DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
335 
U(v) 
T will contain the term 
V , 
2 
' 2 + 
{«!?<! } 
{ Ui u 2 } ' 
modified Lagram 
o 
I v? 
4- 2 4- 
1 r 1 
(82) 
• • • • (83) 
but we saw before in equation (25) that T also contained the term 
iii 2 
2 B 
so that if H be the external magnetising force we have, by the modified Lagrangian 
equations, 
iA(t£) + L rM !^L 
‘‘ dri\ E ! + " J "I !«,)-,! 
u l\ {%« 2 } 
so that if k be the coefficient of magnetic induction 
(84) 
1_JL d^ 
1~J 2 drf 
d V ■ 
(85) 
where © is the temperature. It is convenient to write the terms in this way, because 
f{rj) must be an even function of rj, otherwise the magnetic susceptibility would be 
altered by reversing the direction of magnetisation. If k 0 be the part of the magnetic 
induction which does not depend upon the temperature 
i_i L i A ft 
Jc~k 0 + P 
so that, approximately 
( 86 ) 
(87) 
if we suppose that the second term in the bracket is small compared with the 
first, thus 
dk__ W d_ 
( 88 ) 
Now let us consider the effect of this term on the temperature. There is in the 
expression for the kinetic energy the term 
2x2 
(89) 
