456 H. Nagaoka and E. T. Jones on the Effects 



tbeor}^ makes the stress depend principally on the coefficients 

 K7 and K". The experiments of Villari, Lord Kelvin, and 

 Ewing on the effects of longitudinal stress on magnetization 

 show that 



-.&*+*>)**• Y °tr 8 =- (t + *") 



in iron is a quantity which may amount to 10 5 for moderate 

 magnetizations, so that in this case K is quite negligible 

 in comparison with one or both of the two other coefficients. 



The preponderating influence exercised by these latter factors 

 will, perhaps, explain the existence of a maximum elongation 

 in iron and the continual contraction in nickel. Maxwell's 

 expressions for magnetic stress (Art. 644), in the case when 

 B and H have the same direction, are, however, apparently 

 by a coincidence deduced from the above expressions of 

 Kirchhoff by putting K /x = 0, K' = K = susceptibility. 



About the same time Lorberg*and J. J. Thomsonf discussed 

 the present problem in a manner similar to that of Kirchhoff. 

 More recently Hertz | arrived at expressions of precisely the 

 same form as those given by v. Helmholtz. In comparing 

 his expressions with those given by Maxwell for the general 

 case of a magnet in which the induction and magnetic force 

 have different directions, Hertz says (p. 281) : — 



" A difference of far greater importance (i. e. than the effect 

 of a change of density by electromagnetic strain) is that in 

 Maxwell's theory the tangential stresses V xy and V yx have 

 different values, while in our theory they are identical. 

 Under our system of stresses every material element, when 

 left to itself, will only change its shape ; under that of 

 Maxwell it will also experience a rotation as a whole. The 

 Maxwellian stresses cannot therefore arise from processes in 

 the interior of the element, and can have no place in the 

 present theorv. They are, however, admissible on the assump- 

 tion that in the interior of the body in motion, the aether 

 remains at rest and furnishes the necessary fulcrum for the 

 rotation which takes place." 



In attempting to calculate the change of dimensions of a 

 body due to magnetization we are at once placed face to 

 face with the question as to whether these stresses actually 



* Wied. Ann. xxi. p. 300 (1884). 



t Application of Dynamics, §§ 35-37 (1886). 



\ Ausbreitung der electrischen Kraft, p. 275 (Leipzig-, 1892). 



Hertz, speaking of equation (6 c), p. 284, which is obtained as a 

 simplified form of stress agreeing in the general case with that found by 

 v. Helmholtz, says that the stress is the same as that given by Maxwell 

 in Art. 642 of the treatise. His expression, however, is not that given in 

 Art. 642 but in Art. 105. 



