24 Law of the Induction si an Electric Susie _ itself. 
aS which E represents the length of the chord: mn. Now if a 
straight line revolve about the point ¢ from the position 0-180, 
through a half revolution it will describe all the elementary trie 
angles mco and pen that make up the section abd. he | 
fore integrating (E) between the limits of p=o and g=z2, a 
have finally for the inductive force exerted at ¢ by the ital 
current: 
: dP aap eon! a 
(F), ap = ie ——~_.” Bao, | 
10. If the rate of development ~ be not constant through a 
all parts of the section abd, then EF in equations (E) and 
(F") must be replaced by 
A 
ay 
aro" 
in which 2 and 7’ denote the eines of me and en, and the equa- a 
tions (E) and (F) becom 
6 ae a7% r] dg, and 
~h 
(E’), 
. 
: a? a Beer: Q 
Comparison of the inductive forces at the centre and vale : 
ni- 
of along cylindrical conductor, when the development is 
formly rapid throughout its mass 
11. Let fig. 5, represent the cross sec- 
tion of a cylindrical conductor or wire of 
a great length in comparison with the di- 
ameter, which we will call 2, and let us 
suppose a current to be developed with 
equal rapidity through all parts of the sec- 
tion. Then in finding the whole induc- 
tive force at the centre ¢ by formula (F) 
we have the chord # always a diameter 
or =2R, and consequently 
fr Edo=2R, 
while for the point ¢’, the chord c’ n/= OR sin Te nor Baa @ 
sin g, an 
TE ‘ V4 
Edg=2R ingd AR. 
Jf: Rf pdg= 
