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- 
resented by Ac will be diminished, 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 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 of 
less intensity of the inductive action will be immediately pre- 
sented to the eye, by the greater or less obliquity of the seve 
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 actiot 
will be exhibited at once by the form of AB, the first part of the é 
curve, Fig. 17. The steepness of the part Ag will indicate ale 
intense action for a short time Aa, while the part 2B denotes 4 
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 a 
would be represented by the parts between C and D of the end- 
ing of the curve. 
65. Having thus obtained representations of the different ele- 
ments of action, we are now prepared to apply these to the phe- 
4 
* According to the differential notation, the intensity will be expressed by 3, 
In some cases the effect may be proportional to the intensity multiplied by the 
quantity, and this will be expressed by ai a and y representing, aa usual, the "= 
riable abscissa and ordinate. 
