458 
Proceedings of the Royal Society of Edinburgh. 
[Sess. 
and 
db da 
0H = 0F 
( 6 ) 
The differential coefficients of a, b, and c cannot he easily determined 
experimentally; hence we eliminate them by combining (1) with (4), (2) 
with (5), and (3) with (6), and obtain 
and 
dx 
b 
0T = 
T ’ 
v 0B 
a 
477- 0T 
T ’ 
v 0B 
dx 
47 r 0F 
0H' 
The first of these is the well-known relation between the coefficient of 
linear expansion of a wire and the cooling effect produced on stretching it. 
The second relation states that if the induction in a wire increases with 
temperature, a is positive, and consequently the temperature will fall if 
H is increased ; if the induction diminishes with temperature, the 
temperature of the wire will rise if H is increased. This theorem has 
been derived before by Lord Kelvin,* and in quite another way. He 
states the result differently, — that a substance in which the magnetism 
diminishes with temperature when drawn gently away from a magnet 
experiences a cooling effect ; a substance in which the magnetism increases 
with temperature when drawn gently away from a magnet experiences a 
heating effect. This cooling and heating effect is probably always masked 
by the irreversible heating due to Foucault currents in the wire, and to the 
viscous resistance to the motion of the molecular magnets. 
The third relation states, that if the induction increases when the wire 
is stretched, the length of the wire increases when it is magnetised, and 
vice versa. The connection between magneto-striction and the effect of 
stress on magnetism has been worked out several times, amongst others 
by J. J. Thomson in his Applications of Mathematics to Physics and 
Chemistry. The result nearest mine is given by A. Heydweiller.j* His 
equation is 
0E_ _E 2 02JB 
0H 47 r dp 2 
E being Young’s nodulus for the wire and p the stress per unit area of 
* “ On the Thermo-elastic, Thermo-magnetic, and Pyro-electric Properties of Matter,” 
Phil Mag. (5) 5 (1878), p. 4. 
t“Zur Theorie der magneto-elastischen Wechselbeziehungen,” Ann. d. Phys. (4) 12 
(1903), p. 602. 
