M. G. Kirchhoff on the Motion of Electricity in Wires. 403 



According to the above assumptions, the values of A., and Xg 



^vill be 



en ^ 



h+ -—= 4/_l 



where, for the sake of brevity, we have placed 



32yl~ 



Introducing new constants in the place of Cj and Cg, the ex- 

 pression for X may be brought to the form 



X=e-*M Acos — -= + Bsm — = 1. 

 \ \/2 V'2/ 



Hence w^e obtain 



-hi 



^-- , \(-A- 4^b)cos e^+(4.A+^B)sm^-^l. 

 2 \\n i/2 / \/2 Vv'2 w / \/2\ ' 



I will assume that for / = 0, i is =0, hence also Y = 0; this con- 

 dition gives 



nc 



The quantity n, as above remarked, shall be set equal to a mul- 

 tiple of -J- ; hence the denominator of the expression for B will 

 be a multiple of c 



'^■hwr 



but the quantity here multiplied by tt is 

 _ 327 



~ re v'3 ' 



that is, the precise quantity which has been assumed to be infi- 

 nitely great. Hence B will be infinitely small in comparison 

 with A, and we may set 



X = A . e-*' . cos — ;=, 

 \/2 



Y= — jr — ;=Ae-*'sin— -=. 

 2^2 \/2 



Multiplying these expresions respectively by sin ns and cos ns, 

 and setting the products equal to e and i, we obtain a partial 

 solution of the differential equations for e and i. This solution 

 may be generalized by adding in it to s an arbitrary constant ; we 



