: 
20 Law of the Induction ss an Electric Current upon itself. 
of a line ed’ which makes with cd- he angle 1 either i in the plane 
abe or -out of it,” We must resolvé the force in-the direction of 
ed in the same manner as:any. other-electro-motive force or as a 
mechanical _— so that if MM represent the whole force in the 
direction of cd: and M’ the ie ee ae in the direction of cd’ 
we shallhave °°. W= 
- Thus we shall finally have thie inductive force exerted at c in the 
direction of ed’ proportional to _ - 
; 3 dq costsin 0d2. 
dé Bee Fg : ; 
4, This regards the inductive force as exerted ata ae point, 
but all experiments show that it accumulates along the secondary 
conductor in proportion to its length. Let Ab, ie 2, be the 
primary conductor and cC the secondary, 2 ‘ 
and let I represent the whole. inductive ee ce ae 
force exerted by Aa on the shale second- 
ary cC of which the length =s. Then — ¢ 
the whole inductive force erated on the 
element cd’=ds (and which may be solely assumed to be pro- 
penal to cd’) will he expressed by ds ds, and that exerted on 
d2f 
ed! by “i will have for its expression 24 qpasdl. renee we 
shall have ~ ee x 
d* Fe Od cos t sin 0 
(A) dedin ates ae 
'Phis equation then in which C represents a constant cle 
value has never yet been determined by experiment, is the gen-_ 
“eral differential equation for the induction of electric currents so 
far as concerns the relation of primary and secondary linear con- 
ductors to each other 
The lines 7, D, and s aie circular functions cos t a sin 6 may 
readily be referred to rectangular coordi- : 
nates in space, but ay my present purpose 
this is not necessar 
_ §.*From (A) it Polly follows that, 
ay an electric current be developed in a 
straight wire of unlimited length so small. 
that it may be regarded asa line, the force 
of induction in a direction parallel with 
the wire at any given point. will be in- 
pre as the Penendicular. distance of 
at point from the wire. 
et PN, fig. 3, be fa ‘accaight Spe. 
let cd’ be the gi 
* 
av 
‘wire and let 
