Mr. M. N. Slialia on Maxwell's Stresses. 257 



and (I m, n) are the direction cosines of the normal to the 

 surface. 



By transforming expression (2), we obtain 



+ A \1 M ,W\ 



we have, putting |^=X, *£=*¥, |*=Z, 



O^ Oj/ 0- 



JjJ{^[^-i (X2 - Y2 - Z2) ] + |[ X ^-4^ XY ] 



+ |[^-ixz]^^& = 0. . . (3) 



Maxwell concludes from this that a system of stresses 

 X x = A (X 2 -Y 2 -Z 2 ), Y v = -L(Y 2 -Z 2 -X 2 ), 

 Z.= i(Z*-X»-Y*), X y =A XY , Y,= ^YZ, 



Z -^ Z X, (4) 



distributed over the surface S account for the mechanical 

 action quite satisfactorily, and therefore provide a concrete 

 physical representation of the mechanism of electrostatic 

 action. 



3. But the expressions (4) are not complete solutions of 

 the integral equation (3). Maxwell * himself points out that 

 they can at best be regarded as a first step towards the 

 solution of equation (3). Many investigators, including 

 Sir J. J. Thomson f, have pointed out that sether cannot 

 possibly be at rest under these stresses. Lorentz J goes so 

 far as to say that the stresses are simply mathematical fictions, 

 which can be conveniently utilized for the calculation of 

 radiation pressure and other allied phenomena. The object 



* Loc. cit. p. 165 et seq. t Loc. cit. p. 165, footnote. 



X ' Theory of Electrons,' p. 31. 



Phil. Mag. S. 6. Vol. 33.' No. .195. March 1917. S 



