Mr. M. N. Shaha on Maxwell's Stresses. 259 



Then, after some calculation, the strain-energy function 

 comes out to be 



--vm^^- ■ ; < 6 » 



It will thus be seen that if the stresses are really existent, 



and if they are amenable to the ordinary laws of elasticity, 



th9 strain-energy function, or the energy of elastic deforma- 



r -3 (l + 2<7) /R 2 \ 2 ., , 



tion of the medium, is ^ -^ r ( q— « ) per unit volume. 



2 6(1 + <x) \07T7 



But this is very different from the theorem that the energy 



/R 2 \ 

 density per unit volume is (q- J, which is derived from 



electrostatic principles. \ m '/ 



6. Since nothing definite is known about the elastic con- 

 stants of aether, we cannot draw any conclusion from (6) 

 about the energy distribution in aether. Maxwell's stresses 

 are thus seen to fail to account for the energy of electri- 

 iication, on the understanding that the medium behaves like 

 an elastic solid. 



7. It is well known that the energy-distribution theorem 

 is proved on the basis of the empirical laws of electrostatics. 

 No use is made of the stresses. The result is purely 

 analytical, and says that if energy is distributed all over 



space as a continuous function with volume density jr-, the 



total energy will come out to be the same as the total energy 

 of electrification. The distinction between Maxwell's view 

 •of energy distribution as due to stresses (in the sense we 

 have interpreted it) and the actual case can be better brought 

 .out if we adopt the following modified method of proving 

 the energy-distribution theorem. Suppose we have an 

 electrical system consisting of charged surfaces, and particles 

 in a given configuration. The energy of electrification will 

 be the same in whichever way we may bring about the final 

 configuration. Suppose that, to start with, the charges and 

 the charged surfaces were all at an infinite distance, and the 

 given configuration is brought about by properly moving 

 the charged surfaces and other discreet electrified particles. 

 Then the energy of electrification is 



w 



=%(e8Y, 



S2 



