, this
energy--neglecting certain minor processes (§§ 15, 29)--will be returned
in its original form as the velocity decreases. If, however, the
material be stressed beyond its elastic powers, the excess energy
applied will simply lead to permanent distortion or disruption of the
pendulum arm, and to a complete breakdown and change in the character of
the machine and the associated energy processes (§ 5). The physical
properties of the material thus limit the energy capacity of the
machine. This limiting feature, as already indicated, is not peculiar
to the pendulum machine alone. Every energy process embodied in a
material machine is limited in a similar fashion by the peculiar
properties of the acting materials. Every reversible process is carried
out within limits thus clearly defined. Nature presents no exception to
this rule, no example of a reversible energy system on which energy may
be impressed in unlimited amount. On the contrary, all the evidence
points to limitation of the strictest order in such processes.
24. _Transformations of the Moving Pendulum--b. Frictional
Transformation at the Bearing Surfaces_
The motion of the pendulum, whether it be completely rotatory or merely
vibratory in nature, invariably gives rise to heating at the bearings or
supporting points. Since the heating effect is only evident when motion
is taking place, and since the heat can only make its appearance as the
result of some energy process, it would appear that this persistent heat
phenomenon is the result of a transformation of the original energy of
motion of the pendulum.
The general energy conditions of the apparatus already adverted to (§
21) still hold, and the lubricating oil employed in the apparatus being
assumed to have sufficient capillarity or adhesive power to separate
the metallic surfaces of bearings and journals at all velocities, then
every action of the spindle on the bearings must be transmitted through
the lubricant. The latter is, therefore, strained or distorted against
the internal cohesive or viscous forces of its material. The general
effect of the rotatory motion of the spindle will be to produce a motion
of the material of the lubricant in the field of these incepting forces.
To this motion the heat transformation is primarily due. Other
conditions being the same, the extent of the transformation taking
place, in any given case, is dependent on the physical properties of the
lubricant, such as its viscosity, its cohesive or capillary power,
always provided that the metallic surfaces are separated, so that the
action is really carried out in the lines or field of the internal
cohesive forces of the lubricant. In itself, this transformation is not
a reversible process; no mechanism appears by which this heat energy
evolved at the bearing surfaces could be returned once more to its
original form of energy of motion. It may be, in fact, communicated by
conduction to the metallic masses of the bearings, and thence, by
conduction and radiation, to the air masses surrounding the apparatus.
Its action in these masses is dealt with below (§ 29). The operation of
bearing friction, though in itself not a reversible process, really
forms one link of a complete chain (§ 9) of secondary operations
(transmissions and transformations) which together form a comprehensive
and complete cyclical energy process (§ 32).
When no lubricant is used in the apparatus, so that the metallic
surfaces of bearings and journals are in contact, the heat process is of
a precisely similar nature to that described above (see also § 16).
Distortion of the metals in contact takes place in the surface regions,
so that the material is strained against its internal cohesive forces.
The transformation will thus depend on the physical properties of these
metals, and will be limited by these properties. Different metallic or
other combinations will consequently give rise to quite different
results with respect to the amounts of heat energy evolved.
25. _Stability of Energy Systems_
The ratio of the maximum or limiting energy for reversibility to the
total energy of the system may vary in value. If the pendulum vibrates
only through a very small arc, then, neglecting the minor processes (§§
24, 29), practically the whole energy of the system operates in the
reversible transformation. This condition is maintained as the length of
the arc of vibration increases, until the pendulum is just performing
complete revolutions about the central axis. After this, the ratio will
alter in value, because the greater part of any further increment of
energy does not enter into the reversible cyclical process, but merely
goes to increase the velocity of rotation and the total energy of the
system. The small amount of energy which thus enters the reversible
cycle as the velocity increases, does so in virtue of the increasing
length of the pendulum arm in distortion. To produce even a slight
distortion of the arm, a large amount of energy will require to be
applied to and stored in the system, and thus, at high velocities of
rotation, the energy which operates in the reversible cycle, even at its
limiting value, may form only a very small proportion of the total
energy of the system. At low velocities or low values of the total
energy, say when the pendulum is not performing complete rotations,
practically the whole energy of the system is working in the reversible
cycle; but, in these circumstances, it is clear that the total energy of
the system, which, in this case, is all working in the reversible
process, is much less than the maximum or limiting amount of energy
which might so work in that process. Under these conditions, when the
total energy of the system is less than the limiting value for
reversibility, so that this total energy in its entirety is free to take
part in the reversible process, then the energy system may be termed
stable with respect to that process. Stability, in an energy system,
thus implies that the operation considered is not being, as it were,
carried out at full energy capacity, but within certain reversible
energy limits.
We have emphasised this point in order to draw attention to the fact
that the great reversible processes which are presented to our notice in
natural phenomena are all eminently stable in character. Perhaps the
most striking example of a natural reversible process is found in the
working of the terrestrial atmospheric machine (§§ 10, 38). The energy
in this case is limited by the mass, but in actual operation its amount
is well within the maximum limiting value. The machine, in fact, is
stable in nature. Other natural operations, such as the orbital
movements of planetary masses, (§ 8) illustrate the same conditions.
Nature, although apparently prodigal of energy in its totality, yet
rigidly defines the bounding limits of her active operations.
26. _The Pendulum as a Conservative System_
Under certain conditions the reversible energy cycle produces an
important effect on the rotatory motion of the pendulum. For the purpose
of illustration, let it be assumed that the pendulum is an isolated and
conservative system endowed with a definite amount of rotatory energy.
In its circular movement, the upward motion of the pendulum mass is
accompanied by a gain in its energy of position. This gain is, in the
given circumstances, obtained solely at the expense of its inherent
rotatory energy, which, accordingly, suffers a corresponding decrease.
The manifestation of this decrease will be simply a retardation of the
pendulum's rotatory motion. Its angular velocity will, therefore,
decrease until the highest altitude E (Fig. 2) is attained. After this,
on the downward path, the process will be reversed. Acceleration will
take place from the highest to the lowest point of flight, and the
energy stored as energy of position will be completely returned in its
original form of energy of motion. The effect of the working of the
reversible cycle, then, on the rotatory system, under the given
conditions, is simply to produce alternately a retardation and a
corresponding acceleration. Now, it is to be particularly noted that
these changes in the velocity of the system are produced, not by any
abstraction from or return of energy to the system, which is itself
conservative, but simply in consequence of the transformation and
re-transformation of a certain portion of its inherent rotatory energy
in the working of a reversible process embodied in the system. The same
features may be observed in other systems where the conditions are
somewhat similar.
In the natural world, we find processes of the same general nature in
constant operation. When any mass of material is elevated from the
surface of a rotating planetary body against the gravitative attraction,
it thereby gains energy of position (§ 20). This energy, on the body's
return to the surface in the course of its cycle, reappears in the form
of energy of motion. Now the material mass, in rising from the planetary
surface, is not, in reality, separated from the planet. The atmosphere
of the planet forms an integral portion of its material, partakes of its
rotatory motion, and is bound to the solid core by the mutual
gravitative forces. Any mass, then, on the solid surface of a planet is,
in reality, in the planetary interior, and the rising of such a mass
from that surface does not imply any actual separative process, but
simply the radial movement, or displacement of a portion of the
planetary material from the central axis. If the energy expended in the
upraisal of the mass is derived at the expense of the inherent rotatory
energy of the planet, as it would be if the latter were a strictly
conservative energy system, then the raising of this portion of
planetary material from the surface would have a retarding effect on the
planetary motion of rotation. But if, on the other hand, the energy of
such a mass as it fell towards the planetary surface were converted once
more into its original form of energy of axial motion, exactly
equivalent in amount to its energy of position, it is evident that the
process would be productive of an accelerating effect on the planetary
motion of rotation, which would in magnitude exactly balance the
previous retardation. In such a process it is evident that energy
neither enters nor leaves the planet. It simply works in an energy
machine embodied in planetary material. This point will be more fully
illustrated later. The reader will readily see the resemblance of a
system of this nature to that which has already been illustrated by the
rotating pendulum.
In the meantime, it may be pointed out that matter displaced from the
planetary surface need not necessarily be matter in the solid form. All
the operations mentioned above could be quite readily--in fact, more
readily--carried out by the movements of gaseous material, which is
admirably adapted for every kind of rising, falling, or flowing motion
relative to the planetary surface (§ 13).
27. _Some Phenomena of Transmission Processes--Transmission of Heat
Energy by Solid Material_
The pendulum machine described above furnishes certain outstanding
examples of the operation of energy transformation. It will be noted,
however, that it also portrays certain processes of energy transmission.
In this respect it is not peculiar. Most of the material machines in
which energy operates will furnish examples of both energy transmissions
and energy transformations. In some instances, the predominant operation
seems to be transformation, in others, transmission; and the machines
may be classified accordingly. It is, however, largely a matter of
terminology, since both operations are usually found closely associated
in one and the same machine. The apparatus now to be considered is
designed primarily to illustrate the operative features of certain
energy transmissions, but the description of the machines with their
allied phenomena will show that energy transformations also play a very
important part in their constitution and working.
A cylindrical metallic bar about twelve inches long, say, and one inch
in diameter, is placed with its ends immersed in water in two separate
vessels, A and B, somewhat as shown.
[Illustration: FIG. 3]
By the application of heat energy, the temperature of the water in the
vessel A is raised to a point say 100° F. above that of B, and steadily
maintained at that point. It is assumed that B is also kept at the
constant lower temperature. In these circumstances, a transmission of
heat energy takes place from A to B through the metallic bar. When the
steady temperature condition is reached, the transmission will be
continuous and uniform; the rate at which it is carried out will be
determined by the length of the bar, by the material of which it is
composed, and by the temperature difference maintained between its
ends. Now what has really happened is that by a combination of
phenomena the bar has been converted into a machine for the transmission
of heat energy. A full description of these phenomena is, in reality,
the description of this machine, and vice versa. Let us, therefore, now
try to outline some of these phenomena.
The first feature of note is the gradient of temperature which exists
between the ends of the bar. Further research is necessary regarding the
real nature of this gradient--it appears to differ greatly in different
materials--but the existence of such a gradient is one of the main
features of the energy machine, one of the essential conditions of the
transmission process.
Another feature is that of the expansive motion of the bar itself. The
expansion of the bar due to the heating varies in value along its
length, from a maximum at the hot end to a minimum at the cool end. The
expansion, also, is the evidence of a transformation of energy. The bar
has been constrained into its new form against the action of the
internal molecular or cohesive forces of its material (§ 16). The energy
employed and transformed in producing the expansion is a part of the
original heat energy applied to the bar, and before any transmission of
this heat energy takes place between its extreme ends, a definite
modicum of the applied energy has to be completely transformed for the
sole purpose of producing this distortive movement or expansion against
cohesion. This preliminary straining of the bar is, in fact, a part of
the process of building up or constituting the energy transmission
machine, and must be completely carried out before any transmission can
take place. It is clear, then, that concurrent with the gradient of
temperature, there also exists, along the bar, what might be termed a
gradient of energy stored against cohesion, and that both are
characteristic and essential features of this particular energy machine.
A point of some importance to note is the permanency of these features.
Once the machine has been constituted with a constant temperature
difference, the transmission of energy will take place continuously and
at a uniform rate. But no further transformation against cohesion takes
place; no further expenditure of energy against the internal forces of
the material is necessary. Neglecting certain losses due to possible
external conditions, the whole energy applied to the machine at the one
end is transmitted in its entirety to the other, without influencing in
any way either the temperature or the energy gradient.
Such is the general constitution of this machine for energy
transmission. Its material foundation is, indeed, the metallic bar, but
the temperature and energy gradients may be termed the true determining
factors of its operation. As already indicated, the magnitude of the
transformation is dependent on the temperature difference between the
ends of the bar. But this applies only within certain limits. With
respect to the cool end, the temperature may be as low as we please--so
far as we know, the limit is absolute zero of temperature; but with the
hot end, the case is entirely different, because here the limit is very
strictly imposed by the melting-point of the material of the bar. When
this melting temperature is attained, the melting of the bar indicates,
simply, that the heat energy stored or transformed against the cohesive
forces of the material has reached its limiting value; change of state
of the material is taking place, and the machine is thereby being
destroyed.
It is evident, then, that the energy which is actually being transmitted
has itself no effect whatever in restricting the action or scope of the
transmission machine. It is, in reality, the residual energy stored
against the cohesive forces which imposes the limits on the working. It
is the maximum energy which can be transformed in the field of the
cohesive forces of the material which determines the power of that
material as a transmitting agent. This maximum will, of course, be
different for different materials according to their physical
constitution. It is attained in this machine in each case when melting
of the bar takes place.
28. _Some Phenomena of Transmission Processes--Transmission by Flexible
Band or Cord_
This method is often adopted when energy of motion, or mechanical
energy, is required to be transmitted from one point to another. For
illustration, consider the case of two parallel spindles or shafts, A
and B (Fig. 4), each having a pulley securely keyed upon it. Spindle A
is connected to a source of of mechanical energy, and it is desired to
transmit this energy across the intervening space to spindle B.
[Illustration: FIG. 4]
This, of course, might be accomplished in various ways, but one of the
most simple, and, at the same time, one of the most efficient, is the
direct drive by means of a flexible band or cord. The band is placed
tightly round, and adheres closely to both pulleys; the coefficient of
friction between band and pulleys may, in the first instance, be assumed
to be sufficiently great to prevent slipping of the band up to the
highest stress which it is capable of sustaining in normal working.
Connected in this fashion, the spindles will rotate in unison, and
mechanical energy, if applied at A, may be directly transmitted to B.
The material operator in the transmission is the connecting flexible
band, and associated with this material are certain energy processes
which are also essential features of the energy machine. When
transmission of energy is taking place, a definite tension or stress
exists in the connecting band, and neglecting certain inevitable losses
due to bearing friction (§ 24) and windage (§ 29), practically the whole
of the mechanical or work energy communicated to the one spindle is
transmitted to the other. Now the true method of studying this or any
energy process is simply to describe the constitution and principal
features of the machine by which it is carried out. These are found in
the phenomena of transmission. One of the most important is the peculiar
state of strain or tension existing in the connecting band. This, as
already indicated, is an absolutely essential condition of the whole
operation. No transmission is possible without some stress or pull in
the band. This pull is exerted against the cohesive forces of the
material of the band, so that before transmission takes place it is
distorted and a definite amount of the originally applied work energy is
expended in straining it against these forces. This energy is
accordingly stored in the form of strain energy or energy of separation
(§ 22), and, if the velocity is uniform, the magnitude of the
transmission is proportional to this pull in the band, or to the
quantity of energy thus stored against the internal forces of its
material. But, in every case, a limit to this amount of energy is
clearly imposed by the strength of the band. The latter must not be
strained beyond its limiting elastic stress. So long as energy is being
transmitted, a certain transformation and return of energy of strain or
separation is taking place in virtue of the differing values of the
tensions in the two sides of the band; and if the latter were stressed
beyond the elastic limit, permanent distortion or disruption of the
material would take place. Under such conditions, the reversible energy
process, involving storage and restoration of strain energy as the band
passes round the pulleys, would be impossible, and the energy
transmission machine would be completely disorganised. The magnitude of
the energy operation is thus limited by the physical properties of the
connecting band.
Another important feature of this energy transmission machine is the
velocity, or rather the kinetic energy, of the band. The magnitude of
the transmission process is directly proportional to this velocity, and
is, therefore, also a function of the kinetic energy. At any given rate
of transmission, this kinetic energy, like the energy stored against the
cohesive influence, will be constant in amount, and like that energy
also, will have been obtained at the expense of the originally applied
energy. This kinetic energy is an important feature in the constitution
of the transmission machine. As in the case of the strain energy, its
maximum value is strictly limited, and thus imposes a limit on the
general operation of the machine. For, at very high velocities, owing to
the action of centrifugal force, it is not possible to keep the band in
close contact with the surface of the pulleys. When the speed rises
above a certain limit, although the energy actually being transmitted
may not have attained the maximum value possible at lower speeds with
greater tension in the band, the latter will, in virtue of the strain
imposed by centrifugal action, be forced radially outwards from the
pulley. The coefficient of friction will be thereby reduced; slipping
will ensue, and the transmission may cease either in whole or in part.
In this way the velocity or kinetic energy limit is imposed. The machine
for energy transmission may thus be limited in its operation by two
different factors. The precise way in which the limit will be applied in
any given case will, of course, depend on the circumstances of working.
29. _Some Phenomena of Transmission Processes--Transmission of Energy to
Air Masses_
The movement of the pendulum (§ 23) is accompanied by a certain
transmission of energy to the surrounding medium. When this medium is a
gaseous one such as air, the amount of energy thus transmitted is
relatively small. The process, however, has a real existence. To
illustrate its general nature, let it be assumed that the motion of the
pendulum is carried out, not in air, but in a highly viscous fluid, say
a heavy oil. Obviously, a pendulum falling from its highest position to
its lowest, in such a medium would transmit its energy almost in its
entirety to the medium, and would reach its lowest position almost
devoid of energy of motion. The energy of position with which it was
originally endowed would thus be transformed and transmitted to the
surrounding medium. The agent by which the transmission is carried out
is the moving material of the pendulum, which, as it passes through the
fluid, distorts that fluid in the lines or field of its internal
cohesive or viscous forces which offer a continuous resistance to the
motion. As the pendulum passes down through the liquid, the succeeding
layers of the latter are thus alternately distorted and released. The
distortive movement takes place in virtue of the communication of energy
from the moving pendulum to the liquid, and during the movement energy
is stored in the fluid as energy of strain and as kinetic energy. At the
same time, a transformation of the applied energy into heat takes place
in the distorted material. The release of this material from strain, and
its movement back towards its original state, is also accompanied by a
similar transformation, in which the stored strain energy is, in turn,
converted into the heat form. The whole operation is similar in nature
to that frictional process already described (§ 16) in the case of a
body moving on a rough horizontal table. The final action of the heat
energy thus communicated to the fluid is to expand the latter against
the internal cohesive or viscous forces of its material, and also
against the gravitative attraction of the earth.
Now when the pendulum moves in air, the action taking place is of the
same nature, and the final result is the same as in oil. It differs
merely in degree. Compared with the oil, the air masses offer only a
slight resistance to the motion, and thus only an exceedingly small part
of the pendulum's energy is transmitted to them. The pendulum, however,
does set the surrounding air masses in motion, and by a process similar
in nature to that in the oil, a modicum of the energy of the falling
pendulum is converted into heat, and thence by the expansion of the air
into energy of position. In the downward motion from rest, the first
stage of the process is a transformation peculiar to the pendulum
itself, namely, energy of position into energy of motion. The
transmission to the fluid is a necessary secondary result. It is
important to note that this transmission is carried out in virtue of the
actual movement of the material of the pendulum, and that the energy
transmitted is in reality mechanical or work energy (§ 31). This
mechanical or work energy, then actually leaves or is transmitted from
the pendulum system, and is finally absorbed by the surrounding air
masses in the form of energy of position.
Considered as a whole, there is evidently no aspect of reversibility
about the operation, but it will be shown later (§ 32) that with the
introduction of other factors, it really forms part of a comprehensive
cyclical process. It is itself a process of direct transmission. It is
carried out by means of a definite material machine which embodies
certain energy transformations, and which is strictly limited in the
extent of its operations by certain physical factors. These factors are
the cohesive properties of the moving pendulum mass and the fluid with
which it is in contact (§ 16). It is clear, also, that in an apparatus
in which the motion is carried out in oil, any heat energy communicated
to the oil would inevitably find its way to the surrounding air masses
by conduction and radiation. The final result of the pendulum's motion
would therefore be the same in this case as in air; the heat energy
would, when communicated to the surrounding air masses, cause an
expansive movement against gravity.
30. _Energy Machines and Energy Transmission_
[Illustration: FIG. 5]
The various examples of energy transformation and transmission which
have been discussed above (§§ 13-27) will suffice to show the essential
differences which exist in the general nature of these operations. But
they will also serve another purpose in portraying one striking and
important aspect in which these processes are alike. From the
descriptions given above, it will be amply evident that each of these
processes, whether transformation or transmission, requires as an
essential condition of its existence, the presence of a certain
arrangement of matter; each process is of necessity associated with and
embodied in a definite physical and material machine. This material
machine is simply the contrivance provided by Nature to carry out the
energy operation. It differs in construction and in character for
different processes, but in every case there must be in its constitution
some material substance, perceptible to the senses, with which the
acting energy is intimately associated. This fact is but another aspect
of the principle that energy is never found dissociated from matter (§
11). In every energy machine, the material substance or operator forms
the real foundation or basis of the energy operation, but besides this
there are also always other phenomena of a secondary nature, totally
different, it may be, from the main energy operation, which combine with
that operation to constitute the whole. These subsidiary energy
phenomena are the incepting factors, and are most important
characteristics. Their presence is just as essential in energy
transmission as it is in energy transformation. As demonstrated above,
they are usually associated with the physical peculiarities of the basis
or acting material of the energy machine, and their peculiar function is
to conserve or limit the extent of its action. A complete description of
these phenomena, in any given case, would not only be equivalent to a
complete description of the machine, but would also serve as a complete
description of the main energy operation embodied in that machine.
Sometimes, however, the description of the machine is a matter of
extreme difficulty, and may be, in fact, impossible owing to the lack of
a full knowledge of the intimate phenomena concerned. An illustrative
example of this is provided by the familiar phenomenon of heat
radiation. Take the case of two isolated solid bodies A and B (Fig. 5)
in close proximity on the earth's surface. If the body A at a high
temperature be sufficiently near to B at a lower temperature, a
transmission of energy takes place from A to B. This transmission is
usually attributed to "radiation," but, after all, the use of the term
"radiation" is merely a descriptive device which hides our ignorance of
the operation. It is known that a transmission takes place, but the
intimate phenomena are not known, and, accordingly, it is impossible to
describe the machine or mechanism by which it is carried out. From
general considerations, however, it appears that the material basis of
this machine is to be found in the air medium which surrounds the two
bodies. Experiment shows, indeed, that if this intervening material
medium of air be even partially withdrawn or removed, the transmission
is immensely reduced in amount. In fact, this latter phenomenon is
largely taken advantage of in the so-called vacuum flasks or other
devices to maintain bodies at a temperature either above or below that
of the external surrounding bodies. The device adopted is, simply, as
far as practicable to withdraw all material connection between the body
which it is desired to isolate thermally and its surroundings. But it is
clearly impossible to isolate completely any terrestrial body in this
way. There must be some material connection remaining. As already
pointed out (§ 5), we have no experimental experience of really separate
bodies or of an absolute vacuum. It is to be noted that any vacuous
space which we can experimentally arrange does not even approximately
reproduce the conditions of true separation prevailing in interplanetary
space. Any arrangement of separate bodies which might thus be contrived
is necessarily entirely surrounded or enclosed by terrestrial material
which, in virtue of its stressed condition, constitutes an energy
machine of the same nature as those already described (§ 21). Even
although the air could be absolutely exhausted from a vessel, it is
still quite impossible to enclose any body permanently within that
vessel without some material connection between the body and the
enclosing walls. If for example, as shown in Fig. 6, CC represents a
spherical vessel, completely exhausted, and having two bodies, A and B
at different temperatures, in its interior, it is obvious that if these
bodies are to maintain continuously their relative positions of
separation, each must be united by some material connection to the
containing vessel. But when such a connection is made, say as shown at D
and E (Fig. 7), it is clear that A and B are no longer separate bodies
in the fullest sense of the word, but are now in direct communication
with one another through the supports at D and E and the enclosing sides
of the vessel CC. The practicable conditions are thus far from those of
separate bodies in a complete vacuum. It would seem, indeed, to be
beyond human experimental contrivance to reproduce such conditions in
their entirety. So far as these conditions can be achieved, however,
and judging solely by the experimental results already attained with
respect to the effect of exhaustion on radiation, it may be quite justly
averred that, if the conditions portrayed in Fig. 6 could be realised,
no transmission of energy would take place between two bodies, such as A
and B, completely isolated from one another in a vacuous space. It
appears, in fact, to be a quite reasonable and logical deduction from
the experimental evidence that the energy operation of transmission of
heat from one body to another by radiation is dependent on the existence
between these bodies of a real and material substance which forms in
some way (at present unknown) the transmitting medium or machine. The
difficulty which arises in the description of this machine is due, as
already explained above, simply to lack of knowledge of the intimate
phenomena of its working. Many other energy processes will, no doubt,
occur to the reader in which the same difficulty presents itself, due to
the same cause.
[Illustration: FIG. 6]
In dealing with terrestrial operations generally, and particularly when
transmission processes are under consideration, it is important to
recognise clearly the precise nature of these operations and the
peculiar conditions under which they work. It must ever be borne in mind
that the terrestrial atmosphere is a real and material portion of the
earth's mass, extending from the surface for a limited distance into
space (§ 34), and whatever its condition of gaseous tenuity, completely
occupying that space in the manner peculiar to a gaseous substance. When
the whole mass of the planet, including the atmosphere, is taken into
consideration, it is readily seen that all energy operations embodied in
or associated with material on what is usually termed the surface of the
earth take place at the bottom of this atmospheric ocean, or, in
reality, in the interior of the earth. The operations themselves are the
manifestations of purely terrestrial energy, which, by its working in
various devices or arrangements of material is being transformed and
transmitted from one form of matter to another. As will be fully
demonstrated later (Part III.), the nature of the terrestrial energy
system makes it impossible for this energy ever to escape beyond the
confines of the planetary atmospheric envelope. These are briefly the
general conditions under which the study of terrestrial or secondary
energy operations is of necessity conducted, and it is specially
important to notice these conditions when it is sought to apply the
results of experimental work to the discussion of celestial phenomena.
It must ever be borne in mind that even the direct observation of the
latter must always be carried out through the encircling planetary
atmospheric material.
[Illustration: FIG. 7]
In this portion of the work it is proposed to investigate in the light
of known phenomena the possibility of energy transmission between
separate masses. As explained above, the term separate is here meant to
convey the idea of perfect isolation, and the only masses in Nature
which truly satisfy this condition are the celestial and planetary
bodies, separated as they are from one another by interplanetary space
and in virtue of their energised condition (§ 5). Since this state of
separation cannot be experimentally realised under terrestrial
conditions, it is obvious, therefore, that no purely terrestrial energy
process can be advanced either as direct verification or direct disproof
of a transmission of energy between such truly separate masses as the
celestial bodies. But as we are unable to experiment directly on these
bodies themselves or across interplanetary space, we are forced of
necessity to rely, for experimental facts and conclusions, on the
terrestrial energy phenomena to which access is possible. As already
indicated in the General Statement (§ 11), the same energy is bestowed
on all parts of the cosmical system, and by the close observation of the
phenomena of its action in familiar operations the truest guidance may
be obtained as to its general nature and working. In such
investigations, however, only the actual phenomena of the operation are
of scientific or informative value. There is no gain to real knowledge
in assuming, say in the examination of the phenomena of magnetic
attraction between two bodies, that the one is urged towards the other
by stresses in an intervening ethereal medium, when absolutely no
phenomenal evidence of the existence of such a medium is available. It
may be urged that the conception of an ethereal medium is adapted to the
explanation of phenomena, and appears in many instances to fulfil this
function. But as already pointed out (see Introduction), it is
absolutely impossible to explain phenomena. So-called explanations must
ever resolve themselves simply into revelations of further phenomena.
While the value of true working hypotheses cannot be denied, it is
surely evident that such hypotheses, unless they embody and are under
the limitation of controlling facts, are not only useless, but, from the
misleading ideas they are apt to convey, may even be dangerous factors
in the search for truth. Now, if all speculative ideas or hypotheses are
banished from the mind, and reliance is placed solely on the evidential
phenomena of Nature, the study of terrestrial energy operations leads
inevitably to certain conclusions on the question of energy
transmission. In the first place, it must lead to the denial of what has
been virtually the great primary assumption of modern science, namely,
that a mass of material at a high temperature isolated in interplanetary
space would radiate heat in all directions through that space. Such a
conception is unsupported by our experimental or real knowledge of
radiation. The fact that heat radiation takes place from a hot to a cold
body in whatever direction the latter is placed relatively to the
former, does not justify the assumption that such radiation takes place
in all directions in the absence of a cold body. And since there is
absolutely no manifestation of any real material medium occupying
interplanetary space, no sign of the material agency or machine which
the results of direct experiment have led us to conclude is a necessity
for the transmission process of heat radiation, the whole conception
must be regarded as at least doubtful. Even with our limited knowledge
of radiation, the doctrine of heat radiation through space stands
controverted by ordinary experimental experience. With this doctrine
must fall also the allied conception of the transmission of heat energy
by radiation from the sun to the earth. It is to be noted, however, that
only the actual transmission of heat energy from the sun to the earth is
inadmissible; the _heating effect_ of the sun on the earth, which leads
to the manifestation of terrestrial energy in the heat form, is a
continuous operation readily explained in the light of the general
principle of energy transformation already enunciated (§ 4). With
respect to other possible processes of energy transmission between the
sun and the earth or across interplanetary space, the same general
methods of experimental investigation must be adopted. The transmission
of energy under terrestrial conditions is carried out in many different
forms and by the working of a large variety of machines. In every case,
no matter in what form the energy is transmitted, that energy must be
associated with a definite arrangement of terrestrial material
constituting the transmission machine. Each energy process of
transmission has its own peculiar conditions of operation which must be
completely satisfied. By the study of these conditions and the allied
phenomena it is possible to gain a real knowledge of the precise
circumstances in which the process can be carried out. Now let us apply
the knowledge of transmission processes thus gained to the general
celestial case, to the question of energy transmission between truly
separate bodies, and particularly to the case of the sun and the earth.
Do we find in this case any evidence of the presence of a machine for
energy transmission? It is impossible, within the limits of this work,
to deal with all the forms in which energy may be transmitted, but let
the reader review any instance of the transmission of energy under
terrestrial conditions, or any energy-transmission machine with which he
is familiar, noting particularly the essential phenomena and material
arrangements, and let him ask himself if there is any evidence of the
existence of a machine of this kind in operation between the sun and
the earth or across interplanetary space. We venture to assert that the
answer must be in the negative. The real knowledge of terrestrial
processes of energy transmission at command, on which all our deductions
must be based, does not warrant in the slightest degree the assumption
of transmission between the sun and the earth. The most plausible of
such assumptions is undoubtedly that which attributes transmission to
heat radiation, but this has already been shown to be at variance with
well-known facts. The question of light transmission will offer no
difficulty if it be borne in mind that light is not in itself a form of
energy, but merely a manifestation of energy as an incepting influence,
which like other incepting influences of a similar nature, can readily
operate across either vacuous or interplanetary space (§ 19).
On these general considerations, deduced from the observation of
terrestrial phenomena, allied with the conception of energy machines and
separate masses in space, the author bases one aspect of the denial of
energy transmission between celestial masses. The doctrine of
transmission cannot be sustained in the face of legitimate scientific
deduction from natural phenomena. In the later parts of this work, and
from a more positive point of view, the denial is completely justified.
31. _Identification of Forms of Energy_
Before leaving the question of energy transmission, there are still one
or two interesting features to be considered. Although energy, as
already pointed out, is ever found associated with matter, this
association does not, in itself, always furnish phenomena sufficient to
distinguish the precise phase in which the energy may be manifested.
Some means must, as a rule, be adopted to isolate and identify the
various forms.
Now one of the most interesting and important features of the process of
energy transmission is that it usually provides the direct means for the
identification of the acting energy. Energy, as it were, in movement, in
the process of transmission, is capable of being detected in its
different phases and recognised in each. The phenomena of transmission
usually serve, either directly or indirectly, to portray the precise
nature of the energy taking part in the operation. One of the most
direct instances of this is provided by the transmission of heat energy.
For illustrative purposes, let it be assumed that a body A, possessed of
heat energy to an exceedingly high degree, is isolated within a
spherical glass vessel CC, somewhat as already shown (Fig. 6). If it be
assumed that the space within CC is a perfect vacuum, and that no
material connection exists between the walls of the vessel and the body
A, the latter is completely isolated, and no means whatever are
available for the detection of its heat qualities (§ 30). It may seem
that, if the temperature of the body A were sufficiently high, its
energy state might be detected, and in a manner estimated, by its effect
on the eye or by its luminous properties, but we take this opportunity
of pointing out that luminosity is not invariably associated with high
temperature. On the contrary, many bodies are found in Nature, both
animate and inanimate, which are luminous and affect the eye at
comparatively low temperatures. How then is the energy condition of the
body to be definitely ascertained? The only means whereby it is possible
to identify the energy of the body is by transmitting a portion of that
energy to some other body and observing the resultant phenomena.
Suppose, then, another body, such as B (Fig. 6), at a lower temperature
than A, is brought into contact with A, so that a transmission of heat
energy ensues between the two. The phenomena which would result in such
circumstances will be exactly as already described in the case of the
transmission of energy through a solid (§ 27). Amongst other
manifestations it would be noticeable that the material of B was
expanded against its inherent cohesive forces. Now if, instead of a
spherical body such as B, a mercurial thermometer were utilised, the
phenomena would be of precisely the same nature. A definite portion of
the heat energy would be transmitted to the thermometer, and would
produce expansion of the contained fluid. By the amount of this
expansion it becomes possible to estimate the energy condition and
properties of the body A, relative to its surroundings or to certain
generally accepted standard conditions. Thermometric measurement is, in
fact, merely the employment of a process of energy transmission for the
purpose of identifying and estimating the heat-energy properties of
material substances.
In everyday life, rough ideas of heat energy are constantly being
obtained by the aid of the senses. This method is, however, only another
aspect of transmission, for it will be clear that the sensations of heat
and cold are, in themselves, but the evidence of the transformation of
heat energy to or from the body.
The process of energy transmission by a flexible band or cord (§ 28)
also provides evidence leading to the identification of the peculiar
form of energy which is being transmitted. At first sight, it would
appear as if this energy were simply energy of motion or kinetic energy.
A little reflection, however, on the general conditions of the process
must dispel this idea, for it is clear that the precise nature of the
energy transmitted has no real connection with the kinetic properties of
the system. The latter, truly, influence the rate of transmission and
impose certain limits, but evidently, if the pull in the band increases
without any increase in its velocity, the actual amount of energy
transmitted by the system would increase without altering in any respect
the kinetic properties. It becomes necessary, then, to distinguish
clearly the energy inherent to, or as it were, latent in the system,
from the energy actually transmitted by the system, to recognise the
difference between the energy transmitted by moving material and the
energy of that material. In this special instance, to identify the form
of energy transmitted it must of necessity be associated with the
peculiar phenomena of transmission. Now the energy is evidently
transmitted by the movement of the connecting belt or band. Before any
transmission can take place, however, a certain amount of energy must be
stored in the moving system, partly as cohesion or strain energy and
partly as energy of motion or kinetic energy. It is this preliminary
storage of energy which, in reality, constitutes the transmission
machine, and for a given rate of transmission, the energy thus stored
will be constant in value. It is obtained at the expense of the applied
energy, and, neglecting certain minor processes, will be returned (or
transmitted) in its entirety when the moving system once more comes to
rest. This stored energy, in fact, works in a reversible process. But
when the transmission machine is once constituted, the energy
transmitted is then that energy which is being continually applied at
the spindle A (Fig. 4) and as continually withdrawn at the spindle B. It
must be emphasised that the energy thus transmitted is absolutely
different from the kinetic or other energy associated with the moving
material of the system. It is the function of this energised material of
the band to transmit the energy from A to B, but this is the only
relationship which the transmitted energy bears to the material. The
energy thus transmitted by the moving material we term mechanical or
work energy. We may thus define mechanical or work energy as "_that form
of energy transmitted by matter in motion_."
The idea of work is usually associated with that of a force acting
through a certain distance. The form of energy referred to above as work
energy is, in the same way, always associated with the idea of a thrust
or of a pressure of some kind acting on moving material. Work energy
thus bears two aspects, which really correspond to the familiar product
of pressure and volume. Both aspects are manifested in transmission.
Since work energy is invariably transmitted by matter in motion, every
machine for its transmission must possess energy of motion as one of its
essential features. As shown above (see also § 28), this energy of
motion is really obtained at the expense of the originally applied work
energy, and as it remains unaltered in value during the progress of a
uniform transmission, it may be regarded as simply transformed work
energy, stored or latent in the system, which will be returned in its
entirety and in its original form at the termination of the operation.
The energy stored against cohesion or other forces may be regarded in
the same way. It is really the manifestation of the pressure or thrust
aspect of the work energy, just as the kinetic energy is the
manifestation of the translational or velocity aspect.
Our definition of work energy given above enables us to recognise its
operation in many familiar processes. Take the case of a gas at high
pressure confined in a cylinder behind a movable piston. We can at once
say that the energy of the gas is work energy because this energy may
quite clearly be transmitted from the gas by the movement of the piston.
If the latter form part of a steam-engine mechanism of rods and crank,
the energy may, by the motion of this mechanism, be transmitted to the
crank shaft, and there utilised. This is eminently a case in which
energy is _transmitted_ by matter in motion. The moving material
comprises the piston, piston-rod, and connecting-rod, which are, one and
all, endowed with both cohesive and kinetic energy qualities, and form
together the transmission machine. So long as the piston is at rest only
one aspect of the work energy of the gas is apparent, namely, the
pressure aspect, but immediately motion and transmission take place,
both aspects are presented. The work energy of the gas, obtained in the
boiler by a _transformation_ of heat energy is thus, by matter in
motion, transmitted and made available at the crank shaft. The shaft
itself is also commonly utilised for the further transmission of the
work energy applied. By the application of the energy at the crank, it
is thrown into a state of strain, and at the same time is endowed with
kinetic energy of rotation. It thus forms a machine for transmission,
and the work energy applied at one point of the shaft may be withdrawn
at another point more remote. The transmission is, in reality, effected
by the movement of the material of the shaft. So long as the shaft is
stationary, it is clear that no actual transmission can be carried out,
no matter how great may be the strain imposed. If our engine mechanism
were, by a change in design, adapted to the use of a liquid substance as
the working material instead of a gas, it is clear that no change would
be effected in the general conditions. The energy of a liquid under
pressure is again simply work energy, and it would be transmitted by the
moving mechanism in precisely the same manner.
From the foregoing, it will now be evident to the reader that the energy
originally applied to the primary mass (§ 3) of our cosmical system must
be work energy. It is this form of energy also which is inherent to each
unit of the planetary system associated with the primary. In this system
it is of course presented outwardly in the two phases of kinetic energy
and energy of strain or distortion. It is apparent, also, that work
energy could be transmitted from the primary mass to the separate
planets on one condition only, that is, by the movement of some material
substance connecting each planet to the primary. Since no such material
connection is admitted, the transmission of work energy is clearly
impossible.
32. _Complete Secondary Cyclical Operation_
A general outline of the conditions of working and the relationships of
secondary processes has already been given in the General Statement (§
9), but it still remains to indicate, in a broad way, the general
methods whereby these operations are linked to the atmospheric machine.
In the example of the simple pendulum, it has been pointed out that the
energy processes giving rise to heating at the bearing surfaces and
transmission of energy to the air masses are not directly reversible
processes, but really form part of a more extensive cyclical operation,
in itself, however, complete and self-contained. This cyclical operation
may be regarded as a typical illustration of the manner in which
separate processes of energy transmission or transformation, such as
already described, are combined or united in a continuous chain forming
a complete whole.
It has been assumed, in all the experiments with the pendulum, that the
operating energy is initially communicated from an outside source, say
the hand of the observer. This energy is, therefore, the acting energy
which must be traced through all its various phases from its origin to
its final destination. At the outset, it may be pointed out that this
energy, applied by hand, is obtained from the original rotational energy
of the earth by certain definite energy processes. Due to the influences
of various incepting fields which emanate from the sun (§§ 17-19), a
portion of the earth's rotational energy is transformed into that form
of plant energy which is stored in plant tissue, and which, by the
physico-chemical processes of digestion, is in turn converted into heat
and the various other forms of energy associated with the human frame.
This, then, is the origin of the energy communicated to the pendulum.
Its progress through that machine has already been described in detail
(§§ 21-26). The transformation of energy of motion to energy of position
which takes place is in itself a reversible process and may in the
meantime be neglected. But the final result of the operations, at the
bearing surfaces and in the air masses surrounding the moving pendulum,
was shown to be, in each case, that heat energy was communicated to
these air masses. The effect of the heat energy thus impressed, is to
cause the expansion of the air and its elevation from the surface of the
earth in the lines or field of the gravitative attraction, so that this
heat energy is transformed, and resides in the air masses as energy of
position. The energy then, originally drawn from the rotational energy
of the earth, has thus worked through the pendulum machine, and is now
stored in the air masses in this form of energy of position. To make the
process complete and cyclical this energy must now, therefore, be
returned once more to the earth in its original rotational form. This
final step is carried out in the atmospheric machine (§ 41). In this
machine, therefore, the energy of position possessed by the air masses
is, in their descent to their original positions at lower levels,
transformed once more into axial or rotational energy. In this fashion
this series of secondary processes, involving both transformations and
transmissions, is linked to the great atmospheric process. The amount of
energy which operates through the particular chain of processes we have
described is, of course, exceedingly small, but in this or a similar
manner all secondary operations, great or small, are associated with the
atmospheric machine. Instances could readily be multiplied, but a little
reflection will show how almost every energy operation, no matter what
may be its nature, whether physical, chemical, or electrical, leads
inevitably to the communication of energy to the atmospheric air masses
and to their consequent upraisal.
It is interesting to note the infallible tendency of energy to revert
to its original form of axial energy, or energy of rotation, by means of
the air machine. All Nature bears witness to this tendency, and although
the path of energy through the maze of terrestrial transformation often
appears tortuous and uncertain, its final destination is always sure.
The secondary operations are thus interlinked into one great whole by
their association in the terrestrial energy cycle. Many of these
secondary operations are of short duration; others extend over long
periods of time. Energy, in some cases, appears to slumber, as in the
coal seams of the earth, until an appropriate stimulus is applied, when
it enters into active operation once more. The cyclical operations are
thus long or short according to the duration of their constituent
secondary energy processes. But the balance of Nature is ever preserved.
Axial energy, transformed by the working of one cyclical process, is
being as continuously returned by the simultaneous operation of others.
PART III
TERRESTRIAL CONDITIONS
33. _Gaseous Expansion_
Before proceeding to the general description of the atmospheric machine
(§ 10), it is desirable to consider one or two features of gaseous
reaction which have a somewhat important bearing on its working. Let it
be assumed that a mass of gaseous material is confined within the lower
portion of a narrow tube ABCD (Fig. 8) assumed to be thermally
non-conducting; the upper portion of the tube is in free communication
with the atmosphere. The gas within the tube is assumed to be isolated
from the atmosphere by a movable piston EF, free to move vertically in
the tube, and for the purpose of illustration, assumed also frictionless
and weightless. With these assumptions, the pressure on the confined gas
will simply be that due to the atmosphere. If heat energy be now
applied to the gas, its temperature will rise and expansion will ensue.
This expansion will be carried out at constant atmospheric pressure; the
gaseous material, as it expands, must lift with it the whole of the
superimposed atmospheric column against the downward attractive force of
the earth's gravitation on that column. Work is thus done by the
expanding gas, and in consequence of this work done, a definite quantity
of atmospheric material gains energy of position or potential energy
relative to the earth's surface. At the same time, the rise of
temperature of the gas will indicate an accession of heat energy to its
mass. These familiar phenomena of expansion under constant pressure
serve to illustrate the important fact that, when heat energy is applied
to a gaseous mass, it really manifests itself therein in two aspects,
namely, heat energy and work energy. The increment of heat energy is
indicated by the increase in temperature, the increment of work energy
by the increase in pressure. In the example just quoted, however, there
is no increase in pressure, because the work energy, as rapidly as it is
applied to the gas, is transformed or worked down in displacing the
atmospheric column resting on the upper side of the moving piston. The
energy applied, in the form of heat from the outside source, has in
reality been introduced into a definite energy machine, a machine in
this case adapted for the complete transformation of work energy into
energy of position. As already indicated, when the expansive movement is
completed, the volume and temperature of the gaseous mass are both
increased but the pressure remains unaltered. While the increase in
temperature is the measure and index of a definite increase in the heat
energy of the gas, it is important to note that, so far as its work
energy is concerned, the gas is finally in precisely the same condition
as at the commencement of the operation. Work energy has been, by the
working of this energy machine, as it were passed through the gaseous
mass into the surrounding atmosphere. The pressure of the gas is the
true index of its work energy properties. So long as the pressure
remains unaltered, the inherent work energy of the material remains
absolutely unaffected. A brief consideration of the nature of work
energy as already portrayed (§ 31) will make this clear. Work energy has
been defined as "_that form of energy transmitted by matter in motion_,"
and it is clear that pressure is the essential factor in any
transmission of this nature. Temperature has no direct bearing on it
whatever. It is common knowledge, however, that in the application of
heat energy to a gaseous substance, the two aspects of pressure and
temperature cannot be really dissociated. They are mutually dependent.
Any increment of heat energy to the gas is accompanied by an increment
of work energy, and vice versa. The precise mode of action of the work
energy will, of course, depend on the general circumstances of the
energy machine in which it operates. In the case just considered the
work energy does not finally reside in the gaseous mass itself, but, by
the working of the machine, is communicated to the atmosphere. If, on
the other hand, heat energy were applied in the same fashion to a mass
of gas in a completely enclosed vessel, that is to say at constant
volume instead of at constant pressure, the general phenomena are merely
altered in degree according to the change in the precise nature of the
energy machine. In the former case, the nature of the energy machine was
such that the work energy communicated was expended in its entirety
against gravitation. Under what is usually termed constant volume
conditions, only a portion of the total work energy communicated is
transformed, and the transformation of this portion is carried out, not
against gravitation, but against the cohesive forces of the material of
the enclosing vessel which restrains the expansion. No matter how great
may be the elastic properties of this material, it will be distorted,
more or less, by the application of work energy. This distortional
movement is the external evidence of the energy process of
transformation. Energy is stored in the material against the forces of
cohesion (§ 15). But the energy thus stored is only a small proportion
of the total work energy which accrues to the gas in the heating
process. The remainder is stored in the gas itself, and the evidence of
such storage is found simply in the increase of pressure. Different
energy machines thus offer different facilities for the transformation
or the storage of the applied energy. In every case where the work
energy applied has no opportunity of expending itself, its presence will
be indicated by an increase in the pressure or work function of the gas.
[Illustration: FIG. 8]
The principles which underlie the above phenomena can readily be applied
to other cases of gaseous expansion. It is a matter of common experience
that if a given mass of gaseous material be introduced into a vessel
which has been exhausted by an air-pump or other device for the
production of a vacuum, the whole space within the vessel is instantly
permeated by the gas, which will expand until its volume is precisely
that of the containing vessel. Further phenomena of the operation are
that the expanding gas suffers a decrease in temperature and pressure
corresponding to the degree or ratio of the expansion. Before the
expansive process took place the gaseous mass, as indicated by its
initial temperature and pressure, is endowed with a definite quantity of
energy in the form of heat and work energy. After expansion, these
quantities are diminished, as indicated by its final and lower
temperature and pressure. The operation of expansion has thus involved
an expenditure of energy. This expenditure takes place in virtue of the
movement of the gaseous material (§ 4). It is obvious that if the volume
of the whole is to be increased, each portion of the expanding gas
requires to move relatively to the remainder. This movement is carried
out in the lines of the earth's gravitative attraction, and to a certain
extent over the surface of the containing vessel. In some respects, it
thus corresponds simply to the movement of a body over the earth's
surface (§ 16). It is also carried out against the viscous or frictional
forces existing throughout the gaseous material itself (§ 29). Assuming
no influx of energy from without, the energy expended in the movement of
the gaseous material must be obtained at the expense of the inherent
heat and work energy of the gas, and these two functions will decrease
simultaneously. The heat and work energy of the gas or its inherent
energy is thus taken to provide the energy necessary for the expansive
movement. This energy, however, does not leave the gas, but still
resides therein in a form akin to that of energy of position or
separation. It will be clear also, that the reverse operation cannot, in
this case, be carried out; the gas cannot move back to its original
volume in the same fashion as it expanded into the vacuum, so that the
energy utilised in this way for separation cannot be directly returned.
The expansion of the gas has been assumed above to take place into a
vacuous space, but a little consideration will show that this condition
cannot be properly or even approximately fulfilled under ordinary
experimental conditions. The smallest quantity of gas introduced into
the exhausted vessel will at once completely fill the vacuous space,
and, on this account, the whole expansion of the gas does not in reality
take place _in vacuo_ at all. To study the action of the gas under the
latter conditions, it is necessary to look on the operation of expansion
in a more general way, which might be presented as follows.
34. _Gravitational Equilibrium of Gases_
Consider a planetary body, in general nature similar to the earth, but,
unlike the earth, possessing no atmosphere whatever. The space
surrounding such a celestial mass may then be considered as a perfect
vacuum. Now let it be further assumed that in virtue of some change in
the conditions, a portion of the material of the planetary mass is
volatilised and a mass of gas thereby liberated over its surface. The
gas is assumed to correspond in temperature to that portion of the
planet's surface with which it is in contact. It is clear that, in the
circumstances, the gas, in virtue of its elastic and energetic
properties, will expand in all directions. It will completely envelop
the planet, and it will also move radially outwards into space. In these
respects, its expansion will correspond to that of a gas introduced
into a vacuous space of unlimited extent.
The question now arises as to the nature of the action of the gaseous
substance in these circumstances. It is clear that the radial or outward
movement of the gas from the planetary surface is made directly against
the gravitative attraction of the planet on the gaseous mass. In other
words, matter or material is being moved in the lines or field of this
gravitative force. This movement, accordingly, will be productive of an
energy transformation (§ 4). In its initial or surface condition each
portion of the gaseous mass is possessed of a perfectly definite amount
of energy indicated by and dependent on that condition. As it moves
upwards from the surface, it does work against gravity in the raising of
its own mass. But as the mass is thus raised, it is gaining energy of
position (§ 20), and as it has absolutely no communication with any
external source of energy in its ascent, the energy of position thus
gained can only be obtained at the expense of its initial inherent heat
and work energy. The operation is, in fact, a simple transformation of
this inherent energy into energy of position, a transformation in which
gravity is the incepting agency. The external evidence of transformation
will be a fall in temperature of the material. Since the action is
exactly similar for all ascending particles, it is evident that as the
altitude of the gaseous mass increases the temperature will
correspondingly diminish. This diminution will proceed so long as the
gaseous particles continue to ascend, and until an elevation is finally
attained at which their inherent energy is entirely converted into
energy of position. The expansion of the gas, and the associated
transformation of energy, thus leads to the erection of a gaseous column
in space, the temperature of which steadily diminishes from the base to
the summit. At the latter elevation, the inherent energy of the gaseous
particles which attain to it is completely transformed or worked out
against gravity in the ascent; the energy possessed by the gas at this
elevation is, therefore, entirely energy of position; the energy
properties of heat and work have entirely vanished, and the temperature
will, therefore, at this elevation, be absolute zero. It is important to
note also that in the building of such a column or gaseous spherical
envelope round the planet, the total energy of any gaseous particle of
that column will remain unchanged throughout the process. No matter
where the particle may be situated in the column, its total energy must
always be expressed by its heat and work energy properties together with
its energy of position. This sum is always a constant quantity. For if
the particle descends from a higher to a lower altitude, its total
energy is still unchanged, because a definite transformation of its
energy of position takes place corresponding to its fall, and this
transformed energy duly appears in its original form of heat and work
energy in accordance with the decreased altitude of the particle. Since
the temperature of the column remains unchanged at the base surface and
only decreases in the ascent, it is clear that the entire heat and work
energy of the originally liberated gaseous mass is not expended in the
movement against gravity. Every gaseous particle--excepting those on the
absolute outer surface of the gaseous envelope--has still the property
of temperature. It is evident, therefore, that in the constitution of
the column, only a portion of the total original heat and work energy of
the gaseous substance is transformed into energy of position.
The space into which the gas expands has been referred to as unlimited
in extent. But although in one sense it may be correctly described thus,
yet in another, and perhaps in a truer sense, the space is very strictly
limited. It is true there is no enclosing vessel or bounding surface,
but nevertheless the expansion of the gas is restrained in two ways or
limited by two factors. The position of the bounding surface of the
spherical gaseous envelope depends, in the first place, on the original
energy of the gas as deduced from its initial temperature and its other
physical properties, and secondly on the value of the gravitative
attraction exerted on the gas by the planetary body. Looking at the
first factor, it is obvious that since the gaseous mass initially
possesses only a limited amount of energy, and since only a certain
portion of this energy is really available for the transformation, the
whole process is thereby limited in extent. The complete transformation
and disappearance of that available portion of the gaseous energy in the
process of erection of the atmospheric column will correspond to a
definite and limited increase of energy of position of gaseous material.
Since the energy of position is thus restricted in its totality, and the
mass of material for elevation is constant, the height of the column or
the boundary of expansion of the gas is likewise rigidly defined. In
this fashion, the energy properties of the gaseous material limit the
expansive process.
Looking at the operation from another standpoint, it is clear that the
maximum height of the spherical gaseous envelope must also be dependent
on the resistance against which the upward movement of the gas is
carried out, that is, on the value of the gravitative attraction. The
expenditure of energy in the ascent varies directly as the opposing
force; if this force be increased the ultimate height must decrease, and
vice versa. Each particle might be regarded as moving in the ascent
against the action of an invisible spring, stretching it so that with
increase of altitude more and more of the energy of the particle is
transformed or stored in the spring in the extension. When the particle
descends to its original position, the operation is reversed; the
spring is now contracting, and yielding up the stored energy to the
particle in the contraction. The action of the spring would here be
merely that of an apparatus for the storage and return of energy. In the
case of the gaseous mass, we conceive the action of gravitation to be
exactly analogous to that of a spring offering an approximately constant
resistance to extension. (The value of gravity is assumed approximately
constant, and independent of the particle's displacement.) The energy
stored or transformed in the ascension against gravity is returned on
the descent in a precisely similar fashion. The operation is a
completely reversible one. The range of motion of the gaseous mass or
the ultimate height of the gaseous column will thus depend on the value
of the opposing attractive force controlling the motion or, in other
words, on the value of gravity. This value is of course defined by the
relative mass of the planet (§ 20).
It is evident that the spherical envelope which would thus enwrap the
planetary mass possesses certain peculiar properties which are not
associated with gaseous masses under ordinary experimental conditions.
It by no means corresponds to any ordinary body of gaseous material,
having a homogeneous constitution and a precise and determinate pressure
and temperature throughout. On the contrary, its properties are somewhat
complex. Throughout the gaseous envelope the physical condition of the
substance is continually changing with change of altitude. The extremes
are found at the inner and outer bounding surfaces. At any given level,
the gaseous pressure is simply the result of the attractive action of
gravitation on the mass of gaseous material above that level--or, more
simply, to the weight of material above that level. There is, of course,
a certain decrease in the value of the gravitative attraction with
increase of altitude, but within the limits of atmospheric height
obtained by ordinary gaseous substances (§ 36) this decrease may be
neglected, and the weight of unit mass of the material assumed constant
at different levels. Increase of atmospheric altitude is thus
accompanied by decrease in atmospheric pressure. But decrease in
pressure must be accompanied by a corresponding decrease in density of
the gas, so that, if uniform temperature were for the time being
assumed, it would be necessary at the higher levels to rise through a
greater distance to experience the same decrease in pressure than at the
lower levels. In fact, given uniform conditions of temperature, if
different altitudes were taken in arithmetical progression the
respective pressures and densities would diminish in geometrical
progression. But we have seen that the energy conditions absolutely
preclude the condition of uniformity of temperature, and accordingly,
the decreasing pressure and density must be counteracted to some extent
at least by the decreasing temperature. The conditions are somewhat
complex; but the general effect of the decreasing temperature factor
would seem to be by increasing the density to cause the available
gaseous energy to be completely worked down at a somewhat lower level
than otherwise, and thus to lessen to some degree the height of the
gaseous envelope.
It is to be noted that a gaseous column or atmosphere of this nature
would be in a state of complete equilibrium under the action of the
gravitative attraction--provided there were no external disturbing
influences. The peculiar feature of such a column is that the total
energy of unit mass of its material, wherever that mass may be situated,
is a constant quantity. In virtue of this property, the equilibrium of
the column might be termed neutral or statical equilibrium. The gas may
then be described as in the neutral or statical condition. This statical
condition of equilibrium of a gas is of course a purely hypothetical
one. It has been described in order to introduce certain ideas which are
essential to the discussion of energy changes and reactions of gases in
the lines of gravitational forces. These reactions will now be dealt
with.
35. _Total Energy of Gaseous Substances_
Since the maximum height of a planetary atmosphere is dependent on the
total energy of the gaseous substance or substances of which it is
composed, it becomes necessary, in determining this height, to estimate
this total energy. This, however, is a matter of some difficulty. By the
total energy is here meant the entire energy possessed by the substance,
that energy which it would yield up in cooling from its given condition
down to absolute zero of temperature. On examination of the recorded
properties of the various gaseous substances familiar to us, it will be
found that in no single instance are the particulars available for
anything more than an exceedingly rough estimate of this total energy.
Each substance, in proceeding from the gaseous condition towards
absolute zero, passes through many physical phases. In most cases, there
is a lack of experimental phenomena or data of any kind relating to
certain of these phases; the necessary information on certain points,
such as the values and variations of latent and specific heats and other
physical quantities, is, in the meantime, not accessible. Experimental
research in regions of low temperature may be said to be in its infancy,
and the properties of matter in these regions are accordingly more or
less unknown. The researches of Mendeleef and others tend to show, also,
that the comparatively simple laws successfully applied to gases under
normal conditions are entirely departed from at very low temperatures.
In view of these facts, it is necessary, in attempting to estimate, by
ordinary methods, the total energy of any substance, to bear in mind
that the quantity finally obtained may only be a rough approximation to
the true value. These approximations, however, although of little value
as precise measurements, may be of very great importance for certain
general comparative purposes.
Keeping in view these general considerations, it is now proposed to
estimate, under ordinary terrestrial atmospheric conditions, the total
energy properties of the three gaseous substances, oxygen, nitrogen, and
aqueous vapour. The information relative to the energy calculation which
is in the meantime available is shown below in tabular form. As far as
possible all the heat and other energy properties of each substance as
it cools to absolute zero have been taken into account.
_Table of Properties_
+--------+---------+----------+----------+-------------+-------+---------+
| I | II | III | IV | V | VI | VII |
+--------+---------+----------+----------+-------------+-------+---------+
| |Specific | Evaporation | | | |
| | Heat at |Temperature of Liquid| Approximate | Latent| Vapour |
| Gas | Constant| at Atmospheric | Latent Heat |Heat of|Pressure.|
| |Pressure.| Pressure. |of Gas 50° F.|Liquid.| 50° F. |
| | | °F. °F. (Abs.)| | | |
+--------+---------+----------+----------+-------------+-------+---------+
|Oxygen | 0·2175 | -296 | 164 | 100 | ... | ... |
+--------+---------+----------+----------+-------------+-------+---------+
|Nitrogen| 0·2438 | -320 | 141 | 100 | ... | ... |
+--------+---------+----------+----------+-------------+-------+---------+
|Aqueous | | | | | | |
|Vapour | 0·4 | 212 | 673 | 1080 | 144 | 0·176 |
+--------+---------+----------+----------+-------------+-------+---------+
Since no reliable data can be obtained with regard to the values and
variations of specific heats at extremely low temperatures, they are
assumed for the purpose of our calculation to be in each case that of
the gas, and to be constant under all conditions. Latent heats are
utilised in every case when available.
With these reservations, the total energy, referred to absolute zero, of
one pound of oxygen gas at normal temperature of 50° F. or 511° F.
(Abs.) will be approximately
(511 × 0·2175) + 100 = 211 Thermal Units Fahrenheit.
This in work units is roughly equivalent to
211 × 778 = 164,000 ft. lbs.
Adopting the same method with nitrogen gas, its energy at the same
initial temperature will be, per unit mass,
174,600 ft. lbs.
There is thus a somewhat close resemblance, not only in the general
temperature conditions but also in the energy conditions, of the two
gases oxygen and nitrogen.
It will be readily seen, however, that under the same conditions the
energy state of aqueous vapour differs very considerably from either,
for by the same method as before the energy per pound of aqueous vapour
is equal to
{(511 × 0·4) + 1080 + 144} × 778 = 1,111,000 ft. lbs.
Under ordinary terrestrial atmospheric conditions, the energy of aqueous
vapour per unit mass is thus nearly seven times as great as that of
either oxygen or nitrogen gas. It is to be observed, also, that
three-fourths of this energy of the vapour under the given conditions is
present in the form of latent energy of the gas, or what we have already
termed work energy.
The values of the various temperatures and other physical features,
which we have included in the Table of Properties above, and which will
be utilised throughout this discussion, are merely those in everyday use
in scientific work. They form simply the accessible information on the
respective materials. They are the records of phenomena, and on these
phenomena are based our energy calculations. Further research may reveal
the true values of other factors which up to the present we have been
forced to assume, and so lead to more accurate computation of the energy
in each case. Such investigation, however, is unlikely to affect in any
way the general object of this part of the work, which is simply to
portray in an approximate manner the relative energy properties of the
three gaseous substances under certain assumed conditions.
36. _Comparative Altitudes of Planetary Atmospheres_
The total energy of equal masses of the gases oxygen, nitrogen, and
aqueous vapour, as estimated by the method above, are respectively in
the ratios
1 : 1·06 : 6·8
Referring back once more to the phenomena described with reference to
the gravitational equilibrium of a gas, let it be assumed that the
gaseous substance liberated on the surface of the planetary body is
oxygen, and that the planetary body itself is of approximately the same
constitution and dimensions as the earth. The oxygen gas thus liberated
will expand against gravity, and envelop the planet in the manner
already described (§ 34). Now the total energy of a mass of one pound of
oxygen has been estimated under certain assumptions (§ 35) to be 164,000
ft. lbs. The value of the gravitative attraction of the planet on this
mass is the same as under ordinary terrestrial conditions, so that if
the entire energy of one pound of the gas were utilised in raising
itself against gravity, the height through which this mass would be
raised, and at which the material would attain the level of absolute
zero of temperature, assuming gravity constant with increasing altitude,
would be simply 164,000 ft. or approximately 31 miles. The whole energy
would not, of course, be expended in the expansive movement; only the
outermost surface material of the planetary gaseous envelope attains to
absolute zero of temperature. In estimating the altitude of this
surface, however, the precise mass of gaseous substance assumed for the
purpose of calculation is of little or no importance. Whatever may be
the value of the mass assumed, its total energy and the gravitative
attraction of the planetary body on it are both alike entirely and
directly dependent on that mass value. It is therefore clear that no
matter how the mass under consideration be diminished, the height at
which its energy would be completely worked down, and at which its
temperature would be absolute zero, is the same, namely 31 miles. At the
planet's surface, the total energy of an infinitesimally small portion
of the gaseous mass is proportional to that mass. This amount of energy
is, however, all that is available for transformation against
gravitation in the ascent. But at the same time, the gravitative force
on the particle, that force which resists its upward movement, is
proportionately small corresponding to the small mass, so that the
particle will in reality require to rise to the same altitude of 31
miles in order to completely transform its energy and attain absolute
zero of temperature. When the expansive process is completed, the outer
surface of the spherical gaseous envelope surrounding the planet is then
formed of matter in this condition of absolute zero; this height of 31
miles is then the altitude or depth of the statical atmospheric column
at a point on the planetary surface where the temperature is 50° F.
It is to be particularly noted that this height is entirely dependent
on the gravitation, temperature, and energy conditions assumed.
With respect, also, to the assumption made above, of constant
gravitation with increasing altitude, the variation in the value of
gravity within the height limits in which the gas operates is so slight,
that the energy of the expanding substance is completely worked down
long before the variation appreciably affects the estimated altitude of
absolute zero. In any case, bearing in mind the approximate nature of
the estimate of the energy of the gases themselves, the variation of
gravity is evidently a factor of little moment in our scheme of
comparison.
Knowing the maximum height to be 31 miles, a uniform temperature
gradient from the planetary surface to the outermost surface of the
atmospheric material may be readily calculated. In the case of oxygen,
the decrease of temperature with altitude will be at the rate of 16° F.
per mile, or 1° F. per 330 ft.
If the planetary atmosphere were composed of nitrogen instead of oxygen,
the height of the statical atmospheric column under the given conditions
would then be approximately
31 × 1·06 = 33 miles,
and the gradient of temperature 15·5° F. per mile.
In the case of aqueous vapour, which is possessed of much more powerful
energy properties than either oxygen or nitrogen, the height of the
statical column, to correspond to the energy of the material, is no less
than 210 miles and the temperature gradient only 2·4° F. per mile.
Each of the gases, then, if separately associated with the planetary
body, would form an atmosphere around it depending in height on the
peculiar energy properties of the gas. A point to be observed is that
the actual or total mass of any gas thus liberated at the planet's
surface has no bearing on the ultimate height of the atmosphere which it
would constitute. When the expansive motion is completed, the density
properties of the atmosphere would of course depend on the initial mass
of gas liberated, but for any given value of gravity it is the energy
properties of the gas per unit mass, or what might be termed its
specific energy properties, which really determine the height of its
atmosphere.
37. _Reactions of Composite Atmosphere_
It is now possible to deal with the case in which not only one gas but
several gases are initially liberated on the planetary surface. Since
the gases are different, then at the given surface temperature of the
planet they possess different amounts of heat energy, and for each gas
considered statically, the temperature-altitude gradient will be
different from any of the others. The limiting height of the gaseous
column for each gas, considered separately, will also depend on the
total energy of that gas per unit mass, at the surface temperature. But
it is evident that in a composite atmosphere, the separate statical
conditions of several gases could not be maintained. In such a mixture,
separate temperature-altitude gradients would be impossible. Absolute
zero of temperature could clearly not be attained at more than one
altitude, and it is evident that the temperature-altitude gradient of
the mixture must, in some way, settle down to a definite value, and
absolute zero of temperature must occur at some determinate height. This
can only be brought about by energy exchanges and reactions between the
atmospheric constituents. When these reactions have taken place, the
atmosphere as a whole will have attained a condition analogous to that
of statical equilibrium (§ 34). Each of its constituents, however, will
have decidedly departed from this latter condition. In the course of the
mutual energy reactions, some will lose a portion of their energy.
Others will gain at their expense. All are in equilibrium as
constituents of the composite atmosphere, but none approach the
condition of statical equilibrium peculiar to an atmosphere composed of
one gas only (§ 35). The precise energy operations which would thus take
place in any composite atmosphere would of course depend in nature and
extent on the physical properties of the reacting constituents. If the
latter were closely alike in general properties, the energy changes are
likely to be small. A strong divergence in energy properties will give
rise to more powerful reactions. A concrete instance will perhaps make
this more clear. Let it be assumed in the first place that the planetary
atmosphere is composed of the two gases oxygen and nitrogen. From
previous considerations, it will be clear that the natural decrease of
temperature of nitrogen gas with increase of altitude is, in virtue of
its slightly superior energy qualities, correspondingly slower than that
of oxygen. The approximate rates are 15·5° F. and 16° F. per mile
respectively. The tendency of the nitrogen is therefore to transmit a
portion of its energy to the oxygen. Such a transmission, however, would
increase the height of the oxygen column and correspondingly decrease
the height of the nitrogen. When the balance is finally obtained, the
height of the atmospheric column does not correspond to the energy
properties of either gas, but to those of the combination. In the case
of these two materials, oxygen and nitrogen, the energy reactions
necessary to produce the condition of equilibrium are comparatively
small in magnitude on account of the somewhat close resemblance in the
energy properties of the two substances. On this account, therefore, the
two gases might readily be assumed to behave as one gas composing the
planetary atmosphere.
But what, then, will be the effect of introducing a quantity of aqueous
vapour into an atmosphere this nature? The general phenomena will be of
the same order as before, but of much greater magnitude. From the
approximate figures obtained (§§ 35, 36), the inherent energy of aqueous
vapour per unit mass is seen to be, under the same conditions,
enormously greater than that of the other two gases. In statical
equilibrium (§ 34), the altitude of the gaseous column formed by aqueous
vapour is almost seven times as great as that of the oxygen or nitrogen
with which, in the composite atmosphere, it would be intermixed. In the
given circumstances, then, aqueous vapour would be forced by these
conditions to give up a very large portion of its energy to the other
atmospheric constituents. The latter would thus be still further
expanded against gravity; the aqueous vapour itself would suffer a loss
of energy equivalent to the work transmitted from it. It is therefore
clear that in a composite atmosphere formed in the manner described, any
gas possessed of energy properties superior to the other constituents is
forced of necessity to transmit energy to these constituents. This
phenomenon is merely a consequence of the natural disposition of the
atmospheric gaseous substances towards a condition of equilibrium with
more or less uniform temperature gradation. The greater the inherent
energy qualities of any one constituent relative to the others, the
greater will be the quantity of energy transmitted from it in this way.
38. _Description of Terrestrial Case_
Bearing in mind the general considerations which have been advanced
above with respect to planetary atmospheres, it is now possible to place
before the reader a general descriptive outline of the circumstances and
operation of an atmospheric machine in actual working. The machine to be
described is that associated with the earth.
In the earth is found an example of a planetary body of spheroidal form
pursuing a clearly defined orbit in space and at the same time rotating
with absolutely uniform velocity about a central axis within itself. The
structural details of its surface and the general distribution of
material thereon will be more or less familiar to the reader, and it is
not, therefore, proposed to dwell on these features here. Attention may
be drawn, however, to the fact that a very large proportion of the
surface of the earth is a liquid surface. Of all the material familiar
to us from terrestrial experience there is none which enters into the
composition of the earth's crust in so large a proportion as water. In
the free state, or in combination with other material, water is found
everywhere. In the liquid condition it is widely distributed. Although
the liquid or sea surface of the planet extends over a large part of
the whole, the real water surface, that is, the _wetted_ surface, if we
except perhaps a few desert regions, may be said to comprise practically
the entire surface area of the planet. And water is found not only on
the earth's crust but throughout the gaseous atmospheric envelope. The
researches of modern chemistry have revealed the fact that the
atmosphere by which the earth is surrounded is not only a mixture of
gases, but an exceedingly complex mixture. The relative proportions of
the rarer gases present are, however, exceedingly small, and their
properties correspondingly obscure. Taken broadly, the atmosphere may be
said to be composed of air and water (in the form of aqueous vapour) in
varying proportion. The former constituent exists as a mixture of oxygen
and nitrogen gases of fairly constant proportion over the entire surface
of the globe. The latter is present in varying amount at different
points according to local conditions. This mixture of gaseous
substances, forming the terrestrial atmosphere, resides on the surface
of the planet and forms, as already described (§ 34), a column or
envelope completely surrounding it; the quantity of gaseous material
thus heaped up on the planetary surface is such that it exerts almost
uniformly over that surface the ordinary atmospheric pressure of
approximately 14·7 lb. per sq. inch. It is advisable, also, at this
stage to point out and emphasise the fact that the planetary atmosphere
must be regarded as essentially a material portion of the planet itself.
Although the atmosphere forms a movable shell or envelope, and is
composed of purely gaseous material, it will still partake of the same
complete orbital and rotatory axial motion as the solid core, and will
also be subjected to the same external and internal influences of
gravitation. Such are the general planetary conditions. Let us now turn
to the particular phenomena of axial revolution.
In virtue of the unvarying rotatory movement of the planetary mass in
the lines of the various incepting fields of its primary the sun,
transformations of the axial or mechanical energy of the planet will be
in continuous operation (§§ 17-19). Although the gaseous atmospheric
envelope of the planet partakes of this general rotatory motion under
the influence of the incepting fields, the latter have apparently no
action upon it. The sun's influence penetrates, as it were, the
atmospheric veil, and operating on the solid and liquid material below,
provokes the numerous and varied transformations of planetary energy
which constitute planetary phenomena. At the equatorial band, where the
velocity or axial energy properties of the surface material is greatest,
these effects of transformation will naturally be most pronounced. In
the polar regions of low velocity they will be less evident. One of the
most important of these transforming effects may be termed the heating
action of the primary on the planet--a process which takes place in
greater or less degree over the entire planetary surface, and which is
the result of the direct transformation of axial energy into the form of
heat (§ 18). In virtue of this heat transformation, or heating effect of
the sun, the temperature of material on the earth's surface is
maintained in varying values from regions of high velocity to those of
low--from equator to poles--according to latitude or according to the
displacement of that material, in rotation, from the central axis. Owing
to the irregular distribution of matter on the earth's surface, and
other causes to be referred to later, this variation in temperature is
not necessarily uniform with the latitude. This heating effect of the
sun on the earth will provoke on the terrestrial surface all the
familiar secondary processes (§ 9) associated with the heating of
material. Most of these processes, in combination with the operations of
radiation and conduction, will lead either directly or indirectly to the
communication of energy to the atmospheric masses (§ 27).
Closely associated with the heat transformation, there is also in
operation another energy process of great importance. This process is
one of evaporative transformation. Reference has already been made to
the vast extent of the liquid or wetted surface of the earth. This
surface forms the seat of evaporation, and the action of the sun's
incepting influence on the liquid of this surface is to induce a direct
transformation of the earth's axial or mechanical energy into the
elastic energy of a gas, or in other words into the form of work energy.
By this process, therefore, water is converted into aqueous vapour.
Immediately the substance attains the latter or gaseous state it becomes
unaffected by, or transparent to, the incepting influence of the sun (§
18). And the action of evaporation is not restricted in locality to the
earth's surface only. It may proceed throughout the atmosphere. Wherever
condensation of aqueous vapour takes place and water particles are
thereby suspended in the atmosphere, these particles are immediately
susceptible to the sun's incepting field, and if the conditions are
otherwise favourable, re-evaporation will at once ensue. Like the
ordinary heating action also, that of transformation will take place
with greater intensity in equatorial than in polar regions. These two
planetary secondary processes, of heating and evaporation, are of vital
importance to the working of the atmospheric machine. But, as already
pointed out elsewhere (§§ 10, 32), every secondary operation is in some
fashion linked to that machine. Other incepting influences, such as
light, are in action on the planet, and produce transformations peculiar
to themselves. These, in the meantime, will not be considered except to
point out that in every case the energy active in them is the axial
energy of the earth itself operating under the direct incepting
influence of the sun. The general conditions of planetary revolution and
transformation are thus intimately associated with the operation of the
atmospheric machine. In this machine is embodied a huge energy process,
in the working of which the axial energy of the earth passes through a
series of energy changes which, in combination, form a complete cyclical
operation. In their perhaps most natural sequence these processes are as
follows:--
1. The direct transformation of terrestrial axial energy into the work
energy of aqueous vapour.
2. The direct transmission of the work energy of aqueous vapour to the
general atmospheric masses, and the consequent elevation of these masses
from the earth's surface against gravity.
3. The descent of the atmospheric air masses in their movement towards
regions of low velocity, and the return in the descent of the initially
transformed axial energy to its original form.
The first of these processes is carried out through the medium of the
aqueous material of the earth. It is simply the evaporative
transformation referred to above. By that evaporative process a portion
of the energy of motion or axial energy of the earth is directly
communicated or passed into the aqueous material. Its form, in that
material, is that of work energy, or the elastic energy of aqueous
vapour, and, as already pointed out, this process of evaporative
transformation reaches its greatest intensity in equatorial or regions
of highest velocity. In these regions also, in virtue of the working of
the heat process already referred to above, the temperature conditions
are eminently favourable to the presence of large quantities of aqueous
vapour. The tension or pressure of the vapour, which really depends on
the quantity of gaseous material present, is directly proportional to
the temperature, so that in equatorial regions not only is the general
action of transformation in the aqueous material most intense, but the
surrounding temperature conditions in these regions are such as to
favour the continuous presence of large quantities of the aqueous vapour
which is the direct product of the action of transformation. The
equatorial regions of the earth, or the regions of high velocity, are
thus eminently adapted, by the natural conditions, to be the seat of the
most powerful transformations of axial energy. As already pointed out,
however, these same transformations take place over the entire
terrestrial surface in varying degree and intensity according to the
locality and the temperature or other conditions which may prevail. Now
this transformation of axial energy which takes place through the medium
of the evaporative process is a continuous operation. The energy
involved, which passes into the aqueous vapour, augmented by the energy
of other secondary processes (§ 32), is the energy which is applied to
the atmospheric air masses in the second stage of the working of the
atmospheric machine. Before proceeding to the description of this stage,
however, it is absolutely necessary to point out certain very important
facts with reference to the energy condition of the atmospheric
constituents in the peculiar circumstances of their normal working.
39. _Relative Physical Conditions of Atmospheric Constituents_
It will be evident that no matter where the evaporation of the aqueous
material takes place, it must be carried out at the temperature
corresponding to that location, and since the aqueous vapour itself is
not superheated in any way (being transparent to the sun's influence),
the axial energy transformed and the work energy stored in the material
per unit mass, will be simply equivalent to the latent heat of aqueous
vapour under the temperature conditions which prevail. In virtue of the
relatively high value of this latent heat under ordinary conditions, the
gas may be regarded as comparatively a very highly energised substance.
It is clear, however, that since the gas is working at its precise
temperature of evaporation, the maximum amount of energy which it can
possibly yield up at that temperature is simply this latent heat of
evaporation, and if this energy be by any means withdrawn, either in
whole or in part, then condensation corresponding to the energy
withdrawal will at once ensue. The condition of the aqueous vapour is in
fact that of a true vapour, or of a gaseous substance operating exactly
at its evaporation temperature, and unable to sustain even the slightest
abstraction of energy without an equivalent condensation. No matter in
what manner the abstraction is carried out, whether by the direct
transmission of heat from the substance or by the expansion of the gas
against gravity, the result is the same; part of the gaseous material
returns to the liquid form.
In the case of the more stable or permanent constituents of the
atmosphere, namely oxygen and nitrogen, their physical conditions are
entirely different from that of the aqueous vapour. Examination of the
Table of Properties (p. 133) shows that the evaporation temperatures of
these two substances under ordinary conditions of atmospheric pressure
are as low as -296° F. and -320° F. respectively. At an ordinary
atmospheric temperature of say 50° F. these two gases are therefore so
far above their evaporation temperature that they are in the condition
of what might be termed true gaseous substances. Although only at a
temperature of 50° F., they may be truly described as highly superheated
gases, and it is evident that they may be readily cooled from 50° F.
through wide ranges of temperature, without any danger of their
condensation or liquefaction. Oxygen and nitrogen gases thus present in
their physical condition and qualities a strong contrast to aqueous
vapour, and it is this difference in properties, particularly the
difference in evaporation temperatures, which is of vital importance in
the working of the atmospheric machine. The two gases oxygen and
nitrogen are, however, so closely alike in their general energy
properties that, in the meantime, the atmospheric mixture of the two can
be conveniently assumed to act simply as one gas--atmospheric air.
From these considerations of the ordinary atmospheric physical
properties of air and aqueous vapour it may be readily seen how each is
eminently adapted to its function in the atmospheric process. The
peculiar duty of the aqueous vapour is the absorption and transmission
of energy. Its relatively enormous capacity for energy, the high value
of its latent heat at all ordinary atmospheric temperatures, and the
fact that it must always operate precisely at its evaporation
temperature makes it admirably suited for both functions. Thus, in
virtue of its peculiar physical properties, it forms an admirable agent
for the storage of energy and for its transmission to the surrounding
air masses. The low temperature of evaporation of these air masses
ensures their permanency in the gaseous state. They are thus perfectly
adapted for expansive and other movements, for the conversion of their
energy against gravity into energy of position, or for any other
reactions involving temperature change without condensation.
40. _Transmission of Energy from Aqueous Vapour to Air Masses_
The working of the second or transmission stage of the atmospheric
machine involves certain energy operations in which gravitation is the
incepting factor or agency. Let it be assumed that a mass of aqueous
vapour liberated at its surface of evaporation by the transformation of
axial energy, expands upwards against the gravitative attraction of the
earth (§§ 34, 38). As the gaseous particles ascend and thus gain energy
of position, they do work against gravity. This work is done at the
expense of their latent energy. Since the aqueous material is always
working precisely at its evaporation temperature, this gain in energy of
position and consequent loss of latent energy will be accompanied by an
equivalent condensation and conversion of the rising vapour into the
liquid form. This condensation will thus be the direct evidence and
measure of work done by the aqueous material against the gravitational
forces, and the energy expended or worked down in this way may now,
accordingly, be regarded as stored in the condensed material or liquid
particles in virtue of their new and exalted position above the earth's
surface. It is this energy which is finally transmitted to the
atmospheric air masses. The transmission process is carried out in the
downward movement of the liquid particles. The latter, in their exalted
positions, are at a low temperature corresponding to that position--that
is, corresponding to the work done--and provided no energy were
transmitted from them to the surrounding air masses, their temperature
would gradually rise during the descent by the transformation of this
energy of position. In fact the phenomena of descent, supposing no
transmission of energy from the aqueous material, would simply be the
reverse of the phenomena of ascent. Since, however, the energy of
position which the liquid particles possess is transmitted from them to
the atmospheric masses, then it follows that this natural increase in
their temperature would not occur in the descent. A new order of
phenomena would now appear. Since the evaporative process is a
continuous one, the liquid particles in their downward movement must be
in intimate contact with rising gaseous material, and these liquid
particles will, accordingly, at each stage of the descent, absorb from
this rising material the whole energy necessary to raise their
temperature to the values corresponding to their decreasing elevation.
In virtue of this absorption of energy then, from the rising material,
these liquid particles are enabled to reach the level of evaporation at
the precise temperature of that level.
Now, considering the process as a whole, it will be readily seen that
for any given mass of aqueous material thus elevated from and returned
to a surface of evaporation, there must be a definite expenditure of
energy (axial energy) at that surface. Since the material always regains
the surface at the precise temperature of evaporation, this expenditure
is obviously, in total, equal to the latent heat of aqueous vapour at
the surface temperature. It may be divided into two parts. One portion
of the axial energy--the transmitted portion--is utilised in the
elevation of the material against gravity; the remainder is expended, as
explained above, in the heating of the returning material. The whole
operation takes place between two precise temperatures, a higher
temperature, which is that of the surface of evaporation, and a lower
temperature, corresponding to the work done, and so related to the
higher that the whole of the energy expended by the working aqueous
substance--in heating the returning material and in transmitted work--is
exactly equivalent to the latent heat of aqueous vapour at the high or
surface temperature. But, as will be demonstrated later, the whole
energy transmitted from the aqueous material to the air masses is
finally returned in its entirety as axial energy, and is thus once more
made available in the evaporative transformation process. The energy
expended in raising the temperature of the working material returning to
the surface of evaporation is obviously returned with that material.
Both portions of the original expenditure are thus returned to the
source in different ways. The whole operation is, in fact, completely
cyclical in nature; we are in reality describing "Nature's Perfect
Engine," which is completely reversible and which has the highest
possible efficiency.[1] Although the higher temperature at the
evaporation surface may vary with different locations of that surface,
in every case the lower temperature is so related to it as to make the
total expenditure precisely equal to the latent heat at that evaporation
temperature.[2] It must be borne in mind also, that all the condensed
material in the upper strata of the atmosphere must not of necessity
return to the planetary liquid surface. On the contrary, immediately
condensation of the aqueous vapour takes place and the material leaves
the gaseous state, no matter where that material is situated, it is once
more susceptible to the incepting influences of the sun. Re-evaporation
may thus readily take place even at high altitudes, and complete
cyclical operations may be carried out there. These operations will,
however, be carried out in every case between precise temperature limits
as explained above.
[1] The conception of "Nature's Perfect Engine" was originally
arrived at by the author from consideration of the phenomena of the
steam-engine. The following extract from the "Review" of his work
(1895) illustrates the various stages which finally lead to that
conclusion:--
"My first steps in the right direction came about thus. I had always
been working with a cylinder and piston, and could make no progress,
till at length it struck me to make my cylinder high enough to do
without a piston--that is, to leave the steam to itself and observe
its behaviour when left to work against gravity. The first thing I
had to settle was the height of my cylinder. And I found, by
calculation from Regnault's experiments that it would require to be
very high, and that the exact height would depend on the temperature
of the water in the boiler which was the bottom of this ideal
cylinder. Now, at any ordinary temperature the height was so great
that it was impossible to get known material to support its own
weight, and I did not wish to use a hypothetical substance in the
construction of this engine. Finally, the only course left me was to
abolish the cylinder as I had done the piston. I then discovered
that the engine I had been trying to evolve--the perfect engine--was
not the ideal thing I had been groping after but an actual reality,
in full working order, its operations taking place every day before
my eyes.
"Every natural phenomenon fitted in exactly; it had its function to
perform, and the performance of its function constituted the
phenomenon. Let me trace the analogy in a few of its details. The
sea corresponds to the boiler; its cylinder surrounds the earth; it
has for its fuel the axial energy of the earth; it has no condenser
because it has no exhaust; the work it performs is all expended in
producing the fuel. Every operation in the cycle is but an energy
transformation, and these various transformations constitute the
visible life of the world."
[2] For definite numerical examples see the author's _Terrestrial
Energy_ (Chap. 1.).
It will be evident, from a general consideration of this process of
transmission of energy from the aqueous vapour, that relatively large
quantities of that vapour are not required in the atmosphere for the
working of the gaseous machine. The peculiar property of ready
condensation of the aqueous vapour makes the evaporative process a
continuous one, and the highly energised aqueous material, although only
present in comparatively small amount, contributes a continuous flow of
energy, and is thus able to steadily convey a very large quantity to
the atmospheric masses. For the same reason, the greater part of the
energy transmission from the aqueous vapour to the air will take place
at comparatively low altitudes and between reasonably high temperatures.
The working of any evaporative cycle may also be spread over very large
terrestrial areas by the free movement of the acting material. Aqueous
vapour rising in equatorial regions may finally return to the earth in
the form of ice-crystals at the poles. In every complete cycle, however,
the total expenditure per unit mass of material initially evaporated is
always the latent heat at the higher or evaporation temperature; in the
final or return stages of the cycle, any energy not transmitted to the
air masses is devoted to the heating of returning aqueous material.
Referring again to the transmitted energy, and speaking in the broadest
fashion, the function of the aqueous vapour in the atmosphere may be
likened to that of the steam in the cylinder of a steam-engine. In both
cases the aqueous material works in a definite machine for energy
transmission. In the case of the steam-engine work energy is transmitted
(§ 31) from the steam through the medium of the moving piston and
rotating shaft, and thence may be further diverted to useful purposes.
In the planetary atmospheric machine the work energy of aqueous vapour
is likewise transmitted by the agency of the moving air masses, not to
any external agent, but back once more to its original source, which is
the planetary axial energy. In neither case are we able to explain the
precise nature of the transmission process in its ultimate details. We
cannot say _how_ the steam transmits its work energy by the moving
piston, nor yet by what agency the elevated particles of aqueous
material transmit their energy to the air masses. Our knowledge is
confined entirely to the phenomena, and, fortunately, these are in some
degree accessible. Nature presents direct evidence that such
transmissions actually take place. This evidence is to be found, in both
cases, in the condensation of the aqueous material which sustains the
loss of its work energy. In the engine cylinder condensation takes place
due to work being transmitted from the steam; in the atmosphere the
visible phenomena of condensation are likewise the ever present evidence
of the transmission of work energy from the aqueous vapour to the air
masses. In virtue of this accession of energy these masses will,
accordingly, be expanded upwards against the gravitational attractive
forces. This upward movement, being made entirely at the expense of
energy communicated from the aqueous vapour, is not accompanied by the
normal fall of temperature due to the expansion of the air. Planetary
axial energy, originally absorbed by the aqueous vapour, in the work
form, has been transferred to the air masses in the same form, and is
now, after the expansive movement, resident in these masses in the form
of energy of position. It is the function of the atmospheric machine in
its final stage to return this energy in the original axial form.
41. _Terrestrial Energy Return_
Let it be assumed that an atmospheric mass has been raised, by the
transmission of work energy, to a high altitude in the equatorial
regions of the earth. The assumption of locality is made merely for
illustrative purposes; it will be evident to the reader that the
transmission of work energy to the atmospheric masses and their
consequent elevation will be continuously proceeding, more or less, over
the whole planetary surface. To replace the gaseous material thus
raised, a corresponding mass of air will move at a lower level, towards
the equator from the more temperate zones adjoining. A circulatory
motion will thus be set up in the atmosphere. In the upper regions the
elevated and energised air masses move towards the poles; at lower
levels the replacing masses move towards the equator, and in their
passage may be operated on by the aqueous vapour which they encounter,
energised, and raised to higher levels. The movement will be continuous.
In their transference from equatorial towards polar regions, the
atmospheric masses are leaving the surfaces or regions of high linear
velocity for those of low, and must in consequence lose or return in
the passage a portion of that natural energy of motion which they
possess in virtue of their high linear velocity at the equator. But on
the other hand, the replacing air masses, which are travelling in the
opposite direction from poles to equator, must gain or absorb a
corresponding amount of energy. The one operation thus balances the
other, and the planetary equilibrium is in no way disturbed. But the
atmospheric masses which are moving from the equator in the polar
direction will possess, in addition, that energy of position which has
been communicated to them through the medium of the aqueous vapour and
by the working of the second stage of the atmospheric machine. These
masses, in the circulatory polar movements, move downwards towards the
planetary surface. In this downward motion (as in the downward motion of
a pendulum mass vibrating under the action of gravitation) the energy of
position of the air mass is converted once more into energy of
motion--that is, into its original form of axial energy of rotation. In
equatorial regions the really important energy property of the
atmospheric mass was indicated by its elevation or its energy of
position. In the descent this energy is thus entirely transformed, and
reverts once more to its original form of energy of rotation.
The continual transformation of axial energy by the aqueous vapour, and
the conversion of that energy by the upward movement of the air masses
into energy of position, naturally tends to produce a retardative effect
on the motion of revolution of the earth. But this retardative effect is
in turn completely neutralised or balanced by the corresponding
accelerative effect due to the equally continuous return as the energy
of the air masses reverts in the continuous polar movement to its
original axial form. Speaking generally, the equatorial regions, or the
regions of high velocity, are the location of the most powerful
transformation or abstraction of axial energy by the aqueous vapour.
Conversely, the polar or regions of low velocity are the location of the
greatest return of energy by the air. As no energy return is possible
unless by the transference of the atmospheric material from regions of
high to regions of low velocity, the configuration of the planet in
rotation must conform to this condition. The spheroidal form of the
earth is thus exquisitely adapted to the working of the atmospheric
machine. As already pointed out, however, the energising and raising of
atmospheric masses is by no means confined to equatorial regions, but
takes place more or less over the whole planetary surface. The same
applies to the energy return. The complete cycle may be carried out in
temperate zones; gaseous masses, also, leaving equatorial regions at
high altitudes do not necessarily reach the polar regions, but may
attain their lowest levels at intermediate points. Neither do such
masses necessarily proceed to the regions of low velocity by purely
linear paths. On the contrary, they may and do move both towards the
poles and downwards by circuitous and even vortical paths. In fact, as
will be readily apparent, their precise path is of absolutely no moment
in the consideration of energy return.
It might naturally be expected that such movements of the atmospheric
air masses as have been described above would give rise to great
atmospheric disturbance over the earth's surface, and that the transfer
of gaseous material from pole to equator and vice versa would be
productive of violent storms of wind. Such storms, however, are
phenomena of somewhat rare occurrence; the atmosphere, on the whole,
appears to be in a state of comparative tranquillity. This serenity of
the atmosphere is, however, confined to the lower strata, and may be
ascribed to an inherent stability possessed by the air mass as a whole
in virtue of the accession of energy to it at high levels. As already
explained, the transfer of energy from the vapour to the air masses is
accomplished at comparatively low altitudes, and when this reaction is
taking place the whole tendency of the energised material is to move
upwards. In so moving it tends to leave behind it the condensed aqueous
vapour, and would, therefore, rise to the higher altitudes in a
comparatively dry condition. This dryness is accentuated by the further
loss of aqueous vapour by condensation as the air moves toward regions
of low velocity. That air which actually attains to the poles will be
practically dry, and having also returned, in its entirety, the surplus
energy obtained from the aqueous vapour, it will be in this region
practically in the condition of statical equilibrium of a gas against
gravity (§ 34). But the general state of the atmosphere in other regions
where a transference of energy from the aqueous vapour has taken or is
taking place is very different from this condition of natural statical
equilibrium which is approached at the poles. In the lower strata of the
atmosphere the condition in some cases may approximate to the latter,
but in the upper strata it is possessed of energy qualities quite
abnormal to statical equilibrium. Its condition is rather one of the
nature of stable equilibrium. It is in a condition similar to that of a
liquid heated in its upper layers; there is absolutely no tendency to a
direct or vertical downward circulation. In statical equilibrium, any
downward movement of an air mass would simply be accompanied by the
natural rise in temperature corresponding to the transformation of its
energy of position, but in this condition of stable equilibrium any
motion downwards must involve, not only this natural temperature rise,
but also a return, either in whole or in part, of the energy absorbed
from the aqueous vapour. The natural conditions are therefore against
any direct vertical return. These conditions, however, favour in every
respect the circulatory motion of the highly energised upper air masses
towards regions of low velocity. All circumstances combine, in fact, to
confine the more powerfully energised and highly mobile air masses to
high altitudes. In the lower atmosphere, owing to the continuous action
of the aqueous vapour on the air masses moving from regions of low to
those of high velocity, the circulation tends largely to be a vertical
one, so that this locality is on the whole preserved in comparative
tranquillity. It may happen, however, that owing to changes in the
distribution of aqueous vapour, or other causes, this natural stability
of the atmosphere may be disturbed over certain regions of the earth's
surface. The circumstances will then favour a direct or more or less
vertical return of the energy of the air masses in the neighbourhood of
these regions. This return will then take the form of violent storms of
wind, usually of a cyclonic nature, and affording direct evidence of the
tendency of the air masses to pursue vortical paths in their movement
towards lower levels.
Under normal conditions, however, the operation of the atmospheric
machine is smooth and continuous. The earth's axial energy, under the
sun's incepting influence, steadily flows at all parts of the earth's
surface through the aqueous vapour into the atmospheric masses, and the
latter, rising from the terrestrial surface, with a motion somewhat like
that of a column of smoke, spread out and speed towards regions of lower
velocity, and travelling by devious and lengthened paths towards the
surface, steadily return the abstracted energy in its original form.
Every operation is exactly balanced; energy expenditure and energy
return are complementary; the terrestrial atmospheric machine as a whole
works without jar or discontinuity, and the earth's motion of rotation
is maintained with absolute uniformity.
Like every other energy machine, the atmospheric machine has
clearly-defined energy limits. The total quantity of energy in operation
is strictly limited by the mass of the acting materials. It is well,
also, to note the purely mechanical nature of the machine. Every
operation is in reality the operation of mechanical energy, and involves
the movement of matter in some way or other relative to the earth's
surface and under the incepting action of the earth's gravitation (§§
16, 20). The moving gaseous masses have as real an existence as masses
of lead or other solid material, and require as real an expenditure of
energy to move them relative to the terrestrial surface (§ 18). This
aspect of the planetary machine will be more fully treated later.
Throughout this description we have constantly assumed the atmospheric
mixture of oxygen and nitrogen to act as one gas, and at ordinary
temperatures the respective energy properties of the two substances (§
35) make this assumption justifiable. Both gases are then working far
above their respective evaporation temperatures. But, in the higher
regions of the atmosphere, where very low temperatures prevail, a point
or altitude will be reached where the temperature corresponds to the
evaporation or condensation temperature of one of the gases. Since
oxygen appears to have the highest temperature of evaporation (see Table
of Properties, p. 133), it would naturally be the first to condense in
the ascent. But immediately condensation takes place, the material will
become susceptible to the incepting influence of the sun, and working as
it does at its temperature of evaporation it will convey its energy to
the surrounding nitrogen in precisely the same fashion as the aqueous
vapour conveys the energy to the aerial mixture in the lower atmosphere.
The whole action is made possible simply by the difference existing in
the respective evaporation temperatures of the two gases. It will give
rise to another cyclical atmospheric energy process exactly as already
described for lower altitudes. Axial energy of rotation will be
communicated to the nitrogen by the working material, which is now the
oxygen, and by the movement of the nitrogen masses towards regions of
low velocity, this transmitted energy will be finally returned to its
original axial form.
It has been already explained (§§ 10, 32) how all terrestrial energy
processes, also, great or small, are sooner or later linked to the
general atmospheric machine. The latter, therefore, presents in every
phase of its working completely closed energy circuits. In no aspect of
its operation can we find any evidence of, or indeed any necessity for,
an energy transmission either to or from any external body or agent such
as the sun. Every phenomenon of Nature is, in fact, a direct denial of
such transmission.
The student of terrestrial phenomena will readily find continuous and
ample evidence in Nature of the working of the atmospheric machine. In
the rising vapour and the falling rain he will recognise the visible
signs of the operation of that great secondary process of transmission
by which the inherent axial energy of the earth is communicated to the
air masses. The movements of bodies, animate and inanimate, on the
earth's surface, the phenomena of growth and decay, and in fact almost
every experience of everyday life, will reveal to him the persistent
tendency of the energy of secondary processes to revert to the
atmospheric machine. And in the winds that traverse the face of the
globe he will also witness the mechanism of that energy return which
completes the atmospheric cyclical process. It may be pointed out here
also that the terrestrial cyclical energy processes are not necessarily
all embodied in the atmosphere. The author has reason to believe, and
phenomenal evidence is not awanting to show, that the circulatory
motions of the atmosphere are in some degree reproduced in the sea. The
reader will readily perceive that as regards stability the water
composing the sea is in precisely the same condition as the atmosphere,
namely, that of a liquid heated in its upper strata, and any circulatory
motion of the water must therefore be accompanied by corresponding
transformations of energy. That such a circulatory motion takes place is
undoubted, and in the moving mass of sea-water we have therefore a
perfectly reversible energy machine of the same general nature as the
atmospheric machine, but working at a very much slower rate. It is not
beyond the limits of legitimate scientific deduction to trace also the
working of a similar machine in the solid material of the earth. The
latter is, after all, but an agglomeration of loose material bound by
the force of gravitation into coherent form. By the action of various
erosive agencies a movement of solid material is continually taking
place over the earth's surface. The material thus transported, it may
be, from mountain chains, and deposited on the sea-bed, causes a
disturbance of that gravitational equilibrium which defines the exact
form of the earth. The forces tending to maintain this equilibrium are
so enormous compared with the cohesive forces of the material forming
the earth that readjustment continuously takes place, as evidenced by
the tremors observed in the earth's crust. Where the structure of the
latter is of such a nature as to offer great resistance to the
gravitational forces, the readjustment may take the form of an
earthquake. Geological evidence, as a whole, strongly points to a
continuous kneading and flow of terrestrial material. The structure of
igneous rocks, also, is exactly that which would be produced from
alluvial deposits subjected during these cyclical movements to the
enormous pressure and consequent heating caused by superimposed
material. The occurrence of coal in polar regions, and of glacial
residue in the tropics, may be regarded as further corroborative
evidence. From this point of view also, it becomes unnecessary to
postulate a genesis for the earth, as every known geological formation
is shown to be capable of production under present conditions in Nature,
and in fact to be in actual process of production at all times.
42. _Experimental Analogy and Demonstration of the General Mechanism of
Energy Transformation and Return in the Atmospheric Cycle_
In the preceding articles, the atmospheric machine has been regarded
more or less from the purely physical point of view. The purpose of this
demonstration is now to place before the reader what might be termed
the mechanical aspects of the machine; to give an outline, using simple
experimental analogies, of its nature and operation when considered
purely and simply as a mechanism for the transformation and return of
mechanical energy.
Familiar apparatus is used in illustration. In all cases, it is merely
some adaptation of the simple pendulum (§ 21). Its minute structural
details are really of slight importance in the discussion, and have
accordingly been ignored, but the apparatus generally, and the energy
operations embodied therein, are so familiar to physicists and engineers
that the experimental results illustrated can be readily verified by
everyday experience. It is of great importance, also, in considering
these results, to bear in mind the principles already enunciated (§§ 13,
20) with reference to the operation of mechanical energy on the various
forms of matter. The general working conditions of energy systems with
respect to energy limits, stability, and reversibility (§ 23) should
also be kept in view.
As an introductory step we shall review first a simple system of
rotating pendulums. Two simple pendulums CM and DM{1} (Fig. 9) are
mounted by means of a circular collar CD upon a vertical spindle AB,
which is supported at A and B and free to rotate. When the central
spindle AB is at rest the pendulums hang vertically; when energy is
applied to the system, and AB is thereby caused to rotate, the
spherical masses M and M{1} will rise by circular paths about C and D.
This upward movement, considered apart from the centrifugal influence
producing it, corresponds in itself to the upward movement of the simple
pendulum (§ 21) against gravity. It is representative of a definite
transformation, namely, the transformation of the work energy originally
applied to the system and manifested in its rotary motion, into energy
of position. The movements of the rotating pendulums will also be
accompanied by other energy operations associated with bearing friction
and windage (§§ 23, 29), but these operations being part of a separate
and complete cyclical energy process (§ 32), they will in this case be
neglected.
[Illustration: FIG. 9]
It will be readily seen, however, that the working of this rotating
pendulum machine, when considered as a whole, is of a nature somewhat
different from that of the simple pendulum machine in that the energy of
position of the former (as measured by the vertical displacement of M
and M{1} in rotation) and its energy of rotation must increase
concurrently, and also in that the absolute maximum value of this energy
of position will be attained when the pendulum masses reach merely the
horizontal level HL in rotation. The machines are alike, however, in
this respect, that the transformation of energy of motion into energy of
position is in each case a completely reversible process. In the working
of the rotating pendulums the limiting amount of energy which can
operate in this reversible process is dependent on and rigidly defined
by the maximum length of the pendulum arms; the longer the arms, the
greater is the possible height through which the masses at their
extremities must rise to attain the horizontal position in rotation. It
will be clear also that it is not possible for the whole energy of the
rotating system to work in the reversible process as in the case of the
simple pendulum. As the pendulum masses rise, the ratio of the limiting
energy for reversibility to the total energy of the system becomes in
fact smaller and smaller, until at the horizontal or position of maximum
energy it reaches a minimum value. This is merely an aspect of the
experimental fact that, as the pendulum masses approach the ultimate
horizontal position, a much greater increment of energy to the system is
necessary for their elevation through a given vertical distance than at
the lower levels. A larger proportion of the applied energy is, in fact,
stored in the material of the system in the form of energy of strain or
distortion.
The two points which this system is designed to illustrate, and which
it is desirable to emphasise, are thus as follows. Firstly, as the whole
system rotates, the movement of the pendulum masses M and M{1} from the
lower to the higher levels, or from the regions of low to those of
higher velocity, is productive of a transformation of the rotatory
energy of the system into energy of position--a transformation of the
same nature as in the case of the simple pendulum system. Neglecting the
minor transformations (§§ 24, 29), this energy process is a reversible
one, and consequently, the return of the masses from the higher to the
lower positions will be accompanied by the complete return of the
transformed energy in its original form of energy of rotation. Secondly,
the maximum amount of energy which can work in this reversible process
is always less than the total energy of the system. The latter,
therefore, conforms to the general condition of stability (§ 25).
But this arrangement of rotating pendulums may be extended so as to
include other features. To eliminate or in a manner replace the
influence of gravitation, and to preserve the energy of position of the
system--relative to the earth's surface--at a constant value, the
pendulum arms may be assumed to be duplicated or extended to the points
K and R (Fig. 10) respectively, where pendulum masses equal to M and
M{1} are attached.
The arms MK and M{1}R are thus continuous. Each arm is assumed to be
pivoted at its middle point about a horizontal axis through N, and as
the lower masses M and M{1} rise in the course of the rotatory movement
about AB the upper masses K and R will fall by corresponding amounts.
The total energy of position of the system--referred to the earth's
surface--thus remains constant whatever may be the position of the
masses in the system. The restraining influence on the movement of the
masses, formerly exercised by gravitation, is now furnished by means of
a central spring F. A collar CD, connected as shown to the pendulum
arms, slides on the spindle AB and compresses this spring as the masses
move towards the horizontal level HL. As the masses return towards A and
B the spring is released.
[Illustration: FIG. 10]
If energy be applied to the system, so that it is caused to rotate about
the central axis AB, the pendulum masses will tend to move outwards from
that axis. Their movement may be said to be carried out over the surface
of an imaginary sphere with centre on AB at N. The motion of the masses,
as the velocity of rotation increases, is from the region of lower
peripheral velocity, in the vicinity of the axis AB, to the regions of
higher velocity, in the neighbourhood of H and L. This outward movement
from the central axis towards H and L is representative of a
transformation of energy of an exactly similar nature to that described
above in the simple case. Part of the original energy of rotation of the
system is now stored in the pendulum masses in virtue of their new
position of displacement. But in this case, the movement is made, not
against gravity, but against the central spring F. The energy, then,
which in the former case might be said to be stored against gravitation
(acting as an invisible spring) is in this case stored in the form of
energy of strain or cohesion (§ 15) in the central spring, which thus as
it were takes the place of gravitation in the system. As in the previous
case also, the operation is a reversible energy process. If the pendulum
masses move in the opposite direction from the regions of higher
velocity to those of lower velocity, the energy stored in the spring
will be returned to the system in its original form of energy of motion.
A vibratory motion of the pendulums to and from the central axis would
thus be productive of an alternate storage and return of energy. It is
obvious also, that due to the action of centrifugal force, the pendulum
masses would tend to move radially outwards on the arms as they move
towards the regions of highest velocity. Let this radial movement be
carried out against the action of four radial springs S{1}, S{2},
S{3}, S{4}, as shown (Fig. 11). In virtue of the radial movement of
the masses, these springs will be compressed and energy stored in them
in the form of energy of strain or cohesion (§ 15). The radial movement
implies also that the masses will be elevated from the surface of the
imaginary sphere over which they are assumed to move. The elevation from
this surface will be greatest in the regions of high velocity in the
neighbourhood of H and L, and least at A and B. As the masses move,
therefore, from H and L towards the axis AB, they will also move inwards
on the pendulum arms, relieving the springs, so that the energy stored
in them is free to be returned to the system in its original form of
energy of rotation. Every movement of the masses from the central axis
outwards against the springs is thus made at the expense of the original
energy of motion, and every movement inwards provokes a corresponding
return of that energy to the system. Every movement also against the
springs forms part of a reversible operation. The sum total of the
energy which works in these reversible operations is always less than
the complete energy of the rotatory system, and the latter is always
stable (§ 25), with respect to its energy properties. Let it now be
assumed that the complete system as described is possessed of a precise
and limited amount of energy of rotation, and that with the pendulum
masses in an intermediate position as shown (Fig. 11) it is rotating
with uniform angular velocity. The condition of the rotatory system
might now be described as that of equilibrium. A definite amount of its
original rotatory energy is now stored in the central spring and also in
the radial springs. If now, without alteration in the intrinsic rotatory
energy of the system, the pendulum masses were to execute a vibratory or
pendulum motion about the position of equilibrium so that they move
alternately to and from the central axis, then as they move inwards
towards that axis the energy stored in the springs would be returned to
the system in the original form of energy of rotation. This inward
motion would, accordingly, produce acceleration. But, in the outward
movement from the position of equilibrium, retardation would ensue on
account of energy of motion being withdrawn from the system and stored
in the springs.
[Illustration: FIG. 11]
Under the given conditions, then, any vibratory motion of the pendulum
masses to and from the central axis would be accompanied by alternate
retardation and acceleration of the moving system. The storage of energy
in the springs (central and radial) produces retardation, the
restoration of this energy gives rise to a corresponding acceleration.
The angular velocity of the system would rise and fall accordingly.
These are the natural conditions of working of the system. As already
pointed out, the motion of the pendulum masses may be regarded as
executed over the surface of an imaginary sphere. Their motion against
the radial springs would therefore correspond to a displacement outwards
or upwards from the spherical surface. A definite part of the effect of
retardation is, of course, due to this outward or radial displacement of
the masses.
Assuming still the property of constancy of energy of rotation, let it
now be supposed that in such a vibratory movement of the pendulum masses
as described above, the energy required merely for the displacement of
the masses _against the radial springs_ is not withdrawn from and
obtained at the expense of the original rotatory energy of the system,
but is obtained from some energy agency, completely external to the
system, and to which energy cannot be returned. The retardation,
normally due to the outward displacement of the masses against the
radial springs, would not then take place. But the energy is,
nevertheless, stored in the springs. It now, therefore, forms part of
the energy of the system, and consequently, on the returning or inward
movement of vibration of the masses towards the central axis, this
energy, received from the external source, would pass directly from the
springs to the rotational energy of the system. It is clear, then, that
while the introduction of energy in this fashion from an external source
has in part eliminated the effect of retardation, the accelerating
effect must still operate as before. Each vibratory movement of the
pendulum system, under the given conditions, will lead to a definite
increase in its energy of rotation by the amount stored in the radial
springs. If the vibratory movement is continuous, the rotatory velocity
of the system will steadily increase in value. Energy once stored in the
radial springs can only be released by the return movement of the masses
and _in the form of energy of rotation_; the nature of the mechanical
machine is, in fact, such that if any incremental energy is applied to
the displacement of the masses against the radial springs, it can only
be returned in this form of energy of motion.
These features of this experimental system are of vital importance to
the author's scheme. They may be illustrated more completely, however,
and in a form more suitable for their most general application, by the
hypothetical system now to be described. This system is, of course,
devised for purely illustrative purposes, but the general principles of
working of pendulum systems and of energy return, as demonstrated above,
will be assumed.
43. _Application of Pendulum Principles_
The movements of the pendulum masses described in the previous article
have been regarded as carried out over the surface of an imaginary
sphere. Let us now proceed to consider the phenomena of a similar
movement of material over the surface of an actual spherical mass. The
precise dimensions of the sphere are of little moment in the discussion,
but for the purpose of illustration, its mass and general outline may be
assumed to correspond to that of the earth or other planetary body. This
spherical mass A (Fig. 12) rotates with uniform angular velocity about
an axis NS through its centre. Associated with the rotating sphere are
four auxiliary spherical masses, M{1}, M{2}, M{3}, M{4}, also of
solid material, which are assumed to be placed symmetrically round its
circumference as shown. These masses form an inherent part of the
spherical system; they are assumed to be united to the main body of
material by the attractive force of gravitation in precisely the same
fashion as the atmosphere or other surface material of a planet is
united to its inner core (§ 34); they will therefore partake completely
of the rotatory motion of the sphere about its axis NS, moving in paths
similar to those of the rotating pendulum masses already described (§
42). The restraining action of the pendulum arms is, however, replaced
in this celestial case by the action of gravitation, which is the
central force or influence of the system. Opposite masses are thus only
united through the attractive influence of the material of the sphere.
The place of the springs, both central and radial, in our pendulum
system is now taken by this centripetal force of gravitative attraction,
which therefore forms the restraining influence or determining factor in
all the associated energy processes. While the auxiliary masses M{1}
M{2}, &c., partake of the general motion of revolution of the main
spherical mass about NS, they may also be assumed to revolve
simultaneously about the axis WE, perpendicular to NS, and also passing
through the centre of the sphere. Each of these masses will thus have a
peculiar motion, a definite velocity over the surface of the sphere from
pole to pole--about the axis WE--combined with a velocity of rotation
about the central axis NS. The value of the latter velocity is, at any
instant, directly proportional to the radius of the circle of latitude
of the point on the surface of the sphere where the mass happens to be
situated at that instant in its rotatory motion from pole to pole; this
velocity accordingly diminishes as the mass withdraws from the equator,
and becomes zero when it actually reaches the poles of rotation at N and
S; and the energy of each mass in motion, since its linear velocity is
thus constantly varying, will be itself a continuously varying quantity,
increasing or diminishing accordingly as the mass is moving to or from
the equatorial regions, attaining its maximum value at the equator and
its minimum value at the poles. Now, since the masses thus moving are
assumed to be a material and inherent portion of the spherical system,
the source of the energy which is thus alternately supplied to and
returned by them is the original energy of motion of the system; this
original energy being assumed strictly limited in amount, the increase
of the energy of each mass as it moves towards the equator will,
therefore, be productive of a retardative effect on the revolution of
the system as a whole. But, in a precisely similar manner, the energy
thus gained by the mass would be fully returned on its movement towards
the pole, and an accelerative effect would be produced corresponding to
the original retardation. In the arrangement shown (Fig. 12), the moving
masses are assumed to be situated at the extremities of diameters at
right angles. With this symmetrical distribution, the transformation
and return of energy would take place concurrently. Retardation is
continually balanced by acceleration, and the motion of the sphere
would, therefore, be approximately uniform about the central axis of
rotation. It will be clear that the movements thus described of the
masses will be very similar in nature to those of the pendulum masses in
the experimental system previously discussed. The fact that the motion
of the auxiliary masses over the surface of the sphere is assumed to be
completely circular and not vibratory, as in the pendulum case, has no
bearing on the general energy phenomena. These are readily seen to be
identical in nature with those of the simpler system. In each case every
movement of the masses implies either an expenditure of energy or a
return, accordingly as the direction of that movement is to or from the
regions of high velocity.
[Illustration: FIG. 12]
The paths of the moving auxiliary masses have been considered, so far,
only as parallel to the surface of the sphere, but the general energy
conditions are in no way altered if they are assumed to have in addition
some motion normal to that surface; if, for example, they are repelled
from the surface as they approach the equatorial regions, and return
towards it once more as they approach the poles. Such a movement of the
masses normal to the spherical surface really corresponds to the
movement against the radial springs in the pendulum system; it would
now be made against the attractive or restraining influence of
gravitation, and a definite expenditure of energy would thus necessarily
be required to produce the displacement. Energy, formerly stored in the
springs, corresponds now to energy stored as energy of position (§ 20)
against gravitation. If this energy is obtained at the expense of the
inherent rotatory energy of the sphere, then its conversion in this
fashion into energy of position will again be productive of a definite
retardative effect on the revolution of the system. It is clear,
however, that if each mass descends to the surface level once more in
moving towards the poles, then in this operation its energy of position,
originally obtained at the expense of the rotatory energy of the sphere,
will be gradually but completely returned to that source. In a balanced
system, such as we have assumed above, the descent of one mass in
rotation would be accompanied by the elevation of another at a different
point; the abstraction and return of the energy of rotation would then
be equivalent, and would not affect the primary condition of uniformity
of rotation of the system. In the circumstances assumed, the whole
energy process which takes place in the movement of the masses from
poles to equator and normal to the spherical surface would obviously be
of a cyclical nature and completely reversible. It would be the working
of mechanical energy in a definite material machine, and in accordance
with the principles already outlined (§ 20) the maximum amount of
energy which can operate in this machine is strictly limited by the mass
of the material involved in the movement. The energy machine has thus a
definite capacity, and as the maximum energy operating in the reversible
cycle is assumed to be within this limit, the machine would be
completely stable in nature (§ 25). The movements of the auxiliary
masses have hitherto also been considered as taking place over somewhat
restricted paths, but this convention is one which can readily be
dispensed with. The general direction of motion of the masses must of
course be from equator to pole or vice versa; but it is quite obvious
that the exact paths pursued by the masses in this general motion is of
no moment in the consideration of energy return, nor yet the precise
region in which they may happen to be restored once more to the surface
level. Whatever may be its position at any instant, each mass is
possessed of a definite amount of energy corresponding to that position;
this amount will always be equal to the total energy abstracted by that
mass, less the energy returned. The nature of the energy system is,
however, such that the various energy phases of the different masses
will be completely co-ordinated. Since the essential feature of the
system is its property of uniformity of rotation, any return of energy
in the rotational form at any part of the system--due to the descent of
material--produces a definite accelerating effect on the system, which
effect is, however, at once neutralised or absorbed by a corresponding
retardative effect due to that energy which must be extracted from the
system in equivalent amount and devoted to the upraising of material at
a different point. For simplicity in illustration only four masses have
been considered in motion over the surface of the sphere, but it will be
clear that the number which may so operate is really limited only by the
dimensions of the system. The spherical surface might be completely
covered with moving material, not necessarily of spherical form, not
necessarily even material in the solid form (§ 13), which would rise and
fall relative to the surface and flow to and from the poles exactly in
the fashion already illustrated by the moving masses. The capacity of
the reversible energy machine--which depends on the mass--would be
altered in this case, but not the general nature of the machine itself.
If the system were energised to the requisite degree, every energy
operation could be carried out as before.
As already pointed out, the dominating feature of a spherical system
such as we have just described would be essentially its property of
energy conservation manifested by its uniformity of rotation. All its
operations could be carried out independently of the direct action of
any external energy influences. For if it be assumed that the energy
gained by the auxiliary moving surface material _in virtue of its
displacement normal to the spherical surface_ be derived, not from the
inherent rotational energy of the sphere itself, but by an influx of
energy from some source completely external to the system, then since
there has been no energy abstraction there will be no retardative effect
on the revolution due to the upraising of this material. But the influx
of energy thus stored in the material must of necessity work through the
energy machine. In the movement towards the poles this energy would
therefore be applied to the system in the form of energy of rotation,
and would produce a definite accelerative effect. If the influx of
energy were continuous, and no means were existent for a corresponding
efflux, the rotatory velocity of the system would steadily increase. The
phenomena would be of precisely the same nature as those already alluded
to in the case of the system of rotating pendulums (§ 42). Acceleration
would take place without corresponding retardation. A direct
contribution would be continuously made to the rotatory energy of the
system, and would under the given conditions be manifested by an
increase in its velocity of revolution.
44. _Extension of Pendulum Principles to Terrestrial Phenomena_
The energy phenomena illustrated by the experimental devices above are
to be observed, in their aspects of greatest perfection, in the natural
world. In the earth, united to its encircling atmosphere by the
invisible bond of gravitation, we find the prototype of the hypothetical
system just described. Its uniformity of rotation is an established fact
of centuries, and over its spheroidal surface we have, corresponding to
the motion of our illustrative spherical masses, the movement of
enormous quantities of atmospheric air in the general directions from
equatorial to polar regions and vice versa. This circulatory movement,
and the internal energy reactions which it involves, have been already
fully dealt with (§ 88); we have now to consider it in a somewhat more
comprehensive fashion, in the light of the pendulum systems described
above. As already explained (§ 13), the operation of mechanical energy
is not confined to solid and liquid masses only, but may likewise be
manifested by the movements of gaseous masses. The terrestrial
atmospheric machine provides an outstanding example. In its working
conditions, and in the general nature of the energy operations involved,
the terrestrial atmospheric machine is very clearly represented by the
rotating pendulum system (§ 42). The analogy is still closer in the case
of the hypothetical system just described. The actual terrestrial energy
machine differs from both only in that the energy processes, which they
illustrate by the movements of solid material, are carried out in the
course of its working by the motion of gaseous masses. It is obvious,
however, that this in no way affects the inherent nature of the energy
processes themselves. They are carried out quite as completely and
efficiently--in fact, more completely and more efficiently--by the
motions of gaseous as by the motions of solid material.
The atmospheric circulation, then, may be readily regarded as the
movement, over the terrestrial surface, of gaseous masses which absorb
and return energy in regions of high and low velocity exactly in the
fashion explained above for solid material. In their movement from polar
towards equatorial regions these masses, by the action of the aqueous
vapour (§ 38), absorb energy (axial energy) and expand upwards against
gravity. Here we have an energy operation identical in nature with that
embodied in the movements of a pendulum mass simultaneously over a
spherical surface and against radial springs as in the system of
rotating pendulums, or identical with the equatorial and radial movement
of the auxiliary masses in the hypothetical system. The return movement
of the aerial masses over the terrestrial surface in the opposite
direction from equatorial to polar regions provides also exactly the
same phenomena of energy return as the return movement of the masses in
our illustrative systems. These systems, in fact, portray the general
operation of mechanical energy precisely as it occurs in the terrestrial
atmospheric machine. But obviously they cannot illustrate the natural
conditions in their entirety. The passage or flow of the atmospheric air
masses over the earth's surface is a movement of an exceedingly complex
nature, impossible to illustrate by experimental apparatus. And indeed,
such illustration is quite unnecessary. As already pointed out (§ 38),
no matter what may be the precise path of an aerial mass in its movement
towards the planetary surface the final energy return is the same.
Sooner or later its energy of position is restored in the original axial
form.
The terrestrial atmospheric machine will be thus readily recognised as
essentially a material mechanical machine corresponding in general
nature to the illustrative examples described above. The combination of
its various energy processes is embodied in a complete cyclical and
reversible operation. Its energy capacity, as in the simpler cases, is
strictly limited by the total mass of the operating material. The active
or working energy is well within the limit for reversibility (§ 23), and
the machine is therefore essentially stable in nature. The continuous
abstraction of axial energy by the aqueous vapour is balanced by an
equally continuous return from the air masses, and the system, so far as
its energy properties are concerned, is absolutely conservative. Energy
transmission from or to any external source is neither admissible nor
necessary for its working.
45. _Concluding Review of Terrestrial Conditions--Effects of Influx of
Energy_
The aspect of the earth as a separate mass in space, and its energy
relationship to its primary the sun and to the associated planetary
masses of the solar system have been broadly presented in the General
Statement (§§ 1-12). In that statement, based entirely on the
universally accepted properties of matter and energy, an order of
phenomena is described which is in strict accordance with observed
natural conditions, and which portrays the earth and the other planetary
bodies, so far as their material or energy properties are concerned, as
absolutely isolated masses in space. The scientific verification of this
position must of necessity be founded on the terrestrial observation of
phenomena. So far as the orbital movements of the planet are concerned
these are admittedly orderly; each planetary mass wheels its flight
through space with unvarying regularity; the energy processes, also,
associated with the variations of planetary orbital path, and which
attain limiting conditions at perihelion and aphelion, are readily
acknowledged to be reversible and cyclical in nature. In fact, even a
slight observation of the movements of celestial masses inevitably leads
to the conviction that the great energy processes of the solar system
are inherently cyclical in nature, that every movement of its material
and every manifestation of its energy is part of some complete
operation. The whole appears to be but the natural or material
embodiment of the great principle of energy conservation. It has been
one of the objects of this work to show that the cyclical nature of the
energy operations of the solar system is not confined only to the more
prominent energy phenomena, but that it penetrates and is exhibited in
the working of even the most insignificant planetary processes. Each one
of the latter in reality forms part of an unbroken series or chain of
energy phenomena. Each planet forms in itself a complete, perfect, and
self-contained energy system. Every manifestation of planetary energy,
great or small, whether associated with animate or inanimate matter, is
but one phase or aspect of that energy as it pursues its cyclical path.
It is a somewhat remarkable fact that in this age of scientific reason
the observation of the strictly orderly arrangement of phenomena in the
solar system as a whole should not have led to some idea in the minds of
philosophical workers of a similar order of phenomena in its separate
parts, but the explanation lies generally in the continual attempts to
bring natural phenomena into line with certain preconceived hypotheses,
and more particularly to the almost universal acceptance of the doctrine
of the direct transmission of energy from the sun to the earth and the
final rejection or radiation of this energy into space. There is no
denying the eminent plausibility of this doctrine. The evidence of
Nature _prima facie_ may even appear to completely substantiate it. But
we would submit that the general circumstances in which this doctrine is
now so readily accepted are very similar to those which prevailed in
more ancient times, when the revolution of the sun and stars round the
earth was the universal tenet of natural philosophy. This conception,
allied to the belief that the sole function of the celestial bodies was
to provide light and heat to the terrestrial mass, appeared to be in
strict accordance with observed phenomena, and held undisturbed
possession of the minds of men for centuries, until it was finally
demolished by Copernicus as the result of simple and accurate
observation of and deduction from natural phenomena. At the present
time, the somewhat venerable belief in the transmission of energy in
various forms from the sun to the earth appears at first sight to be
supported by actual facts. But a more rigid scrutiny of the evidence and
of the mental processes must inevitably lead the unbiassed mind to the
conclusion that this belief has no real foundation on truly scientific
observation, but is entirely unsupported by natural phenomena. Every
operation of Nature, in fact, when considered in its true relationships
is an absolute denial of the whole conception. Like its predecessor
relating to the motion of the sun and stars round the earth, the
doctrine of energy transmission between separate masses in space such as
the sun and the earth cannot be sustained in the face of scientific
observation. This doctrine is found on investigation to be supported not
by phenomena but by the conception of an elastic ethereal medium, of
whose existence there is absolutely no evidential proof, and the
necessity for which disappears along with the hypothesis it supports. It
is, however, not proposed to discuss in any detail either the supposed
transmission of energy from the sun to the planets or the arbitrary
properties of the transmitting medium, but rather to adopt a more
positive method of criticism by summarising briefly the evidential
phenomena which show the cyclical nature of the whole terrestrial energy
process, and which remove the basis of belief in such a transmission.
To recapitulate the more general conditions, we find the earth, alike
with other planetary masses, pursuing a defined orbital path, and
rotating with uniform angular velocity in the lines or under the
influence of the gravitation, thermal, luminous, and other incepting
fields (§§ 17, 18, 19) which originate in the sun. Its axial rotation,
in these circumstances, gives rise to all the secondary transformations
(§ 9) of terrestrial axial energy, which in their operation provide the
varied panorama of terrestrial phenomena. Terrestrial axial energy is
thus diverted into terrestrial secondary processes. Each of these
processes is found to be united to or embodied in a definite material
machine (§§ 27-30), and is, accordingly, limited in nature and extent by
the physical properties and incepting factors associated with the
materials of which the machine is composed. By ordinary methods of
transmission, energy may pass from one material to another, that is to
say from one machine to another, and by this means definite chains of
energy processes are constituted, through which, therefore, passes the
axial energy originally transformed by the action of the sun. These
series or chains of energy processes are also found to be one and all
linked at some stage of their progress to the general atmospheric
machine (§ 29). The energy operating in them is, in every case, after
many or few vicissitudes according to the nature of the intermediate
operations, communicated to the gaseous atmospheric material. By the
movement of this material in the working of the atmospheric machine (§
38) the energy is finally returned in its original form of axial energy
of rotation. The sun's action is thus in a manner to force the inherent
rotatory energy of the planet into the cyclical secondary operations,
all of which converge alike towards the general atmospheric mechanism of
return. The passage of the energy through the complete secondary
operations, and its re-conversion into its original axial form, may be
rapid or slow according to circumstances. In equatorial regions, where
the influence of the sun's incepting fields is most intense, we find
that the inherent planetary axial energy is communicated with great
rapidity through the medium of the aqueous vapour to the air masses. By
the movement of the latter it may be just as rapidly returned, and the
whole operation completed in a comparatively short interval of time. In
the same equatorial regions, the transformations of axial energy which
are manifested in plant life attain their greatest perfection and
vigour. But in this case the complete return of the operating energy may
be very slow. The stored energy of tropical vegetation may still in
great part remain in the bosom of the earth, awaiting an appropriate
stimulus to be communicated to more active material for the concluding
stages of that cyclical process which had its commencement in the
absorption of axial energy into plant tissue. The duration of the
complete secondary operation has, however, absolutely no bearing on the
conservative energy properties of the planet. In this respect, the
system is perfectly balanced. Every transformation or absorption of
rotatory energy, great or small, for long or short periods of time, is
counteracted by a corresponding return. Absolute uniformity of planetary
axial rotation is thus steadily maintained.
It is scarcely necessary at this stage to point out that the
verification of this description of natural operations lies simply and
entirely in the observation of Nature's working at first hand. The
description is based on no theory and obscured by no preconceived ideas,
it is founded entirely on direct experimental evidence. The field of
study and of verification is not restricted, but comprises the whole
realm of natural phenomena. In a lifetime of observation the author has
failed to discern a single contradictory phenomenon; every natural
operation is in reality a direct confirmation.
The conception of energy, working only through the medium of definite
material machines with their incepting and limiting agencies, is one
which is of great value not only in natural philosophy but also in
practical life. By its means it is possible in many cases to co-ordinate
phenomena, apparently antagonistic, but in reality only different phases
of energy machines. It aids materially also in the obtaining of a true
grasp of the inexorable principle of energy conservation and its
application to natural conditions, and it emphasises the indefensible
nature of such ideas as the radiation of energy into _space_.
It will be evident that in a planetary system such as described above
there is no room for any transmission of energy to the system from an
external source. The nature of the system is, in fact, such that a
transmission of this kind is entirely unnecessary. As already
demonstrated, every phenomenon and every energy operation can be
carried out independently of any such transmission. For the purpose of
illustration, however, it may be assumed that such a communication of
energy does take place; that according to the accepted doctrines of
modern science the sun pours energy in a continuous stream into the
terrestrial system. Now, no matter in what form this energy is
communicated, it is clear that once it is associated with or attached to
the various planetary materials it is, as it were, incorporated or
embodied in the planetary energy machines, and must of necessity work
through the secondary energy operations. But these operations have been
shown to be naturally and irresistibly connected to the general
atmospheric machine. Into this machine, then, the incremental energy
must be carried, and it will be there directly converted into the form
of axial energy of rotation. Once the incremental energy is actually in
the planet, once it is actually communicated to planetary material, the
nature of the system absolutely forbids its escape. The effect of a
direct and continuous influx such as we have assumed would inevitably be
an increase in the angular velocity of the system. This effect has
already been verified from an experimental point of view by
consideration of the phenomena of a rotating pendulum system (§§ 42,
43). Whilst the influx of energy proceeds, then in virtue of the
increasing velocity of the planetary material in the lines of the
various incepting fields of the sun, all terrestrial phenomena involving
the transformation of rotary or axial energy would be increased in
magnitude and intensified in degree. The planet would thus rapidly
attain an unstable condition; its material would soon become energised
beyond its normal capacity, and the natural stability (§ 25) of its
constituent energy machines would be destroyed; the system as a whole
would steadily proceed towards disruption.
But, happily, Nature presents no evidence of such a course of events.
The earth spins on its axis with quiet and persistent regularity; the
unvarying uniformity of its motion of axial rotation has been verified
by the observations of generations of philosophers. Its temperature
gradations show no evidence of change or decay in its essential heat
qualities, and the recurrence of natural phenomena is maintained without
visible sign of increase either in their intensity or multiplicity. The
finger of Nature ever points to closed energy circuits, to the earth as
a complete and conservative system in which energy, mutable to the
highest degree with respect to its plurality of form, attains to the
perfection of permanence in its essential character and amount.
Printed by BALLANTYNE, HANSON & CO.
Edinburgh & London
TRANSCRIBER'S NOTE:
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within {} brackets, such as: M{1}.
Obvious typographical errors from the original printed version of this
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