142 Royal Society :- * 



the end O, let it be actually limited at a point E. If the ends of the 

 two wires at E be subjected to electric action, so as to make each 

 vary arbitrarily wth the time, the new conditions to be satisfied, in 

 addition to the others, (5) and (7), will be 



«'i=%i(0andt>2=X2(0 



(9), 



if X\ ^"^^ Xs denote two arbitrary functions, and a the length OE. 

 Or, on the other hand, if they be connected together, so that a cur- 

 rent may go from O to E along one and return along the other, the 

 new conditions will be 



^^-^^=^' -^. ^' \ (9)'. 



when 



1 



+ 



+ 



Either of these requirements may be fulfilled in an obvious way 

 by the method of successive images, and we so obtain the following 

 respective solutions : — 



-r-^[^{4'.(0)+4',(0)}dF(/)(^,#-0)+^{%,(0)+%.(0)}^^^ 



+r|{^:(0)+^.(0)}<S(/)(^. t-e) -^^ 



+ r i{^i(0)-^.(0)}dr(-/)(a;, t-6)-JL^^ 



Jo ^ (f— e)2jj 



where F, ^^ £, <B denote for brevity the following fimctiona : — 



(10) 



(10)1 



