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Title: A new discovery for finding the longitude
Author: William Herbert Hobbs
Release date: January 4, 2025 [eBook #75039]
Language: English
Original publication: London: William Hobbs, 1714
Credits: John Welch, MWS, Cambridge Digital Library and the Online Distributed Proofreading Team at https://www.pgdp.net
*** START OF THE PROJECT GUTENBERG EBOOK A NEW DISCOVERY FOR FINDING THE LONGITUDE ***
A
New DISCOVERY
For Finding the
LONGITUDE.
Humbly Submitted to the
Approbation of the Right Honourable
the Lords Spiritual and Temporal, and
the Rest of the Honourable Persons,
appointed by the late _Act of Parliament_,
for Hearing and Determining _Proposals_
relating to the said LONGITUDE.
_By_ William Hobbs, _Philo Mathem._
[Illustration]
_LONDON:_
Printed for the Author, and are to be Sold by _Fard.
Burleigh_ in _Amen-Corner_.
Price Six-pence.
_Note_, The former Impression was Printed _July 12. 1714._
_A New Discovery for Finding the ~Longitude~._
For Finding the Longitude, it is to be noted, That if the true Hour, and
Minute of the Day, at the Place of our first ~Departure~, and where we
are ~Arrived~, can be both obtained, the Difference of Longitude may be
found, as truly as the Difference of Latitude.
For which purpose the _Spring-Movement_ hereunto subjoined, is most
humbly proposed to effect the same, even to the Tenth of a Minute
of Time. So that should the Error of a Minute happen to be found in
Practice, it must proceed from the Influence or Vicissitude of the
Air, and not from any Defect in the Rules by which the said Movement
is composed, as will plainly appear by the Explication thereof, in the
following Lines; and first of
_The Description of the said Movement._
This Movement may be either of the Form and Bigness of that in a Common
Clock; or else of the Smallness of a Pocket Watch, as may be thought
convenient in Practice. But the larger it is, the better the Divisions
in the _Horologe_ will appear. And as for the Numbers, they may be at
pleasure: Only this must be observ’d, That the swiftest Index must make
just One Revolution, whilst the slow one goes but One of the Hundred
Divisions, (as is common in Minute Watches, wherein 60 Minutes goes to an
Hour) but the rest of the Numbers may be at pleasure, as aforesaid. And
if the Slowest moves round in 3, 4, or 5 Days; and the Movement requires
to be wound up once in 26 or 27 Hours, it will be sufficient: For the
more Vigor the Motion is calculated for, the less the Air will affect it.
_How to set it first in Motion._
When it is finished, let it go for a Month or two; after which put the
two _Indexes_ right one with the other, and both of them pointing just to
100. Then the Spring being wound up, keep it from Going (with the Key)
till the Shadow of the Sun is exactly come to a _Meridian_ Line, which
must be rightly prepared for that purpose. Then let it go till the Shadow
comes just to the same Line the next Day, or rather 40, 50, or 100 Days
after, (the longer the Better.) At which time enter down the _Centesms_
that the swiftest _Index_ points to, as also the _Integers_ and _Tenths_
of the slowest, (but put the last first in your Numbers) by this you will
be furnished with two general Numbers, _viz._ the said Numbers pointed
to, and the Time (in Hours) spent therein, to find the Hour of the Day to
the Tenth of a Minute, at any time; for that Place where it was so set
going, tho’ you remove it afterwards to any Distance whatsoever. Which
two Numbers ought to be entered in a Book; to be used whensoever you
would find the Hour of the Day.
And it is to be noted, That if the Sun be not then in its Mean Motion,
you must Add to, or Substract from what the _Indexes_ do Give, according
to the Inequality thereof: But if you try it for one whole Year, there
will be no need of either. And that what is said may be the better
understood, I shall give an Example.
_How to find the Hour and Minute of the Day at ~London~, by the said
Movement._
Suppose it should be made for the Slowest to Revolve in about five
Days, and after it has gone just two Days, the Slowest _Index_ should
then point between 39 and 40, and the Swiftest to 21.5. Then both these
Numbers (as set in Order) will make 3921.5. And if the Sun be in its
Mean Motion (if not, you must Add or Substract, as aforesaid) then the
said Numbers 3921.5 must always be the First; the said two Days, or 48
Hours, the Second; and the two Numbers pointed to by the _Indexes_, at
the time for which you would find the Hour and Minute of the Day (as
suppose the slow one should point to 87, and the swift one to 65.2, both
making 8765.2) must be the Third; by which the Fourth will be obtained as
followeth: Which Fourth Number being Divided by 12, the Remainder will
be the Hour and Minute of the Day at _London_, as was required.
Hours Hours.
As 3921.5 : 48 :: 8765.2 : 107.18
ho. min. }
Remains 11 : 10.8 hours. } Requir’d
or 11¹⁸⁄₁₀₀ }
And so for any quantity of time less than one Revolution.
But if the time required to find the Hour and Minute at _London_, (when
at Sea or Land,) be some Weeks or Months, _after_ it was first set going;
or (if cleansed) after it was last _Cleansed_; then you must add 10000.0
to what the two Indexes do shew, for each _Revolution_, that it has made,
since it was so set going, or last cleansed. And if you would at any
time know how many such Revolutions must be added, to what is shewn by
the Horologe; you must first note the _Day_ of the Month, that you are
then seeking the Hour for; as suppose _Novem. 12. 1715._ After which note
the _Day_ last entred, when cleansed; as suppose _Sept. 5. 1715._ Then
compute the number of Days between _Sept. 5._ and _Novem. 12._ which is
25, 31, and 12, In all 68. After which observe the _Time_ last spent in
one Revolution; which you see was 5 Days, 4 Hours, and ⅛ (for which set
down ⅒ for ’twill make no sensible Difference) and having thus done, say,
Days Hours Hours Revo. Days
As 5 4⅛ equal to 124.1 : 1 :: 68 : 13. whole Revolutions;
For which, as before directed, you must add 13 times 10000.0 to the
Numbers pointed to, by the two Indexes: Which if we suppose 3752.2 making
in all 133752.2 will be the Number required, for the 12ᵗʰ of _November_,
if the Indexes should both point as before proposed. And having now found
this Number, you are prepared to find the Hour and Minute at _London_,
in manner following (_viz._) suppose you are in or near 44 Degrees of
Latitude, in the Autumn Season. Then seek the Latitude 44 Deg. and the
Season _Autumn_, in the Book that is peculiar to your Movement, and
having found both, take the Numbers Answering thereunto, which (in this
Example) is 29274.2 and 240 Hours; and then say,
Hours Hours
As 29274.2 : 240 :: 133752.2 : 1096.84
Which being devided by 12, leaves remaining 4.84 ho. or 4 ho. 50.4 min.
required, for the Hour and Minute at _London_, by which the Longitude
will be found, as before directed.
And seeing it was near the Winter Season: If you should add the Autumn
and Winter Numbers, and Hours respectively together; and make them
the two first Numbers in your Proportion; it would Æquate the Seasons
more exactly: I mean, if the said Numbers had been really entred from
Practice; but these are only supposed. And by this method you may Æquate
the Numbers for finding the true Hour and Minute at any Season; or for
any other Latitudes whatsoever.
_How to find the Hour and Minute, at the place where you are, when
abroad, either at Sea or Land._
For Solving this, there are Two Ways, the First and Infallible is, when
the Sun is either Rising or Setting; at which times, if the Air be clear,
observe what Numbers are pointed to by the two _Indexes_, (but observe
the swiftest first, because it will soon be removed) just as the Center
of the Sun is in the Horizon; and enter both the Numbers down, as before
directed, with the Day of the Month, and the Latitude you are then in:
Which having done, by the following Cannon, say,
As ℞
Is to t. c. of the Sun’s Decl.
So is t. Lat.
To s. c. of an Angle; which, if converted into Time (by 15)
Gives the Hour and Minute of the Sun’s Rising from Midnight;
and if Substracted from 12 ho. gives the Setting. Which shews
the true Hour and Minute at the Place where you then are,
either at Sea or Land.
The Second way for Solving the said Question, is by taking the Sun’s
Altitude, when about 5 or 10 degrees above the Horizon; and at the same
time let another Person see what Number the Swiftest Index points to,
and after that the Slowest: Then put them both down as before directed,
with the Day of the Month, and the Latitude of the place where you are;
then have you the Sun’s _Altitude_, the said _Latitude_, and the Sun’s
_Declination_, to find the Hour and Minute of the Day at the place
required.
Now having by the said Observations and Cannons found the Hour and Minute
of the Day for the Place where you are, when abroad; and by the Numbers
pointed to, by the two Indexes, also found the Hour and Minute that it
is at _London_, (if the Movement was there set going;) If you take the
Lesser of these from the Greater, and bring the Remainder into Minutes,
it will give the difference between the two places in ~Time~; by which
you may find their difference of Longitude either _East_ or _West_ to a
Minute, by the following proportion, (_viz._)
Suppose the Difference of Time was 37 Minutes, then say,
{ Minutes of} {Minutes of} {Minutes of} {Minutes of}
As { Time } : { Longitude} :: { Time } : { Longitude}
{ 1440. } { 21600 } { 37 } { 555.5 }
{or 24 hours} { Deg. Min.}
or 9 : 15.5
Required.
Which 9 deg. 15.5. min. being added to, or taken from the Longitude of
the Place, where the said Movement was first set in Motion, gives the
Longitude you are come into, as effectually as the Latitude is obtained
by Observation, as was at first proposed. So that it is evident, that
if any defect should be found in practice, it must proceed from the
Vicissitude of the Air; and not from any Deficiency in this Discovery, or
from the Cannons relating thereunto.
And that we may Answer all _Objections_, which may arise, on Account of
the said Vicissitude of the Air, Motion of the Ship, Foulness of the
Movement, _&c._ as well as render this Discovery more intelligible, we
will descend to speak thereof more particularly: And,
In the first place, let Five or Six (or what Number you please) of these
Movements be made; and after they have gone for a Month or two, (or if
designed for the Sea, ’till within two or three Weeks of your Sailing)
then take them asunder, and set them going by the _Meridian_ Line,
as before directed. And having entred down in the Book, herein after
mentioned, the Day of the Month, when set going; how long it is making
one Revolution; and what Number is produced, in just Ten Days Motion,
(all which must be done, before you Sail in every Voyage;) Let them be
carry’d to Sea, into any Latitude, (suppose 50 Deg. or _Newfoundland_)
and at their Return bring them again to the said _Meridian_ Line, and
thereby (with the help of the Number of Days from their being first set
in Motion) find the two first ~Proportional Numbers~, as before directed:
Which done, enter them in a Book, peculiar to each Movement, (the Form
whereof followeth) together with the Latitude, and Season of the Year in
which the Voyage was made. Then will they all be fitted for a Voyage to
_Newfoundland_, and Parts adjacent, for any such Season. And so for any
other, when Tried and Entred, as now directed.
After which, send them all in a Ship bound to the Latitude of about 37
Deg. (suppose _Virginia_); and being returned, let the Numbers be found
and entred, as aforesaid, with the Latitude and Season; then will any
one, or all of them, be fitted for a Voyage, either to _Newfoundland_ or
_Virginia_, or any of those Parts, for any such like Season; and so for
any other, when Tried and Entred as aforesaid.
This being done, send them also in a Ship, bound to the Latitude of 13
Deg. (suppose _Barbados_ or _Jamaica_;) and being returned, find the
Numbers, and enter them with the Latitude and Season: So will they all be
fitted for these several Latitudes, (_viz._) 50 Deg. 37 Deg. and 13 Deg.
at such a Season: And by a like Process to the _Æquinoctial_, and towards
the _North Pole_.
Upon which several Tryals, you will have so many Movements fitted for all
the _North Hemisphere_, both for Hot, Cold and Temperate Seasons. And, by
only Counterchanging the Latitudes, for the whole Globe; or at least for
the Marine Parts thereof.
And to what is proposed to be Entred, in respect of Latitude and Season,
you may also add the Time of its being first set in Motion after
Cleansing; which Cleansing must be done only Annually, and as near as
may be on the same Day of the Month; which will much facilitate the
Inequality arising from its Foulness: By which all Objections will be
answer’d, and the Discovery render’d compleat and perfect. Especially
if a true _Meridian Line_ be made in every considerable Port in this
Kingdom, and elsewhere; for Examining the Movement at your Arrival
abroad, and setting it in _Motion_, before your Departure. But remember,
that where you set it going, from thence your _Departure_ must be
reckon’d.
And by this Method all the said Vicissitudes that may arise in respect of
Latitude or Seasons, Motion of the Ship (which will be near the same in
one Voyage, as in another) and Cleanness or Foulness of the Work, will
also plainly appear upon Record, (by comparing one Number in the said
Book with another) and will be Accounted for, and Æquated, as occasion
requires: Namely, by only taking such Numbers from the said Book, to work
your Proportion by, as are entred for the Latitude and Season, that you
are again Arrived to, or Sailing under: As suppose into 50 Deg. in the
Summer Season, then take the Number and Hours answering thereunto; and
so, if in Winter, those for the Winter. By which proportionable Numbers,
the said Contingencies will be truly and effectually Allowed, and the
Difference in Motions justly Æquated, as was before asserted.
_Note_, That in this Movement, the ~Time~ is Regulated or
Conformed to the ~Motion~: Whereas in former Movements, the
~Motion~ is Regulated or Conformed to the ~Time~. And this
ought to be well understood, before you can rightly comprehend
what is herein contained.
Now that this Movement, or Discovery, does not only differ from, but
also far exceed, any that has hitherto been proposed; is evident in this
(_viz._) That if any former Movement whatsoever be Timed here, as usual,
~Before~ it is carried to Sea, (tho’ never so exactly) yet the change of
Climate, _&c._ will so affect it, as to make it go False: And if you fit
it there, then ’twill be also False when brought hither: But if by this
Movement, and the foregoing Rules, the said Numbers be found ~After~ it
is returned from such a Voyage; all the said Defects or Contingencies
will be Æquated by the said Numbers only. So that it will be the same in
use, as if no such Accidents did attend it at all. And this Assertion
must, and will be granted, by every one that does fully comprehend the
Nature and Use thereof. For altho’ this _Horologe_ has no certain _Hours_
or _Time_ pre-assigned to it; yet it hath nevertheless, greater or
lesser Numbers Æquated to the Variableness of Motion or Time, (_viz._)
If fitted to be used here in _England_, then it hath (or may have) one
sort of Numbers (or Time) for finding the Hour and Minute, in the Summer
Season; another for Winter; and a third for the Spring and Fall; one when
it lyeth undisturbed in one and the same place; another (if you please)
when carry’d always in a Rattling Coach. And on the other hand, if you
carry it to Sea, then it has one for the _Torrid_, one for the _Frigid_,
and a third for the _Temperate Zones_, &c. And yet still but one and the
same _Horologe_, and but one and the same _Indexes_. So that all manner
of Natural Vicissitudes or Contingencies whatsoever, may be Regulated
or Æquated in and by the said Numbers; and consequently, the true Hour
and Minute of the Day, where it is first set going, may be hereby as
effectually found, as if no such Impediments did at any time or place
attend it, as aforesaid.
And as for what may be suggested in relation to the Inequality between
the Spring and Fusie, if any should be, it will be compensated, in that
there are five or six Windings up of them, to one Revolution in the
_Horologe_. So that there is nothing wanting to compleat this Discovery,
but to put it into Practice: And seeing the Charge and Trouble is very
Inconsiderable; and the Legislature by _Act of Parliament_, hath been
graciously pleased to Incourage hereunto, it is thought expedient to make
this publick Proposal, _viz._
That if any one Person is willing to Engage in this so Noble an
Enterprize, he will be readily received as a Partner, on such Conditions
as may be Reasonably Concerted therein.
_You may hear of the Author at Mr. ~Burleigh~’s in
~Amen-Corner, London~._
MEMORANDUM.
1. All Departures must be reckon’d from _London_, if the Movement was
there Set going.
2. That wheresoever they are Set going, there must be a large and exact
Meridian Line prepared by a Perpendicular, set up in an Horizontal
Circle, as is Mathematically taught, _&c._
3. That an Equal time be spent in Winding it up, as near as possible; for
which no time need be allowed, if Equated for 10 or 12 Months; because
the time required will be the same for the same time, and greater for a
greater, _&c._
4. That the said Movement be carefully kept in one and the same
Temperature of Air, as near as possible.
5. That after this Movement is fully proved, if it should not (by reason
of any sudden change of Air) agree to a Minute, yet it ought not in this
respect to be altered or much regarded, because the moistness of one
Month, may compensate the Dryness of another: So that by such time as you
are arrived to the end of your Voyage, the Movement may even Rectifie or
Correct it self.
6. It is to be noted, That if the Sun comes too soon to the Meridian, it
will also come too soon to the Horizon; and therefore, Watch too fast, or
too slow, must be Added or Substracted, as aforesaid.
7. That it be always wound up, as near as may be, at one certain time of
the Day, (_viz._) if at Sea, about Twylight, or Break of Day, as may be
thought expedient. And if it should happen to be omitted, so long as to
stand still; you must not set it going again, but by taking it assunder,
and putting the two Indexes together, and bringing the Movement to the
Meridian Line, as at first directed. Therefore when at Sea be careful of
such Omissions.
8. It is to be noted, That altho’ every Minute of Time, does Answer to
about 15 or 16 Miles _English_, under the _Equinoctial_; yet it is not
above 9 or 10 Miles in our Latitude to one such Minute. And altho’ it
be so many under the Equinoctial, yet _there_ the Sun’s Altitude will
be taken very exact, because 90 degrees of Altitude, is for 6 hours of
Time; whereas in our Latitude, it is but 62 degrees, for 8 hours of Time;
both which Advantages will Facilitate the Practice. I shall at present
conclude with acquanting,
That if a common Minute Watch (by Filing or Loading the Ballance, or
otherwise) be made to go, or does already go, any unknown quantity of
Time, either too Fast, or too Slow; by this Device, we may find the Hour
and Minute of the Day by such a Watch, more exactly than can be done by
the best timed common Watch whatever. And this even without touching it,
other than by Winding up the Spring as usual.
There are other Improvements that may be made of this Discovery, but I
reserve them to some other Opportunity.
_The FORM of the Book to be kept for each Movement, wherein must be
entred the Numbers, &c. (which are to be found at the Returning of the
Ship) for finding the Hour and Minute at ~London~._
--------------------------------------------------------------------------
The Movement, Number 1. was } and { Then made one Revolution, in 5
first Set Going _Sept. 4. 1714._ } { days, 4 hours, and a quarter.
+-------+---------+---------+------+--------+---------------+------------+
|Degrees|Numbers | Hours | Diff-|Seasons | Time when the |Numbers, |
| of |to be |spent in |erence|in which| Movement was |shewing how |
| Lati- |found and|producing| in |the Ship| set in Motion |the Motion |
| tude. |used in |the said | Num- |was | & Try’d; at |is retarded |
| |finding |Numbers. | bers.|Sailing.| & after first |by Foulness,|
| | the | | | | Making or |on a Tryal |
| |Hour at | | | | Cleaning. |of 10 Days |
| |_London_.| | | | |at a time. |
| | | | | | | |
| I. | II. | III. | IV. | V. | VI. | VII. Days.|
| 50 | 29276.2 | 240 | |_Autumn_|_Sep. 16. 1714_|29276.2| 10 |
| 52 | 37962.4 | 432 | |_Winter_|_Dec. 4. 1714_|29272.5| 10 |
| 44 | 37942. | 430 | |_Spring_|_Ma. 20. 1715_|29264. | 10 |
| 48 | 37912.2 | 431 | |_Summer_|_June 1. 1715_|29237.4| 10 |
+-------+---------+---------+------+--------+---------------+-------+----+
| Cleansed _Sept. 5. 1715._ Then made one Revol. in 5 days, 4 ho. and ⅛.|
+-------+---------+---------+------+--------+---------------+-------+----+
| 50 | 29274.2 | 240 | |_Autumn_|_Sept. 5. 1715_|29274.2| 10 |
| 52 | 37957.9 | 432 | |_Winter_|_Dec. 17. 1715_|29268. | 10 |
| 44 | 37942. | 430 | |_Spring_|_Ma. 16. 1715_|29264. | 10 |
| 48 | 37907.5 | 431 | |_Summer_|_June 8. 1716_|29232.7| 10 |
+-------+---------+---------+------+--------+---------------+-------+----+
_Note_, That the Numbers to be used after _Cleaning_, (_viz._ after
_Sept. 5. 1715._) are found by Substracting or Adding the Difference
between the two Numbers in the Seventh Column, (_viz._ that of _Sept.
5._) and that of _Sept. 16._ (which is only 2.) out of the former Numbers
to be used for the same Latitude; on which there will remain 29274.2 for
the _New_ Number to be used in Lat. 50. Deg. in _Autumn_, instead of the
former, until the next Cleaning, (which must be only Annually) and so
of the rest, from one Cleaning to another. And this method must be used
for the respective Latitudes, according as Observations shall be made
therein, and Numbers found to answer thereunto.
_Note also_, That this Experiment may be sufficiently Tryed and Proved,
by only two or three Voyages, to the South-West parts of _Ireland_, or to
_Newfoundland_ at farthest.
But notwithstanding what has been said, It is chiefly to be noted, That
altho’ I have proposed (for Example sake) that the General Numbers
should be found, by Sailing to _Newfoundland_, _Virginia_, _Barbados_,
&c. and returning again to a _Meridian Line_ at _London_: Yet if the
_Honourable Persons_ before-mentioned in this Title-Page, to whom the
whole is most humbly submitted, will please to appoint a Ship for this
purpose, the said Numbers may be much better found in manner following;
(that is to say) By ordering that the said Ship shall first make a true
_Meridian Line_, at or near the Lat. of 60 Degrees; and thereby set the
Movements going, in manner aforesaid: After which let them Sail about
40 or 50 Leagues distant from the Shore, and there Cruise _Northward_
and _Southward_ for about a Month’s time; after which let them return
again to the same _Line_, and find the Numbers, and also enter them, as
before directed. And having so done, let them make another _Meridian
Line_, about 15 Deg. more Southward, and there do in like manner: And so
at the like Distance to the _Equinoctial_. After which, let them begin
again, and repeat the same Process for three or four times: By which
means the Numbers will be found, and the different Motion of the Movement
discover’d, for all Latitudes and Seasons, as near as needful.
And being returned home, by these Numbers we may find the true
_Difference_ of Motion, in and for the several Latitudes and
Seasons. Which _Difference_ must be entred in the 4th Column of the
respective Books, reserved for that purpose. By the help of which said
_Differences_, you may make as many Movements as may be needful, at any
time; as also Books and Numbers peculiar to each Movement. The _Rules_
for which will be imparted to any such Watchmaker, as may Reasonably
desire the same.
_FINIS._
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