PHYSICAL ASTRONOMY. 313 



another, will be best seen by projecting a part of 

 the circles on a plane touching the Earth in A. 



If AC (fig. 27. N 2.) be a small part of the ecliptic 

 represented by a straight line ; AP' a like portion 

 of the solstitial colure ; and AQ of the equator. 

 Then if A A' be taken equal to PP', in the former 

 figure; and if A'C be drawn perpendicular to A'P', 

 it will represent the new equator ; and AC, which is 

 evidently in antecedently will represent the preces- 



1 



sion, and will be = PP' X - rr = = rr- 



sin obi. v sin obi. 



The Earth, however, cannot permanently revolve 

 about any diameter that is oblique to the plane of 

 the ring, because the centrifugal forces on opposite 

 sides of such a diameter would not balance one 

 another, and must therefore tend to bring the 

 plane of the ring to be perpendicular to the new 

 axis of rotation, or to make the primitive axis of 

 the diurnal rotation coincide with this last. 



The whole system of change, therefore, will begin 

 anew, as in the former case, and the pole of the 

 equator will constantly move in antecedentia round 

 G. But the curve in which it will move is the 

 circle HPK ; for as the great circle APB touches 

 this last in P, and as the arch PP' is very small, P' 

 will deviate from the circunjference of the latter 

 circle, only by a quantity that is evanescent in re- 

 spect of PP'. P' will therefore describe a circle 



round 



