Dr. Hirst on Equally Attracting Bodies. 367 



18 of a system of four equally attrai 



general equations of a system of four equally attracting surfaces 

 will be 



Y ' (21) 



24. As an example of the above method, let us assume f{0, <f>) 

 to be a product of two functions ; one of alone, and another 

 <!> of (f) alone. Under this hypothesis the variables in (20) are 

 at once separable, and we have 





so that the four equally attracting surfaces of (31) are represented 

 by the equations 



1.(23) 



25. To descend to particular cases of these formula); let, in the 



first place, 



©=<I> = l=M«/>); 



the equations (23) will then become 



r = ^ =M.[log(tan I) +^] .% [log(ta4) -,;,], 



". >■'■ ^,[log(tan|)-.J,]' 



whose form is somewhat similar to that of the equations in art. 

 22. Hero, however, the surfaces (r) and (r,) have not in general 

 tlR'ir corresponding normal vector-planes perpendicular to each 

 other; in fact, it may be shown that it is only when 



^(?)=%(?)=^^^ 

 where m is an arbitrary constant, that (r) and (?*,) possess this 



