RIGID BODY ABOUT A FIXED POINT. 303 



so that, finally, 



3M 

 BV«a - AQa = JP (A - B)Sa g Ya S . 



The most striking peculiarity of this equation is that the/orm of the solution 

 is entirely changed, not modified as in ordinary cases of disturbed motion, accord- 

 ing to the nature of the value of f. 



Thus, when the right hand side vanishes, we have the equation (49) with the 

 restriction that the body moves about its centre of inertia (easily seen to be 

 identical with that at the beginning of § 50) ; which, in the case of the earth, 

 would represent the rolling of a cone fixed in the earth on one fixed in space, 

 the angles of both being exceedingly small. 



If f e be finite, but constant, we have a case nearly the same as that of the top 

 in §§ 53, 54, the axis on the whole revolving conically about ^ . 



But if we assume the expression 



g = r(j cos mt + k cos rat) 



(which represents a circular orbit described with uniform velocity) a revolves on 

 the whole conically about the vector i, perpendicular to the plane in which f lies. 

 I hope, on a future occasion, to give detailed solutions of these problems, 

 to a sufficient degree of approximation. 



