Difference of Latitude 81.3, or 1 Deg. 21 Min. hence the Latitude come to is 55 Deg. 29 Min.

For the Difference of Longitude, the Middle Latitude is 45.48, but the next greater whole Degree is 55, whofe given Number in the fecond Table is 5735, but I fhall only use the first two Figures 57.

The Diff. of Long. 95m.

57)5440(95 the Remain

or id. 35m.

310

der being but

a Fraction of

The fame Day's Work caft up by a New Method.

The Course 33.45 or 33, the Distance 98 Miles.

For the Natural Radius for 33 Deg. by Method the Second, they that can work by crofs Multiplication need not redude the Fraction to a Decimal, but square it as follows;

33.

33 | As 60.7 to 98: 33 to Departure

331

:

33

For Difference of Longitude, the Complement of Middle Latitude is 35, its Natural Radius is 61: Therefore as 35 to 54.4 fo 61 to Difference of Longitude.

35)3318(94 or 95 Minutes, or 1 Degree 35

168

54.4

61

54.4

3264

28

3318.4

Minutes, the Difference of Longitude required.

And thus you fee the Excellency and Usefulness of this New Method, by which, although by Strefs of Weather or

Cruelty

Cruelty of Enemies, you had loft all Charts, Books, Tables and Inftruments, yet you may without any of them keep as juft an Account of your Ship's Way, both in Longitude and Latitude, as you can with them; as this and other Examples inferted elsewhere in this Book make manifeft.

CHAP. VIII.

SECT. I.

How to make an Orthographick Projection of the Sphere, commonly called the Analemma; whereby, most of the necessary Questions in Aftronomy may be refolved without Trigonometrical Calculations, only by the Help of Scale and Compaffes.

AL

LTHOUGH I have inferted all the Aftronomical Tables, ready calculated, that are of Ufe in the Practice of Navigation, and have alfo laid down a Method for finding the Variation of the Compass, without Azimuth or Amplitude, &c. yet for the Sake of fuch as delight in Aftronomical Operations, I fhall fhew the Learner how to folve all neceffary Aftronomical Questions by the Analemma, or Orthographick Projection upon the Plane of the Meridian; and in this Manner of Projection, the Eye is fuppofed to be perpen

dicular

dicular to that great Circle upon whose Plane the Projection is made, and at an infinite Diftance from the said Čircle: fo that any Line let fall from the Eye upon any Place within the faid Circle, fhall be perpendicular to the faid Plane, and then will the Primitive Circle (or Meridian of the Place, when the Projection is upon the Plane of the Meridian) be a perfect Circle. All right Circles that divide the Projection into two equal Parts are ftrait Lines, or Diameters, of the Primitive Circle; and all Oblique Circles that divide the Primitive into two equal Parts, and yet touch it at oppofite Points are Semi-Ellipfes, or Half Oval Circles; and all Parallels, or leffer Circles, are right Lines, cutting the Primitive into two unequal Parts; and Parts of Lines that ferve for the Solution of any Aftronomical Questions, are Parts of fome of thofe Circles, or fuppofed to be fo, and are measured or projected according to the following Directions.

The Primitive Circle (being drawn with the Chord of 60 Degrees of any Radius large or small) any Parts of it is measured upon the Chords of the fame Radius. Any Part of a Right Circle is measured upon the Sines. Any Part of an Oblique Circle (when required to be measured, which is but feldom) may be meafured on the Chords, being first reduced to the Primitive Circle thus; draw two Lines through the two Points in the Oblique Circle, the Distance between which is to be measured, and let the faid two Lines be drawn parallel to that Right Circle which cuts the said Oblique Circle at Right Angles, and mark where these two Parallels cut the Primitive Circle, and the Distance between these two Marks measured on the Chords, is the Measure of the Oblique Circle required.

Note; There is no Way to project thefe Oblique Circles, but by finding a great Number of Points through which they are to pals, and fo by a fteady Hand, or Help of a Bow, draw it through the faid Points; but the Operation being tedious, and of little Ufe, it is feldom put in Practice: Nevertheless I fhall hereafter fhew how they are done, as alfo all the reft, as in the following Example.

An

An Orthographick Projection of the Sphere upon the Plane of the Meridian. For

First, With the Chord of 60, draw the Circle PESQ, to represent the Meridian; then draw the Diameter HO to reprefent the Horizon, and at Fig.65. Right Angles to it draw the Line ZN, to reprefent the Prime Vertical; then fet off the Latitude 51 32 (taken off the Chords) from o to P, and from H to S, and draw the Line P R S to reprefent the Axis of the World, P the North Pole, and S the South Pole: Then at Right Ang'es with the Line PS, draw the Line E Q to reprefentt the Equator: Then fet the Chord off the given Declination 22 30 from E to D, and from Qto C, and draw the Line DC the Parallel of the Sun's Declination: Set off the Chord of 23.30, the Sun's greatest Declination from E to T and from Q to K, and draw the Line T K to represent the Ecliptick Set off alfo the Chord of 23.30 from P to q and g, and draw the Line q g, to reprefent the Artick Circle, and the fame from S to r and v, and draw the Line rv to reprefent the Antartick Circle: Then from P, through the Point draw the Meridian Pho B; thus, herein given is this Meridian the Point P and the Point ; then to find the Point B, another Point through which this Meridian is to pafs, divide the Line ER after the fame Proportion that the Line D F is divided, at the Point O, that is, as F D to FO, fo RE to RB, and make the Mark B, and by the fame Means find the Point b in the Line q g: Then through the Points Pho B with a Bow, Curving or Bending gradually, draw the pricked Curving Line Pho B to reprefent a Part of another Meridian: All which being finished you may proceed to answer the following Problems.

1. To