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XII. On Magnetostriction. By R. A. Houstoun, M.A., 

 D.Sc, Ph.D. j Lecturer on Physical Optics in the University 

 of Glasgow*. 



I^HE object o£ this paper is to derive a relation connecting 

 magnetostriction with the change of magnetization 

 produced by stress and to test it by the results o£ experi- 

 ment. In substance the relation is not new but in method 

 o£ statement it is, and the derivation presented here is shorter 

 and simpler than other methods. The paper also proves in a 

 new and simple way a theorem due to Lord Kelvin. 



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 

 Fd# + rHdB/47r. Let U be the intrinsic energy of the wire 

 and S its entropy. Then — 



= ( c + F BT + S BTf T + V' + F BF + ^ *F) dF 



and 



dS=^T+|dF+|iH. 



Since these are perfect differentials, we have the following 

 six independent relations : — 



B^_, Bf _B?> /-.x 



BF + 3T ~BT w 



Be v_ BB _ B« / 9 \ 



BH + 4ttBT ~bT K "' 



* Communicated by Prof. A. Gray, F.R.S. Part of the matter of this 

 paper has appeared in " On Two Relations in Magnetism," Proc. Roy. 

 Soc. Edin. vol. xxx. p. 457 (1910). 



