Effect of Stress on Magnetization, 101 



effect ; and the discrepancy is remarkable in low magnetic 

 fields, as may be expected from the consideration of the 

 hysteresis effect prominent in that region. 



In our preceding paper, we have remarked that the de- 

 pendence of the change of elastic constants on the different 

 orders of magnetizing and straining i« probably due to the 

 hysteresis effect accompanying magnetization. This ex- 

 planation agrees well with the facts brought out by the 

 present experiment. 



§ 4. Reciprocal Relations. 



Among several important reciprocal relations obtained by 

 J. J. Thomson, the two relations which have connexion with 

 the present experiment are referred to below. 



Let a cylindrical bar of soft iron, whose axis coincides 

 with the axis of x, be magnetized along its axis. Let £, /, g, 

 be the dilatations of the bar parallel to the axes of x, ?/, z 

 respectively; J. J. Thomson obtained the relation 



n -dl 2 ~-2\ 1 R Vbl) e ,fJ L3m-n *I Wh. 



U 



3,u-na\d/y H ,^J' " ' w 



where I, H, k have the usual meanings, n represents the 

 coefficient of rigidity, and m is connected with the modulus 

 of compression k by the relation 7c = m — n/3. In his original 

 work the factor \ is dropped in the right-hand member of 

 the above equation ; the error is to be traced back to his 

 equation (41). 



Since dL = /cdK + Hd/c, we have the relation, supposing the 

 strain to be kept constant, 



l-H^ft = - * 



Hence equation (1) may be written 



dI\dH/ e ,/,<7~"ft(3m— n)\de )kj4 '/i(3m— rc)\B//H,e,/ 

 Again, if T is the tension per unit of area, we have 



