276 H. NAGAOKA AND K. HONDA : 



Since -x~ and k are very small compared with k", the torsional 

 couple twisting the wire amounts nearly to 



^CHR^= ^—^ X Cross section. (C) 



Since the amount of torsion of a cylindrical wire by a given 

 couple is inversely proportional to the fourth power of its radius, 

 it is evident that for given longitudinal current and held, the 

 angle of twist is inversely proportional to the square of the 

 radius. This inference was approximately verified in the present 

 experiments. 



In deducing the three formulie (A), (B), (C), we can 

 not, strictly speaking, put k" outside the sign of integration, 

 because the strain coefficient depends on the field strength, which 

 is not uniform in a wire traversed by electric current. Hence 

 in these formulae, we shall have to use a mean value to obtain 

 a close approximation. 



The mutual relations between twist and magnetization are 

 embodied in the three formuhe above given. There we notice 

 that the strain coefficient k" determines the nature of the three 

 different phenomena studied in the above experiments. The 

 fact that the coefficient k" is principally determined by the 

 elongation in the ferromagnetic metal accounts for the close 

 analogy between the said phenomena and the elongations due 

 to magnetization. As the above result imports, the analogy is 

 not exact, inasmuch as the elongation is also affected by terms 

 depending on k', which depends mostly on the change of volume. 



In order to test the consequences of the theory as regards 

 the twist produced by the joint action of circular and longitudinal 

 magnetizations, we have calculated the twist by assuming the 



