Law of the Induction of an Electric Current upon itself. 33 
rent has reached its maximum and become constant. This is 
the obvious definition, and we shall adopt a like one for the con- 
ducting power for a discharge of common electricity except that, 
in the time, we are confined to the minute space of time occupied 
by the discharge, and in which the current is supposed to make 
but a slight approach toward the maximum or constant state. 
» Let Q’ represent the whole quantity of statical electricity, 
that passes through the wire during the time ¢ elapsed after the 
\ ft 
d 
instant when the electro-motive force begins to act. Then q7- 
will represent the whole quantity of the current at the end of the 
2 t 
aE. 
dz: Will represent the rate of development of the 
current in the whole wire. Let K represent as before the value 
time t, and 
dQ . 
of 7, at the centre of the cross section abd fig. 6, of the wire. 
d : 
Then by the law above laid down, the value of so at any point 
in the circumference of any circle concentric with abd, and 
whose radius is r, will be 
KR 
VR a7? 
and this multiplied into the area of the elementary ring included 
between the limits of r and r+dr will give 
piciayh sac el 
for the rate at which the current is developed through the ele- 
\ mentary ring ; and the integral of this taken between the limits of 
r=Qand r=R will give the rate of development of the whole 
current thus : 
dz? 
whence we have 
d?Q’ ends 
aire — =nKR? 
=2 KR Terk 
d?2Q’ 5 a 
Ka-ip %aR* x 
: of the current to the section of the wire and to the indue- 
‘Seems, Vol. XI, No, 81—Jan, 1851. 5 
