ON ELECTRO-DYNAMIC INDUCTION. 21 



equal ordinate, Cd, will represent the whole induction in the other direction 

 at the ending of the same current. Also, the whole time of continuance of 

 the inductive action at the beginning and ending will be represented by A c 

 and dJ). 



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

 but more rapidly than before, then the time represented by A c will be dimi- 

 nished, while the whole amount of inductive force expended remains the same; 

 hence, since the same quantity of force is exerted in a less time, a greater in- 

 tensity of action will be produced, (57,) and consequently a current of more in- 

 tensity, but of less duration, will be generated in the secondary conductor. 

 The relative intensity of the induced currents will, therefore, evidently be ex- 

 pressed by the ratio of the ordinate cB to the abscissa Ac. Or, in more gene- 

 ral 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 presented 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 gradu- 

 ally immersed 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 Kg will indicate an intense action for a short time A a, 

 while the part ^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 

 afterwards slowly, we may produce an inductive action such as would be re- 

 presented by the parts between C and D of the ending of the curve. 



65. Having thus obtained representations of the different elements of action, 

 we are now prepared to apply these to the phenomena. And, first, however 

 varied may be the intensity of the induction expressed by the different parts 

 of the two ends of the curve, we may immediately infer that a galvanometer, 



* According to the differential notation, the intensity will be expressed by i^ . In some cases the 



dx 



effect may be proportional to the intensity multiplied by the quantity, and this will be expressed by 



dy 



— -J "- — 



VIIT. — F 



, X and y representing, as usual, th(3 variable abscissa and ordinate. 

 ax 



