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

 According to this the values of \j and Xg ^^'^ 



In order to form an idea as to whether these roots are real or 

 iniaginary, a particular case shall be considered. Let the wire 

 be of the standard wire of Jacobi, the resistance of which has 

 been measured by Weber. This is a copper wire of 7*620 inches 

 in length and 0-333 milHm. radius. The value of 7 is, accord- 

 ing to this, very nearly =10. Its resistance, according to the 

 electro-magnetic unit of Weber*, was found to be 



= 598.107, 



regarding the millimetre and second as units of length and time. 

 To find the resistance according to the mechanical unit, that is, 



Q 



the value of r, we must multiply the above value by -g. Now, 

 as according to the same units we havef 



c=4-39.10'S 

 we obtain 



r =2-482. 10- '^ 

 and from this we obtain 



^=2070. 



rcV2 



The quantity n, which is still left undetermined, shall subse- 

 quently be so chosen that nl may be a multiple of ir. The ne- 

 gative member under the vinculum in the expressions for Xj 

 and X2 will then be so large in comparison with 1 that it may 

 be regarded as infinitely great. This circumstance carries with 

 it a considerable simplification of the question. In the following 

 we shall only investigate the case in which the same circumstance 

 takes place, viz. where 



327 



rcV^ 



may be regarded as infinitely great in comparison to 1 : this 

 assumption will be the more nearly fulfilled the smaller the re- 

 sistance of the wire, while the ratio of its length to its radius 

 remains constant ; this resistance, however, may be considerably 

 greater than that of Jacobi's wire, without prejudicing the Vali- 

 dity of the results which we shall obtain. 



* Elektrodynamische Massbestimmungen, 1850, p, 252. 

 t Ibid. (Weber and Kohlrausch) 1856, p. 264. 



