Elasticity of Ferromagnetic Substances by Magnetization. 83 



the change. As the temperature is further increased, a 

 •considerable amount of increase is observed., which steadily 

 increases with field. It attains a maximum and again 

 decreases, till it changes its sign. 



The values of 8a thus obtained may possibly differ from the 

 values obtained by heating the specimens in a constant mag- 

 netic field. They are the changes of a by magnetization, 

 when the temperature is first raised and then the field applied. 

 However, any experiment for the determination of the change 

 of a, in which the thermal expansion is directly observed in a 

 magnetic field, must be welcomed, as affording a counterpart 

 for the analogous comparison. 



Again, if we put, in the last equation, the tension T per 

 unit area for H, we get 



\dt/ T Wo & ' 



or 









a T — a 



lo^t 



but since 





lr-lo T 



/a ~E' 



re have finally 









da 

 T = 



.1 



°E 1 BE 

 " ~dt E 2 3* ' 



Thus the effect of tension upon the coefficient of thermal 

 expansion can be found from the temperature coefficient of 

 the modulus of elasticity. The relation was first obtained by 

 Dahlander"*, and verified by him to agree well with the 

 experiment. In problems which do not relate to magnetism, 

 the hysteresis effect is generally very small, so that the 

 agreement might have been expected. 



* Dahlander, Fogg. Ann. cxly. p. 147, 1872. 





G2 



