A New Discovery for Finding the Longitude

Part 1

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.

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 ℞

Part 2

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.

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