VOL. 



XLV.] 



PHILOSOPHICAL TRANSACTIONS. 



425 



phenomena that I had observed, and at the same time mention what I suspected 

 to be the cause of them. He soon after sent me a table containing the quai>tity of 

 the annual precession in the various positions of the moon's nodes, as also the 

 corresponding nutations of the earth's axis; which was computed on the sup- 

 position that the mean annual precession is 50'', and that the whole is governed 

 by the pole of the moon's orbit only; and therefore he imagined that the numbers 

 in the table would be too large, as in fact they were found to be. But it ap- 

 peared, that the changes which I had observed, both in the annual precession 

 and nutation, kept the same law as to increasing and decreasing, with the num- 

 bers of his table. Those were calculated on the supposition, that the pole of 

 the equator, during a period of the moon's nodes, moved round in the periphery 

 of a little circle, whose centre was 23° 29' distant from the pole of the ecliptic; 

 having itself also an angular motion of 50" in a year about the same pole. The 

 north pole of the equator was conceived to be in that part of the small circle, 

 which is farthest from the north pole of the ecliptic, at the time when the moon's 

 ascending node is in the beginning of Aries: and in the opposite point of it, when 

 the same node is in Libra. 



Such an hypothesis will account for an acceleration and retardation of the an- 

 nual precession, as also for a nutation of the earth's axis : and if the diameter of 

 the little circle be supposed equal to 1 8", (which is the whole quantity of the 

 nutation, as collected from my observations of y Draconis) then all the 

 phenomena, in the several stars which I observed, will be very nearly solved 

 by it. 



Let p represent the mean place of the pole 

 of the equator, about which point, as a cen- 

 ter suppose the true pole to move in the cir- 

 cle ABCD, whose diameter is 18'. Let Ebe 

 the pole of the ecliptic, and ep be equal to 

 the mean distance between the poles of the 

 equator and ecliptic, and suppose the true 

 pole of the equator to be at a, when the 

 moon's ascending node is in the beginning 

 of Aries; and at b, when the node gets back 

 to Capricorn; and at c, >vhen the same 

 node is in Libra: at which time the north pole of the equator being nearer the north 

 pole of the ecliptic, by the whole diameter of the little circle ac equal to 1 8", ' 

 the obliquity of the ecliptic will then be so much less than it was, when the 

 moon's ascending node was in Aries. The point p is supposed to move round 

 E, with an equal retrograde motion, answerable to the mean precession arising 

 from the joint actions of the sun and moon ; while the true pole of the equator 



VOL. IX. 3 I 



