DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
323 
1 
k 
P-( lo-I)* 
6. 
(34) 
where & is the coefficient of magnetisation, I the intensity of magnetisation, I 0 the 
maximum value of this intensity, and a, b, n constants, n being less than unity. If 
we express the intensity of magnetisation in terms of £ and rj the corresponding law 
will be 
1 a' 
k v l ~ n (Vo~v) n 
(35) 
where a' is a new constant and rj 0 the maximum value of rj. 
But by equation (32) 
so that 
therefore 
or 
1 _ 1 cUif 
k 2 r\ 
_ i d a> 
2r) drj\Bj V l ' n (Vo~vY 
-g=V-2a- r- , 
B J oV (vo—v)" 
1_7 2a' C” q" .7 
?? 2 —^)' J 17 
B 
When r)=r]Q, i.e., when rj has its maximum value 
_i_ 2 a! r(l + n)r(l-?t) 
B } Vo r( 2 ) 
where r denotes the ordinary gamma function. But 
and 
so that in this case 
r(l+n)r(l— n)= 
mr 
sin mr 
r(2)=i 
1 j 2a! mr 
B ?; 0 sin mr 
(36) 
(37) 
(38) 
this expression shows that 1/B is finite when rj — Vip but equation (34) shows that 1 [k 
is infinite when 1=I 0 , which corresponds to y] = Vo’ so that when the magnetic force 
is so great that the iron or other magnetisable substance is magnetised to saturation 
