X 



Prof. Thomson on Transient Electric Currents. 397 



since the electro- dynamometer indicates the value of / y'^dtjB.nd 

 the ordinary galvanometer that of / ydt. If for 7 we use the 

 expression in either (6) or (7), we find 



as might have been foreseen, independently of the complete solu- 

 tion, by considering that, as the heat generated in the discharger 

 is the sole final efifect produced by the discharge, the mechanical 



/-»CO 



value of the whole heat generated, or / krfdt, must be equal 



^ -p-, the mechanical value of the primitive charge, and that k 



has been assumed to have a constant value during the discharge. 

 Again, we derive from (1) and (3), 



r\dt=Q, (10). 



*^ 

 Hence in the present case the expressions for the duration and 

 mean strength of the current become 



2kCJ 

 We conclude that the " duration '^ of the discharge is propor- 

 tional to the capacity of the principal conductor, and to the 

 resistance of the discharger ; and that it is independent of the 

 quantity of electricity in the primitive charge, and of the electro- 

 dynamical capacity (denoted above by A) of the discharger. 

 The only doubtful assumption involved in the preceding investi- 

 gation is that of the constancy of k during the discharge. Joule^s 

 experiments show that the value of k remains unchanged for the 

 same metallic conductor kept at the same temperature, whatever 

 be the strength of the current passing through it ; but that it 

 would be increased by any elevation of temperature, whether 

 produced by the current itself or by any other source of heat, 

 since an elevation of temperature always increases the galvanic 

 resistance of a metal. When large quantities of electricity are 

 discharged, or when the discharger is a very fine wire, great 

 augmentations and diminutions may therefore take place in the 

 value of kf and therefore the solution obtained above is not appli- 

 cable to such cases. If, however, k denote the mean resistance of 

 the discharger during the discharge, that is, a quantity such that 



kJ^'^yHt^J'^yHt .... . (1^). 



