772 Dr. J. R. Wilton on the Solution of 



and to get the corresponding term of V» we have to divide 

 the coefficient of the second logarithm in the expression last 

 printed by K. Hence a term of V is 



-E log {cosh (f-f ) -cos (jy-^o)}, 



and the corresponding term of V; is 



- P(l + l/K) log {cosh (f -ft) - cos ( V - Vo ) } 



-|E(1-1/K) log {cosh (f + | )-cos(,- % )}. 



But we must remove the second logarithm, since (if f < X) 

 it becomes infinite at — f , rj . By precisely the same 

 analysis as that just used we thus find a term of V; in the 

 form 



-P(l + l/K) log {cosh (f-f ) -cos (, - %)}, 



and the corresponding term of V is 



-{(K + 1) 2 /1K}E log {cosh (f -fj-oofl (?-%)} 



+ {(K*-1)/4K}E log {cosh (f + f ) -cos (,-*)}. 



In order that this last term should take the correct form 

 a * fo? ^o we must divide through by (K + 1) 2 /4K; and we 

 thus obtain a term of V equal to 



— E log {cosh (f — f )-cos fa-170)} 



+ {(K-1)/(K+1)}E log {cosh (£+"fid-<»fl(*-%)}. 



and the corresponding term of V; 



-{2E/(K + l)}log {cosh (f-f ) -cos fo -,„)}. 



At the singular points £=— X, tj = or tt, the part of 

 dV;/d£ arising from the logarithm in this term is 



— sinh (X + f ) /{cosh (X + f- ) T cos ^ }, 

 and the part of 'dYi/'drj is 



± sin ?? /{cosh (X + f ) + cos 77 )}. 

 Exactly the same terms arise from the expression 



-log {cosh (2\ + ? + f)-cosfo + w)}. • . (6) 

 Hence a possible term for the internal potential is 



-{4E/(K + l)}logr i; 

 and we have to determine the effect on V of the addition of 



