VOL. XLV.J PHILOSOPHICAL TRANSACTIONS. 427 



preached the stars that lie in the equinoctial colure py, and have receded from 

 those that lie in P:£b, 4-^", which is the sine of 30° to the radius ap. For if a perpen- 

 dicular fall from o on pa, it may be conceived as part of a great circle passing 

 through the true pole and any star lying in the equinoctial colure. Now the same 

 proportion, that holds in these stars, will obtain also in all others; and hence 

 we may collect a general rule, for finding how much nearer or farther any 

 particular star is to, or from, the mean pole in any given position of the moon's 

 node. 



For if from the right ascension of the star, we subtract the distance of the 

 moon's ascending node from Aries; then the radius will be to the sine of the re- 

 mainder, as Q", is to the number of seconds that the star is nearer to, or farther 

 from the true, than the mean pole. When that remainder is less than 1 80°, the 

 star is nearer to the true than to the mean pole; and the contrary, when it is 

 greater than 180°. 



This motion of the true pole, about the mean at p, will produce also a change 

 in the right ascensions of the stars, and in the places of the equinoctial points, 

 as well as in the obliquity of the ecliptic, and the quantity of the equations, in 

 either of these cases, may be easily computed for any given position of the moon's 

 nodes. But as it may be needless to dwell longer on the explication of the hypo- 

 thesis, I shall now proceed to show its correspondency with the phenomena, re- 

 lating to the alterations of the polar distances of some of the stars which I have 

 observed: by stating the observations themselves, together with the computations 

 that are necessary, in order to form a right judgment about the cause of these 

 appeai'ances. 



I have endeavoured to find the exact quantity of the mean precession of the 

 equinoctial points, by comparing my own observations made at Greenwich, with 

 those of Tycho Brahe and others, which I jugded to be most proper for that pur- 

 pose. But as many of the stars, which I compared, gave a different quantity, 

 I shall assume the mean result; which gives a precession of one degree in 71 

 years and a half; this agreeing very well likewise with my observations that 

 were taken at Wansted. The numbers in the following tables, which express the 

 change of declination in each star, are computed on the supposition that the 

 mean obliquity of the ecliptic was 23° 28' 30', and that it continued the same 

 during the whole course of my observations. And as the moon's ascending node 

 was in the beginning of Aries about the 27 th day of March, J 727, I have re- 

 duced the place of each star to that time, by allowing the proper change of decli- 

 nation from that day, to the day of each respective observation. 



It being also necessary to make an allowance for the aberrations of light, I 

 have again examined my observations that were most proper to determine the 

 transverse axis of the ellipsis, which each star seems to describe, and have found 



3x2 



