1877.] The Rev. S. Haughton on Physical Geology, 535 



The equations of motion are : — 



Adp + (C—A)qr dt=Itdt, ~\ 



Adq+(A-C)prdt=Mdt,l (1) 



Cdr =mtj 



where 



A = moment of inertia round equatorial axis, 

 C= „ „ „ polar 



^ I = components of rotation round the axes y, z, 

 ^ I inside the earth, 



M V couples of forces acting round axes cc, y, z. 

 NJ 



First Approximation. 

 Let there be no disturbing forces, then 



L=M=N=(Vl 

 A^+(O-A) r ^=0 5 I 



Adq+(A-C)prdt=0,f {) 

 Cdr =0^ 



If we assume 



p=p cos u, 

 q=p sin u, 



p will be the total equatorial component of rotation, and u will be the 

 angle made by the meridian of the axis of rotation, with a meridian sup- 

 posed fixed in the body. Transforming (2) to the new variables, we find 



Apd p = 0, i 



Adu-(C-Aydt = 0,i ........ (3) 



Ccfr=0. J 



Integrating, we obtain 



r=r, 



0' 



u=n't-\- const., 

 where p , r are the initial values of p, r, and 



, C-A 



(4) 



A 



or, substituting for C, A, their values (given in Note I. p. 52), 



r 



The preceding integrals show that the motion of the instantaneous 

 axis is uniform, and that it moves on the surface of a right cone, whose 



2p2 



