Dr. R. A. Houstoun on Magnetostriction. 79 



5H + 4tt3F BK^aH ' ' ' ' v; 



TdF~-dT\Ty~TbL' T 2 * * ' * v / 



13c dc/a\ __ 1 da __ a /n 



T3H"3TW"T3T T 2 " ' " " KJ 



and B^_3^ CQ 



BH~BF 



The differential coefficients of a, 6, and c cannot be easily 

 determined experimentally ; hence we eliminate them by 

 combining (1) with (4), (2) with (5), and (3) with (6), and 

 obtain 



B-r _ \ 



3T " T' 



u 3 B _ a 



4^-3T~r 



and j^3B_3^ 



47rdF"~BH" 



The first o£ these is the well-known relation bet ween the 

 coefficient o£ 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 sub- 

 stance 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 is the one that the paper is mainly con- 

 cerned with. It states, that if the induction increases when 

 the wire is stretched, the length of the wire increases when 

 it is magnetized, and vice versa. The connexion between 



* '' On the Thermo-elastic, Thermo-magnetic, and Pyro-electric 

 Properties of Matter," Phil. Mag. [5] v. (1878) p. 4. 



