398 Prof. Thomson on Ti-ansient Electric Currents. 



where k denotes the actual resistance at any instant of the dis- 

 charge, the last equations (11) become merely the expressions 

 for the elements determined by Weber from observations by 

 means of the two instruments, and they are therefore applicable 

 to all cases. 



In the experiments described by Weber, the discharger con- 

 sisted of a wet cord of various lengths, and all the wire of the electro- 

 dynamometer and the ordinary galvanometer. The '^ durations '' 

 of the discharge in different cases were found to be nearly pro- 

 portional to the length of the wet cord, and equal to '0851 sec, 

 or about y^^th of a second, when the length of the cord was 

 2 metres. As the principal resistance must undoubtedly have 

 been in the wet cord, we may infer from equations (11) and (12) 

 that the mean resistances in all the different discharges must 

 have been nearly proportional to its lengths. In some of the 

 experiments the length was only :y of a metre, and the value of 

 T was about -0095 of a second. Hence the current in the string 

 must have been about eight times as intense as when the dura- 

 tion was -j^, since the quantities of electricity discharged were 

 nearly equal in the different cases. We conclude that the inten- 

 sity of the current cannot have materially affected the resisting 

 power of the cord; probably not nearly so much as inevitable 

 differences arising from accidental circumstances in the different 

 experiments. Hence, although nothing is known with certainty 

 regarding the non-electrolytic resistance of liquid conductors in 

 general, it is probable that the whole resistance of the discharger 

 in Weber^s experiments must have been nearly independent of 

 the strength of the current at each instant ; and we may therefore 

 consider the general solution expressed above by (6) or (7) as at 

 least approximately applicable to these cases. 



The two forms (6) and (7) of the solution of the general pro- 

 blem indicate two kinds of discharge presenting very remarkable 

 distinguishing characteristics. Thus in all cases in which 



k^ 1 



jxa exceeds p^, the exponentials in (6) are all real ; and the 



solution expressed by these equations shows that the quantity of 

 electricity on the principal conductor diminishes continuously, 

 and that the discharging current commences and gradually 

 increases in strength up to a time given by the equation 



j^ (j^ i_y 



1 . 2A "^ \4A« CA/ 



'^UA«"^CA/ 2A V4A« CA/ 



or j^ /j^ i_y 



1 , 2A"^V4A2 CA/ ,,„. 



'=-715 i-Vr^og-I 7-T2 T-TT • • (1^)' 



