Disturbing Force in Problem of Three Bodies. 147 



will then have to be settled is that of the uniqueness of the 

 representation. It seems likely that there is only one set 

 of elementary fields which, when added together, will be 

 equivalent to a given electromagnetic field for the whole 

 domain of the real variables x, y, z, r, but this proposition 

 evidently requires proof. 



A further difficulty arises from the fact that we can find 

 wave-functions which are homogeneous functions of degree n 

 in x—a, y — b, z—c, t — e, where n is not an integer. There 



are also manv valued wave - functions such as tan -1 -. 



x 



Electromagnetic fields in which the components of E and H 

 are represented by wave-functions of this type are, however, 

 excluded by the condition, stated at the outset, that the 

 components of E and H must be one-valued functions of 

 x, y, z, t for the whole real domain of these variables. 



XIV. On the Action of a disturbing Force in the restricted 

 Problem of Three Bodies. By R. J. Pocock, B.A., 

 B.Sc, Queen's College, Oxford*. 



IN the restricted problem of three bodies, let H, J re- 

 present the two larger bodies, P the particle. Let J 

 be of mass unity, H of mass v, and take HJ as unit distance. 

 Let n be the mean angular velocity of J ; r, p the bipolar 

 co-ordinates of P referred to H and J. Then with reference 

 to HJ and a perpendicular thereto through the C. Gr. of H & 

 J as moving axes rotating with angular velocity 71, we have 

 the equations 



.. . 3n"l 



These equations admit of Jacobi's integral, viz. : 



where V denotes the velocity of P and C is a constant. 



2. Let us now suppose that an additional bodv S of mass /u. 

 is introduced into the system. It is assumed that IS is small 



* Communicated by the Author. 

 L2 



