138 Contributions to Electricity and Magnetism. 



and this will, therefore, also represent the whole amount of in- 

 ductive action exerted in one direction at the beginning of the 

 primary current ; and for the same reason, the equal ordinate, Cd, 

 will represent the whole induction in the other direction at the 

 ending of the same current. Also, the whole time of continu- 

 ance of the inductive action at the beginning and ending will be 

 represented by Ac and dD. 



63. If we suppose the battery to be plunged into the acid to 

 the same depth, but more rapidly than before, then the time rep- 

 r'esented by Ac will be diminished, while the whole amount of j 

 inductive force expended remains the same ; hence, since the 

 same quantity of force is exerted in a less time, a greater inten- 

 sity of action will be produced, {57^) and consequently a current 

 of more intensity, but of less duration, will be generated in the 

 secondary conductor. The relative intensity of the induced cur- 

 rents will, therefore, evidently be expressed by the ratio of the 

 ordinate cB to the abscissa Ac. Or in more general and definite 

 terms, the intensity of the inductive action at any moment of 

 time will be represented by the ratio of the rate of increase of 

 the ordinate to that of the abscissa for that moment.* 



64. It is evident from the last paragraph, that the greater or 

 less intensity of the inductive action will be immediately pre- 

 sented to the eye, by the greater or less obliquity of the several 

 parts of the curve to the axis. Thus, if the battery be suddenly 

 plunged into the acid for a short distance, and then gradually im- 

 mersed through the remainder of the depth, the varying action 

 will be exhibited at once by the form of AB, the first part of the 

 curve. Fig. 17. The steepness of the part A^ will indicate an 

 intense action for a short time Aa, while the part g-B denotes a 

 more feeble induction during the time represented by ac. In the 

 same way, by drawing up the battery suddenly at first, and af- 

 terwards slowly, we may produce an inductive action, such as 

 would be represented by the parts between C and D of the end- 

 ing of the curve. 



65. Having thus obtained representations of the diflferent ele- 

 ments of action, we are now prepared to apply these to the phe- 



* According to the differential notation, the intensity will be expressed by -j^. 

 In some cases the effect may be proportional to the intensity multiplied by the 

 quantity, and this will be expressed by -^, x and y representing, as usual, the va- 

 riable abscissa and ordinate. 



