254, 255] ELECTROMAGNETIC WAVES. 541 



and let us suppose that initially the state of the line is given, that 

 is the potential and current are given at all points, by 



(2) 



Let us transform the equation by putting 

 (3) F= e* u. 



Accordingly 



so that if we put p = b the equation becomes 



The initial conditions now become 



The method of Boussinesq may be applied to the more general 

 equation 



which we shall accordingly consider, putting whenever we choose 

 u independent of y. The artifice employed is the introduction 

 into the function u of one more degree of freedom, by making it 

 depend upon another parameter z which is finally to be given any 

 constant value we please. Let then u satisfy the auxiliary equa- 

 tion 



(8) 2 ^ = 62 . 



so that the equation (7) becomes, taking this into account, 



