Elasticity of Ferromagnetic Substances by Magnetization. 37 



by magnetization. The acoustical method* used by several 

 experimenters is also an indirect one, and unsuitable for any 

 accurate determinations. In H. Rensing's experiment t, 

 Kandt/s tube was used ; but the field in which the bar was 

 placed was far from being uniform. 



Our present experiments were undertaken with the main 

 object of measuring the change of elastic constants of the 

 same specimen by the direct as well as the indirect method 

 and comparing the results thus obtained: the specimen to be 

 tested being placed in a nearly uniform field. 



If f be the length or the angle of twist of the specimen, 

 S the applied tension or couple respectively, and H the 

 magnetic field, we have the relation 



9 /^e\_ a_/3n 



(i) 



provided the change is independent of the order of applying 

 the field and the stress. Thence we have 



/df 





8(far-fo) 



(2) 



If 31 be the modulus of elasticity or that of the rigidity 

 respectively, 



M_ e 



where c is a constant depending on the dimensions of the 

 specimen. Hence we have finally 



1 l i 3(fe-&) 



M H 



M. 



B(fa-goi 



or 



Mh-Mq 

 M h 





M °dS 



fo) 



dS 





(3) 



Thus the change of elasticity may be calculated from the 

 effect of tension on the magnetic elongation ; and that of 



* Waitmann, Ann. dc Chim. ct de Phys. xxiv. p. 360 (1848) ; Treves, 

 C. JR. lxvii. p. 321 (1868) ; Archives c/es 8c. Nat. N. S. xxxiii, p. 74 

 (1868) ; Maorain, C. JR. cxxi. p. 248 (1895). 



T Rensing, Ann. der Phys. xiv. p. 363 (1004). 



