426 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1747-8. 



moves round p, in the circumference abcd, with a retrograde motion likewise, 

 in a period of the moon's nodes, or of 18 years, and 7 months. By this means, 

 when the moon's ascending node is in Aries, and the true pole of the equator at 

 a, is moving from a towards b ; it will approach the stars that come to the meri- 

 dian with the sun about the vernal equinox, and recede from those that come 

 with the sun near the autumnal equinox, faster than the mean pole p does. So 

 that, while the moon's node goes back from Aries to Capricorn, the apparent pre- 

 cession will seem so much greater than the mean, as to cause the stars, that lie 

 in the equinoctial colure, to have altered their declination Q" in about 4 years 

 and 8 months, more than the mean precession would do: and in the same time 

 the north pole of the equator will seem to have approached the stars, that come 

 to the meridian with the sun at our winter solstice, about Q''; and to have re- 

 ceded as much from those that come with the sun at the summer solstice. 



Thus the phenomena before recited are in 

 general conformable to this hypothesis. But 

 to be more particular ; let s be the place of 

 a star, ps the circle of declination passing 

 through it, representing its distance from 

 the mean pole, and "]f ps its mean right as- 

 cension. Then if o and r be the points where 

 the circle of declination cuts the little circle 

 ABCD, the true pole will be nearest that star 

 at o, and farthest from it at r; the whole 

 difference amounting to 18', or to the dia- 

 meter of the little circle. As the true pole of the equator is supposed to be at 

 A, when the moon's ascending node is in Aries ; and at b, when that node gets 

 back to Capricorn; and the angular motion of the true pole about p, is likewise 

 supposed equal to that of the moon's node about e, or the pole of the ecliptic ; 

 since in these cases the true pole of the equator is QO degrees before the moon's 

 ascending node, it must be so in all others. 



When the true pole is at a, it will be at the same distance from the stars that 

 lie in the equinoctial colure as the mean pole p is; for I neglect at present the 

 case of such stars as are very near the pole of the equator; and as the true pole 

 recedes back from a towards b, it will approach the stars that lie in that part of 

 the colure represented by py~, and recede from those that lie in p £i: ; not indeed 

 with an equable motion; but in the ratio of the sine of the distance of the moon's 

 node from the beginning of Aries. For if the node be supposed to have gone 

 backwards from Aries 30°, or to the beginning of Pisces; the point which repre- 

 sents the place of the true pole, will in the mean time have moved in the little 

 circle, through an arc, as ao, of 30° also, and would therefore in effect have ap- 



