of Magnetic Stress in Magnetostriction. 457 



exist in the body, or whether they, existing in a medium in 

 which the particles of the body are imbedded, produce modi- 

 fied stresses in the body. 



Kirchhoff supposed the surface tractions acting on a piece 

 of magnetized soft iron to be the same as if the stresses P xx 

 actually existed in the iron and in the surrounding air, where 

 K, K/, K ;/ are put =0, and proceeded to calculate the changes 

 in the dimensions of a soft iron sphere placed in a uniform 

 magnetic field, due to a system of stresses which satisfy the 

 ordinary equations of an elastic solid and at the surface of 

 the sphere have the above given values. 



Having obtained the general solution for the strain of a 

 sphere, Kirchhoff gives a numerical example, neglecting the 

 terms affected with (K — K/) and K", supposing these quan- 

 tities to be very small in comparison with K 2 . Kirchhoff's final 

 value for the elongation of a soft iron sphere is therefore pre- 

 cisely the same as that which would be given by Maxwell's 

 system of stresses (Art. 644) . 



Proceeding exactly on the lines of Kirchhoff, Cantone* 

 has calculated the variations SI and &v of length and volume 

 of a soft iron ellipsoid of revolution, and finds that for an 

 ellipsoid of great eccentricity and length /, 



S/f_ P f K-K' K" ■) 

 I ~E\ 7r+ 4K 2 2K 2 >' 



Bv F f , 3(K-KQ K" \ . : ■ 



where E = Young's Modulus for the iron (on the supposition 

 that the Poisson ratio = J) . He also measured experimentally 

 the changes of length and volume of a soft iron ellipsoid due 

 to uniform magnetization, and, assuming that these were due 

 entirely to Kirchhoff's system of stresses, deduced the values 

 of K' and K". He found the change of volume to be 

 negligibly small, and for K 7 and K" the values 44,000 and 

 -92,000 for the mean field-intensity (H = 33 C.G.S., H 

 (in iron) = 3*5, 1 = 250) which he employed. 



* Mem. R. Ace. Line. ser. 4, vol. vi. p. 487 (1890) ; Wied. Electr. iii. 

 p. 740. 



t More exactly, 



?i_M!/l±^\ IH K'H 2 K"H 2 



/ ~ 3E \l+20/ + 2E(l+^) - 2(l + 2tf;U ~ ~2E~ ' 



■where 6 is a constant defined by the equation 



