Dr. It. H. Jude on the Application of the 

 The electrostatic capacity of the pair of spheres is of course 



Qa+Q b . 



— v — ' *■ e - 



If the spheres he equal, -— —r and are each J. Now 



r * a + b a-\-b 2 



putting n = ^ in (3), we have 



= 21og e 2. 



Hence by (6) the capacity of a pair of equal spheres each 

 of radius a in contact is 2a log e 2. 



In the general case if we put n= — —r, we have 



1-71 = 



a+b' 



a 



a + b 

 Now 



Slll?i7T 



.*. taking logarithmic differentials, 



d\ogT(n) d\ogT(l-n) 



= — 7T cot nir ; 



~d)i d(L—n) 



i. e. 



H(4 7 )-H(4 7 )= OT cot4 K ; 



\a + bj \a + b) a + b 



whence by (5) and (6) 



Qa — Qb irab irb 



cot 



V a + b a + b 7 



a relation otherwise demonstrated by Maxwell. 



Incidentally it may be noted that the Eta function affords 

 -a neat expression for the sum of n terms of an harmonic series 

 provided none of its terms be negative ; the result can easily 

 be shown to be 



a^ a + b x o + 26 ^ 



s*p=m-H H ©- a (r«)J 



