DYNAMICAL PRINCIPLES TO PHYSICAL PHENOMENA. 
337 
The effect of temperature depends, too, upon the magnitude of the magnetising 
force; thus Baur (Wiedemann’s Annalen, xi., 1880) finds that for soft iron the 
coefficient of magnetic induction increases with the temperature if the magnetising 
force be less than about 3'6, while if the magnetising force be greater than this the 
coefficient of magnetic induction diminishes as the temperature increases. Equation (8 8) 
shows that if this is the case df{rj)jdyf must be a function of rj ; it is probably of the 
form a {1 — Kyf }, where the critical value of g is l/\/ k. 
Since the As are kinosthenic coordinates { uu } cannot be a function of them. 
As the coefficients of elasticity depend upon the temperature {uu} will be a function 
of the coordinates which fix the strain configuration of the system ; now the coefficients 
of elasticity are the coefficients of the squares of the strain coordinates in the expression 
for the kinetic energy ; so that using the ordinary notation for the strain coordinates 
we may suppose that the term 
l{ a (c+/+ t q)H^(e 2 +/ 3 +/-2e/-2^-2/^+a 3 +& 2 +c 3 )}{^j+ . . .j (95) 
occurs in the expression for the kinetic energy T ; in T', the function which takes the 
place of T in the modified Lagrangian equations, this term will occur with the opposite 
sign. 
Since the equation for any of the coordinates a, b, c, e, f g is of the type 
clT dY 
——+— = external force of type e .(96) 
de de J1 ' ’ 
we see that the effect of the presence of the term (94) is the same as if the coefficients 
of elasticity denoted by Thomson and Tait in their treatise on Natural Philosophy by 
the letters m and n were increased by 
a 
P 
{ v \ 
L 1 
{^2 %} 
or a 9 
[ugh) {%%} 
+ . . . I or /3d 
1 
J 
(97) 
respectively, if 6 be the temperature, since we may neglect the small part of it due to 
the terms we are considering. Let us now consider the effect of this term upon the 
temperature, and to illustrate the point in the simplest way let us suppose that all the 
strains but e vanish, then if e 3 be increased by Se 3 the corresponding increase S© in the 
temperature is by equation (95) 
i ( “+«( tW + '-') Se5 . (98) 
or 
S0=i( a +/3)l9Se 3 .(99) 
