CO 



JEolotropic Potential. 447 



functions of the time, these terms involve a departure from 

 the category of stationary motions assumed at the outset. 

 The terms involve an exchange of radiation with the outer 

 field, and the period is half that of the rotation. 



TO 7 



Equation (56) also contains the terms -j + 2P -, . If for 



a rotating ellipsoid we take = ^7 a> 3 v + © 2 w j tnen if t 



at 01 JO 



is not explicitly contained -v- = — w s v-tfo 2 w, and — - and 



SP -7- have values. But so far as S depends only on uvw, 



jo 

 P= — 7— and the terms in question are cancelled. The 



contribution of S belonging to co s is co 5 (u, : —v—) or 



z dS dS\ -, </S dS . ,, . p r> i 



\ P ,- - — 'i-r~ I ; and u v -7— is the correct iorm tor the 



V dq 1 dp J dv du 



couple due to dynamical asymmetry. Its value taken from 

 (107) agrees with that given by (119). Thus if we choose 



we may regard 2P -5- + I SX'^cfo-j as the cancelled terms, 



and these terms in -7- as remaining ; which simplifies the 



dynamical statement of (56) . 



The terms pZ' + ^ f (i x /3 — i !/ u) occur in the equation for 



mechanical -force (59). The Z' of the vector potentials and 

 the a/3 of the scalar potential contribute to the integral of 



these terms. Attending to the first type X'= XpF, we 



first evaluate -^dWi quoting the value (§30, p. 441), viz.: 

 %j 



[with I* for &...1 



+ C/8 ,2 +2C' a7 '-|-2B , « / 8'+2A'^V) I, 



=;? (;^ )qn o t i Bg (iu). 



