82 Dr. R. A. Houstoun on Magnetostriction. 



The area ABCD represents the work done against the 

 stretching force, and vjiir multiplied by the area A'B'C'D' 

 the work done by the magnetic field intensity during the 

 cycle. Therefore, by the principle of energy 



ABCD='/-A'B'C'D'. 



47T 



Now ABCD = ^F ||f rfH, and A'B'C'D' = rfH || dF. 



Hence substituting and dividing out by dFdH, 



v B B _ "dx 

 ^r§F~BH* 



Thus the third relation follows solely from the principle of 

 energy ; the second law of thermodynamics has not been used 

 at all. This is not apparent from the former method of 

 proof. 



In the paper by Nagaoka and Honda measurements 

 are given on the change in length of an ovoid of iron and a 

 nickel rod of square cross-section when magnetized in the 

 direction of the axis. The major axis of the ovoid was 

 20 cms. long and its minor axis 0986 cm. ; the length of 

 the nickel rod was 26 cms. and its breadth was 0*514 cm. 

 Measurements are also given on the effect of longitudinal 

 pull on the magnetization of the same nickel rod and on the 

 magnetization of a rod made from the same iron as the ovoid. 

 Since we are dealing with nickel and iron we may write 

 B = 47rl. The relation to be tested then becomes 



dl_da 



if a be the elongation per unit length and p the stretching- 

 force per unit area of cross-section. The results are given 

 by the following curves (fig. 3}. The curves marked by- 

 circles give "dJ/hp and those marked by crosses Ba/BH. 

 They should of course coincide. The differential coefficients 

 were formed by taking the differences of the successive 

 fioures in the tables in the article. The smaller value of 

 Sjw, 0-19 kg./sq. mm. was taken. 



The agreement, such as it is, is as good as that given by 

 Kirchhoff's theory which Nagaoka and Honda tested 

 numerically. 



or 



