Law of the Induction of an Electric Current upon itself. 27 
value of the integral therefore cannot be zero for all values of z 
unless : 
es sin ¢’=0 
and consequently 
; +R sin ¢ 
f sing’= =f F'dx= constant. 
-R sin 9 
Let now the function F' be expressed as a series of powers of its 
root R? sin? g’ — z?, so that 
F=L (R? sin? g’ —2?)"+L/ (R? sin?y’ -7?)"+ &e. 
=2}L(R? sin’g’—ax?)"? 
Then putting z=u Rsin ¢’, we shall have 
+R sin p Ha : 
vz Pas=z| 1 (Rsingyes [(-n2ye| 
R sin g! 
The second member of this sare expresses a series of 
powers of Asin’, and this series cannot be constant or inde- 
pendent of ¢’, except for the single nai in which the exponent 
of the power is =0 or n=—3. The coéfficients of all the 
_ other powers Paes =0, and this requires that Z=0 in those 
terms since 
= | 
_ for all values of m. This reduces the above value of F' to 
a —u*)"du is necessarily greater than zero 
: = (G) F=L(R?sin?¢ -—2*)$ and 
Se a R 
oe a ar =f du 9h sin) 1=L. 
q -R sing’ (1-u?)3 
; Substituting this value in (F”) and putting L=KR we have 
(F”) Fp =CKR*. 
18. If we now draw “6 chord pho perpendicular to mn we 
have (R? sin? 9’ - x? P=(kh. hl)? = hp or ho, and consequently 
the value of a or F'as given in G becomes 
7 ’ therefore, an ‘ae current is generated in a 1 long 
rical wire, by an electro-motive force that acts unt- 
throughout its mass, the rate of initial development Ss the | 
