4^6 PHILOSOPHICAL TRANSACTIONS. [aNNO 1747-8. 



As I apprehend that the observations already set down, will be judged suffi- 

 cient to prove in general the truth of the hypothesis before advanced ; I shall 

 omit the recital of more, that I made of stars lying at greater distances from the 

 zenith ; those not being so proper, for the reasons before mentioned, to establish 

 the point that I had chiefly in view. But as it may perhaps be of some use to 

 future astronomers, to know what were the mean differences of declination, at 

 a given time, between some stars that lie nearly opposite to one another in right 

 ascension, and not far from either of the colures ; I shall set down the result of 

 the comparison of a few, that differs so little in declination, that I could de- 

 termine the quantity of that difference with great certainty. 



By the mean of 64 observations, that were made of a Cassiopeae before the 

 end of the year 1728, I collect, after allowing for the precession, aberration, and 

 nutation, as in the foregoing tables ; that the mean distance of this star was 

 68'' 7 south of 34° 55', on the '27th day of March 1727. By a like comparison 

 of 40 observations, taken of y Ursae Majoris during the same interval of time, 

 I find this s^ar was, at the same time, 39'''.6 south of 34° 45'. I carefully 

 measured, with the screw of the micrometer, the distance between the points 

 with which these stars were compared ; and found them to be 9' 59" from each 

 other, or one second less than they ought to have been. Hence it follows, that 

 the mean distance of declination between these 2 stars, was lO' 28'.!, on the 

 27th day of March 1727. 



By the mean of 65 observations, that were taken of (3 Cassiopeae, before the 

 end of the year 1728, this star was 25".8 north of 32° 20', on the 27th day of 

 March 1727 ; and by the mean of 52 observations, £ Ursae Majoris was 87".6 

 south of 32° 30' at the same time. The distance between these points was 

 found to be 9' 59".3; whence it follows, that the mean difference of declination 

 between these 2 stors was ll' 52".7, on March 27th 1727. 



By the mean of 100 observations, taken before the end of the year 1728, the 

 mean distance of y Draconis was 79"'-8 south of 38° 25' on March 27th 1 727 ; 

 and by the mean of 35 observations, the 35th Camelopard. Hevel. was south of 

 the same spot 76 ".4. So that the mean polar distance of y Draconis was only 

 3".4 greater than that of the 35th Camelopard. Hevel.; but as the equation for 

 the nutation, in both these stars, was then near the maximum, and to be applied 

 with contrary signs ; the apparent polar distance of y Draconis was 21 ".4 greater, 

 on the 27 th day of March 1727. 



The differences of the polar distances of the stars, as here set down, may be 

 presumed, both on account of the radius of the instrument and the number of 

 observations, to be very exactly determined, to the time when the moon's as- 

 cending node was at the beginning of Aries; and if a like comparison be here- 

 after made, of observations taken of the same stars, near the same position of 



