Elasticity of Ferromagnetic Substances by Magnetization. 69 



and then the upper circle was twisted in the opposite sense, 

 until the mirror regained its original position for no field. 

 Let the angle through which the upper circle was twisted be 

 denoted by 0' \ 0' was nearly equal to 0. After demagneti- 

 zation by reversals, the mirror usually turned through a small 

 angle ; but the amount of the rotation was usually so small 

 that we could leave it out of account. Different fields were 

 successively applied and corresponding deflexions were read 

 off. Xext the twist was increased and the procedure repeated. 



The experiments were made also for different tensions. 

 Before increasing the tension, the wire was untwisted to the 

 original state of no twist, after passing through a cyclic twist 

 of gradually decreasing amplitude about the position of no 

 twist. This procedure was always necessary to restore the 

 wire to the state of no twist, since the simple untwisting 

 usually left a residual deflexion. 



If the couples required to give unit twist to the two wires 

 be t and t' respectively, we have 



t9 = t'0' ; 



if the angular deflexion of the mirror due to magnetization 

 be 80, and 8r the increment of r, we have 



t„ = t + 8t and (t + 8t)(0-80) = t'(0' + 89) 



or 





Tn (O-88)=T , (O t + 80) and 8r(0-8e) = S0(T f + r) ; 

 hence by division, we get 



8r _ 80(t + t') _ B0 \ * + t7 



T n ~T , (0' + 80)~ 0'+89 ' 



or SK _ 89(0+0') 



K„~ 9 [9' + 80)' 



where K is the rigidity of the specimen, and SK its change 

 due to magnetization. If -^ be neglected, we have 



k h e\ + e')' 



If the change were greater than 1 per cent., the first equation 

 was used, and if it were less, the second equation was 

 employed. 



