Law of the Induction of an Electric Current upon itself. 23 
the figure e, the portion of current conducted 
by the bundle may be distinguished as the 
current through the figure or area e. We 
shall first suppose the development of current 
to be equally rapid through all parts of the cross section of the 
conductor (i. e., through any two spaces e, e’, of equal area), and 
compare the magnitudes of the inductive forces at different points 
of the cross section abd. 
9. Let ¢ be the point at which the inductive force is to be 
estimated. Through c draw the straight lines men and ocp, 
; part of cp 
and draw the perpendiculars Sh and gk, The inductive force 
exerted at ¢ by the current through the area fk is given by form- 
ula (C). If Q represent the quantity of current passing at a 
_8iven instant through a unit of sectional area, the quantity ¢ 
_ Passing through /& will be 1 
9q=Qx area fk and “i= area fk X ape 
a” f=r, fe=dr, fh=r dg, area fk=r dr dq, and if 
We denote the whole inductive force exerted at ce, in a fibre of 
the length s, by the current through any portion of cgrs of the 
Cross section, by P, we shall have J = drdg?” dg. 
Substituting these values in (C), we have for the inductive 
force exerted at c by the current through /* 
I d?P dQ 
(D = = = = =, drdg. 
(D) ds didrien ** aa; dase: 
As dQ. ae 
4s Q and consequently az is at present supposed to be the 
a Bogs for all parts of the section abd, it follows from (D) that 
‘Me inductive force due to the current through fk is simply pro- 
lene to the magnitude of the elementary angle nep and to the 
length of fg, independently of its distance from c, and that the 
na. vorce due to the current through the triangular spaces 
and meco is 
d4P dQ 
dsd@ Senne 7, H9%, 
