Whofe Complement 14 32, is the Hour

from 6 required.

Then for Latitude 70.

20 0 0.46594

66 30 9,03760

632 9.98446

14932 9.30826

74.46 19.79626 Sum.

63 2 9.89813 Half Sum. Sine Comp. 37 44

11 44

37 44

Doubled, 75.28

Whofe Complement, 14 32, is the Hour from 6, agreeing with the Hour found, by the fore going Operations.

NOTE, This Problem may be folved by finding the Time of the Day when the Sun is in the Prime Vertical, or Eaft or Weft Azimuth, of Latitude 60 (the middle Latitude between 50 and 70) for then is the Altitude equal in Places under the fame Meridian, and equally remote; therefore you have, as in Prob. 11. of Aftronomy Right-angled, the Latitude of the Place, and the Sun's Declination given, to find what Hour and Minute the Sun will be due Eaft or Weft by the following Proportion.

As

This 14 32, converted into Time, gives 58 Minutes paft 6 in the Morning, or 2 Minutes paft 5 in the Afternoon, agreeing exactly with the Operation in Page 141; only I thought fit to infert the former Method, becaufe its Solution depends upon a Quadrantal Triangle.

CHAP.

CHAP. V.

Of the ANALEMMA.

145

SECT. I.

Of the Orthographick Projection of the Sphere, by fome call'd the ANALEMMA.

RTHOGRAPHICK Projection of the Sphere, fuppofeth the Eye perpendicular to the Plain of that great Circle, upon which it is projected, and at an infinite Distance from it, and is most commonly, and indeed, moft intelligibly, perform'd upon the Plain of the Solfticial Colure, viz. the Meridian that interfes

the Ecliptick, in the Tropicks of Cancer and Capricorn: For the projecting and measuring the Parts of the Analemma, there is only Sines and Chords required; the Primitive Circle is meafur'd by the Chords, the right Circles by the Sines, and the Parallels being firft reduced to the Primitive, are alfo measured upon it by the Chords.

I have instanced in an Orthographick Projection of the Sphere for Latitude 54 40, North, Sun's prefent Declination 20 12, North his greatest Declination fuppos'd to be 23 30. Extend your Compaffes to 60 of the Chords, and with one Foot in the Center a, defcribe the Circle Z HN 0, and Plate 9. draw Z N, the prime Vertical, and Fig. 1. H O, the Horizon; then fet 54. 40 (the given Latitude) from 0 to P, and from z to, and from H to S, and from N to Q; and draw PS the Axis of the World, and the Equator; then because the Sun's greatest Declination is 23 30, take 23 30 off the Chords, and fet from A to E, and from Q to C, and draw EC to reprefent the Ecliptick: Set off the Chord of 20 12 the Sun's prefent Declination, from A to b, and from 2, and draw the Line be, which is the Pa rallel of Declination for 20 d. 12 m. North, g i h is a Parallel of Altitude.

Arches

Arches of the Primitive, meafur'd upon the Chords.

Op is the Latitude 54 45,

P

PZ the Complement of Latitude 35 20,

E the Sun's greatest Declination 23 30, Ab the prefent Declination 20 12,

KO the Sun's Altitude at 6 a-clock 16 21.

Arches of right Circles meafur'd on the Sines

a e the Sun's prefent Declination 20 12, af the Sun's Amplitude 36 40, from the East, a the Sun's Longitude 60 oo,

ad the Sun's Altitude when Eaft or Weft 25 3, 1 a the Sun's Altitude when in the Point O 47 48,

an (being equal to e g) is 16 21 the Sun's Al titude at 6 alt coil s

Arches of leffer Circles to be reduced to the Primitive, and measur'd by the Chords.

g the Sun's Azimuth from

the South,

rom

from

O. the Sun's Azimuth from in the Point . the Eaft,

de the Hour from 6 that the Sun is due East

15 7,

we the Sun's Azimuth from the Eaft or Weft at 6

ef the Afcenfional Difference 3 i 16,

e the right Afcenfion 57 48.