22 Law of the Induction of an Electric Current upon itself. 
which expression differs from $7 only by a small quantity of the 
third order, so that if the conductor be extended till it subtends 
an angle wer closely approaching 180°, the inductive force due to 
all beyond that limit will be insensible* in practice, the value of 
fcoos?#d remaining nearly constant. Hence, what was stated 
of that part’of the conductor included jn a fixed angle fcf’, may 
be affirmed also of a determinate length wa of the conductor so 
long as the distance cp is very small compared with either pv or ~ 
pw, that its: inductive action parallel to itself is inversely as the 
distance, and this action is expressed thus : 
(C) ot c dg e 
7. The expression for the induction at right angles to cd’ or 
in the direction of pe will be identical with that for the induction 
in the direction of cd’, except that instead of the circular function 
7! 
cf cos ?6/d © in equation (B) we shall have 
: 
7! 
A sin & cos & d# =4(sin 27’ — sin 77) 
7] 
a 
which is necessarily zero or insensible when the limits 7 and 7! — 
are equal and of contrary signs or when each differs very little 
from 47, whence it follows that for any portion of the conductor — 
bisected in the point p, or for any portion extending to a very 
great distance on both sides of p, the induction in the direction 
“of pe is nothing or insensible. The phenomenon known in ae 
chine electricity as the lateral discharge, cannot be considered at 
variance with this statement, as that is readily explained without 
reference to the existence of an inductive force in that direction 
of the kind now under consideration. foe 
Induction of an electric current upon itself, when developed in — 
a, straight prismatic conductor of great length. i 
8 [have already stated that Prof. Henry was the discoverer 
of the induction of a current upon itself, and that he was the first 
to refer it to the primary law of induction at a distance. A con- — 
4 
—e 
* Similarly it may readily be shown that if the current be returned into i 
through a return circuit passing everywhere at a great distance the inductive fore 
Aue to the return circuit will be insignificant. . 
° 
+ = 
