280 Mr Hicks, On the problem of two [Oct, 27, 



But if V is the image of a , 



b b^ , V 



/^„> 



whence 



» Sdt{c-pJ{c-p:)' 

 and 



" v^^ {c-pjic-pj "^ (c-p,/ic-p:) 6 .?^r 



Next there is to be determined the action on A from B. Using 

 the results already obtained, it is easy to show that this force is 



„ 27ra' ^ d (a-^-aJ)v^, it ^ d , ,. 



^=-r^dt {c- aj\c - a-:) + 3 ^ j/^" " P" ^^»- 



If /u,,j_^j be regarded as the image of v^, it will be found, since 

 the part of Y due to [x^ is zero, that 



^ ((i^ a^ a^ a dt) 



By means of formulse in the paper before referred to* but not yet 

 published, it is easy to express X, Y explicitly in terms of the 

 radii, their rates of change, and the distance of the spheres. 



4. If we are content with approximations so far as to include 

 three images in B and in J. ; X, Y may easily be determined with- 

 out reference to the general formulee. 



For writing r now for c 



and 



Po =^> Po' = ^ , 



_ aV , _ a' 



^ d'rir'-d'-b') , _ d'ir^-a') 



P^ (/ _ by - d'r' ' P-' ~ r{r'-d'^^ ' 



_ ah _ a'b" 



_ ^da _ 1 dm^ 



where m^^ is the mass of the fluid displaced by A at any time. 

 Sabstituting these values 



¥_d{]\Q 



4r' dt ' 



a' dN^ 



4r' dt ' 



* Proceedings, Royal Society, No. 197. 



