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As the Tangent of LI= 32 58 Is to the Tangent of AL = 12 33 So is Radius

To the Co-fine of ALI 69 56

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Thus Jerufalem bears from London E S E, and 2° 26 Eafterly.

3. To find how London bears from Jerufalem, or the Angle at I.

As the Sine of LI= 32 58 Co. Ar. 0.2642805

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9.7837878

9.7938317

9.8419000

Thus London bears from Jerufalem NW, and oo° 59' to the North.

This Problem might be diverfified and branched into feveral others, by having other Data; but that if the Reader pleases he may make his own Exercise.

PROBLEM VI.

Given the Latitude of two Places (one in North, the other in South Latitude,) and their Distance from each other, to find their Difference of Longitude, and Pofition from one another.

Practice.

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Let L reprefent London, and C Cape Horn; through both thefe Places draw proper Circles, and there will be formed the Oblique Triangle P L C, or rather its Supplemental one COS, in which all the Sides are given; for OS = PL = 38° 28′ the Co-Latitude of London; CS 32° 00', the Co-Latitude of Cape Horn; and O C = 52° 061, the Complement of L C

8890 Miles 127° 54' to a Semicircle; to find the Difference of Longitude, or the Angle OS C, by Cafe 5, Of Oblique Triangles. Here OS-SC=

AM 6° 28'.

=

Then the Sine of OS 38° 28' Co. Ar. 0.2061683 the Sine of S C = 32° 00' Co. Ar. 0.2757903

OC+AM

Add the Sine of

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2

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thereof is the Sine of OSC=49° 20 =

14

9.8799857

The

The Double of which is 98° 40′ O SC, whose Complement AS 2= 81° 20', the Difference of Longitude fought.

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2. To find how the faid Cape bears from London, or the Angle at O.

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Now the Angle at O is equal to the Angle at L, therefore Cape Horn bears S. W. by S. and to the W. of London.

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3. Thus alfo the Angle at C will be found to be about 51 Degrees, by the Gunter; fo London bears from Cape Horn N E, and almost half to the E.

Thefe Problems being well understood, any thing further on this Head will be unnecessary.

I fhall now fubjoin (for the Reader's Curiofity, ) a Scheme of the Dimenfions of all the chief Kingdoms of the World in length and breadth, the Metropolis of each, with its Distance and Bearing from the Metropolis of the whole World, viz. the City of London.

Note, The Dimenfions following are to be underftood of English Statute-Miles.

Kingdoms

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CHA P. IV.

Spherical Trigonometry applied to Navigation; fhewing how to find the Differences of Latitude, and Longitude; the Course and Distance failed, and the Departure from the first Meridian; all in the Arches of a Great Circle of the Globe.

G

REAT Circle Sailing is of all others the moft perfect and expeditious; the Reason is evident, because an Arch of a great Circle is the nearest Distance between any two Places on the Spherical Surface of the Earth, and confequently is the fooneft failed.

But because the Motion of a Ship is directed by the Wind, 'twill be fomewhat difficult to fteer a Ship directly on a Circular Arch; however 'tis poffible to keep pretty near it, and the nearer the better.

As this Method is most perfect and expeditious, fo it is the truest and most natural of any; yea could the Ship be all along conducted on the Arch of a Circle, it would then be perfectly true and natural.

The Difference between Plain, Mercator's, and Middle Latitude Sailing, and this, is obvious in the Form of the Charts, and in the Solutions thereby ; the Charts there being all Rectilineal Plans, but in this the Chart is only a Stereographic Projection of VOL. II. Rr

the

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