280 Messrs. H. Nagaoka and K. Honda on Magnetostriction. 

 where 



c^ *' By"" y ' %z » 

 and 



These equations give 



.... (« + 2£) R2 _ _t_ „ 3 



2K(l + 3@) ~2K© > 

 or 



8t> H 2 r- .. 3 



<7 = 



i? ~ 2K(l + 3e) 

 Similarly we obtain 



{27rF+|(^-^)-Y} 



W 



a ~"yTT 2 ^-7 U2 ^^7TJ 



"~" 2K ~* " 2K "*' 2K 



The elongation in the direction of magnetization is thus 



. SI H 2 f 72 *" k-k' ") ,- 



X =T = ^{ 2rf -^ + 2(1+26)}' ' W 



Supposing that the Poisson ratio is J, or © = -£, we find 

 for a prismatic body 



°'~ V -E\ 7r+ 4F 4PJ' 



Corresponding formulae for the ovoid are, according to 

 Cantone, 



X ~ I ~E\ 7r+ W -2k*)' 

 hv_l*,> 3(*-*') *" 



a= v ~E 



/ d^/c — a: ; a: \ 



Comparing the formulae (a), (6), (c), (rf), we find that the 

 change of volume is the same for the ovoid as for the 

 prismatic body ; the difference in the length-change is equal 



2(1 + 4©) I 2 

 to a (1 + 2(H))E > bein & sll g' nt] y greater for the prismatic 



body than for the ovoid. 



The formulas (c) and (d) are never exact, as prismatic 

 bodies cannot be magnetized uniformly, and consequently 

 there must be also internal forces acting. But to the first 

 approximation we can use these formulae, inasmuch as the 

 strain caused by magnetization can only be roughly measured. 



