172 WRITINGS OF JOSEPH HENRY. [1840 



62. The sum of the several increments of the battery cur- 

 rent, up to its full development, will be expressed by the 

 ordinate c B, and this will therefore also represent the whole 

 amount of inductive action exerted in one direction at the 

 beginning of the primary current; and, for the same reason, 

 the equal ordinate, C d, 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 b}^ A c 

 and d D. 



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 ^ c 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 intensity of action will be produced (57), and 

 consequently a current of more intensity, but of less dura- 

 tion, will be generated in the secondary conductor. The 

 intensity of the induced currents will therefore evidently be 

 expressed by the ratio of the ordinate c 5 to the abscissa A c. 

 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 

 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 gradually immersed through the remainder of the 

 depth, the varying action will be exhibited at once by the 

 form of A B, the first part of the curve. Fig. 17. The steep- 

 ness of the part A g will indicate an intense action for a 



* According to the differential notation, the intensity will be expressed by 



dy 



— . In some cases the effect may be proportional to the intensity multiplied 

 dx dy^ 



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



dx 



usual the variable abscissa and ordinate. 



