260 Mr. M. N. Shaha on Maxwell's Stresses. 



where or is the surface density of electricity on a charged 



BY 



surface, and p is the volume density. Since -=— is the 



^-component of electrical force on a surface, o--^— is the- 



^-component of mechanical action per unit surface. Similarly, 



p^— is the ^-component of mechanical force per unit volume 

 Ox 



of electrified particles. We can therefore put 

 W=2 (T(X&*+ Y v 8y+Z v 8z) + 1 fi f (X5> + YBy + ZBz). 



8. Comparing this expression for energy with the 

 expression (6) 



W=^(X^u + Y v Bv + Z^Bw) + i({p(XBu + YBv^Z8w), (6) 



we see that in the present case (X„, Y v , Z v ) are the components 

 of surface-tractions on a charged surface, and (X, Y, Z) are 

 the body-forces on electrified particles. The existence of 

 these forces can be experimentally demonstrated, and they 

 exist only in regions occupied by electricity ; elsewhere 

 they are nil. The energy of electrification is derived from 

 the work done in the actual displacements (8x, By, Bz) of 

 these charged regions towards each other. On the other 

 hand, (X v , Y„, Z r ) in (6) are the tractions on a surface 

 enclosing some of the charged regions, and Bu, Bv, Bw are 

 their elastic displacements. We may by special assumption 

 identify the two systems of surface-tractions and body-forces, 

 but the actual displacements (Bx, By, Bz) and the elastic 

 displacements (Bu, Bv, Bw) cannot be identified in any way* 

 The two expressions represent fundamentally different 

 quantities. 



9. The fact that radiant energy would exert a definite 

 amount of pressure on material surfaces was first predicted 

 by Maxwell on the hypothesis of dielectric stresses. Now 

 that radiation pressure is an experimental fact, it has been 

 supposed by some physicists that Maxwell's stresses must 

 have a material existence. But it is well known that radiant 

 energy can be deduced independently of the stresses. 

 Bartoli lias shown that the pressure of radiant energy can be 

 deduced from thermodynamic principles. Planck * has 

 deduced it from electrodynamical principles, assuming that 

 the perfect reflector is a super-conductor of electricity. This 



* Planck, Wcirmestrahlvng, second edition, pp. 49 et seq. 



