1909-10.] 
On Two Relations in Magnetism. 
457 
XXXI. — On Two Relations in Magnetism. By R. A. Houstoun, 
M.A., D.Sc., Ph.D., Lecturer in Physical Optics in the University of 
Glasgow. Communicated by Professor A. Gray, F.R.S. 
(MS. received April 27, 1910. Read June 6, 1910.) 
The object of this paper is to derive two relations in magnetism. In 
substance they are not new, but in method of statement they are, and the 
derivation presented here is shorter and simpler than other methods. 
Consider a ferro-magnetic wire hanging vertically inside a vertical 
solenoid with heating jacket, a pan being attached to the lower end of 
the wire for holding weights. Then, if hysteresis be neglected, the state 
of the wire may be regarded at any time as a function of the three 
independent variables T, F, and H, — temperature, stretching force, and 
magnetic field intensity. If T, F, and H suffer small changes, then the 
heat received by the whole wire is given by 
dq = cdT + bdF + adK. 
Let B denote the induction in the wire, v its volume, and x the vertical 
displacement of its lower end. Then the work done on the wire when 
F and H are increased is Fc&r + vHcTB/47r. Let U be the intrinsic energy 
of the wire and S its entropy. Then — 
d\J = dq + 'Edx + ' Md - 
4 7T 
0T + 4^ 0T 
W+(i 
-p, dx FH 
+ F 8F + 4^ 
j-n / -ddX vW. 0B 
dF + ( a + F_ + — — 
dR, 
and 
dS=^dT + ^dF + i*dH. 
Since these are perfect differentials, we have the following six 
independent relations : — 
0C 
dx 
db 
0F 
+ ST 
~ 0T 
0C 
V 
0B 
da 
0H 
+ i-. K 
0T = 
"0T 
db 
V 
0B 
da 
dx 
0H 
+ Vtt 
0F = 
~ 0F 
+ 0H 
1 
0C 
d ( 
b \ 
1 
db 
b 
T 
0F = 
II 
OJI 
HI 
T/" 
~ T 
0T 
T 2 
1 
0C 
d f 
a \ 
1 
da 
a 
T 
0H 
0T\ 
t; 
T 
0T 
J2 
( 1 ) 
( 2 ) 
(3) 
(U 
( 5 ) 
