58 NUTATION of the EARTH's AXIS, &c. 



and the conjugate in the equinoctial colure, and has been fettled 

 at 1 4'. 2. — -Let P (fig. 3 Plate I.) reprefent the mean northern 

 axis of the earth. — AB a portion of the folititial colure, and 

 CD a portion of the equinoftial colure, — From P, each way on 

 AB, lay off 9. ^5, fuppofe to F, and G, then from the fame 

 point P, lay off each way 7.1, fuppofe to E and li, through 

 FHGE defcribe an ellipfe, and it will reprefent the path dci- 

 cribed by the axis of the Earth. When the Moon's afcending 

 node is in the beginning of T, the northern axis of the Earth 

 will be at F, when the fame node is in the beginning of v* , the 

 pole will be at H. — conflantly 3' before the Moon's afcending 

 node. From thefe elements it is evident, that the obliquity of 

 the ecliptic mufl: be fubjeci to a periodical change, being greater 

 by 19'. I, when the Moon's afcending node is in T, than when 

 in ^ : and the equinoftial points will alfo be fubjeft to an equa- 

 tion, which will be a maximum when the Moon's afcending node 

 is in the beginning of 55 and vf ; this equation is common to all 

 the flars. 



As in the cafe of aberration, it will be proper to make the 

 calculations from an orthographical projeftion.— From any fcale 

 of equal parts take 9.55, and with that diftance for a ra.dius 

 defcribe a circle, which divide into twelve equal parts for the 

 figns in right afcenfion ; which defignate by numerical letters ; (as 

 in Fig. 4, Plate I.) join III, and IX with a diameter, to repre- 

 fent a portion of the folftitial colure ; and O, and VI, for a 

 portion of the equinocftial colure, from the centre C, towards 

 O, and VI, lay off 7.1, and defignate thofe points by o, and 

 6, then through the points o. III, 6 and IX, defcribe an ellipfe; 

 which muff be divided fimilar to the primitive anfwering to the 

 places of the Moon's afcending node ; and to prevent confufion 

 in the explanation, it will be convenient to defignate the figns by 

 figures. 



To apply & Medufas to the projeftion,* lay off its right afcen- 

 fion P 13° 43' from 0% in the primitive, according to the order 

 of the figns to the point A, then from A, through the centre 

 C, draw the diameter AB for the meridian of the ftar ; which 

 crofs at right angles by the diameter DE. This being done, 



* This projeflion will fei ve for any ftar ; on whit Ii account it differs from 

 a projection for aberration. 



fuppofe 



