Faraday -Maxwell Mechanical Stress, 645 



Inner to the outer sphere, the ♦electromotive intensity has 

 values ranging from ejr 2 to e/r 2 2 , measured in the direction 

 of the outwardly drawn radius. Now keeping the inner 

 sphere insulated, so that its charge e remains unaltered, let 

 this sphere expand symmetrically and infinitesimally, its 

 radius becoming r 1 + dr v The electrostatic energy of the 

 system is thus changed by 



£MH)>*--*$*" • • (1) 



while the Faraday-Maxwell radial tension, reckoned per 

 unit area of the inner sphere, is 



-f-Y • (2) 



8 

 and the work done by this tension per unit area is 



i-,^1 ( ;5 ) 



e 2 

 Thus -A — odri is the work done by the aetherial i{ mechanical 



stress" during the expansion dr u and this work is equivalent 

 to (1) with sign reversed, that is to the loss of electrostatic 

 energy of the system. But, as already pointed out, in order 

 that the radial tension (2) may contribute the work (3) in 

 the displacement dr x , it is essential that the aether between 

 the spheres should contract by the amount di\ along every 

 radius, its volume being thus reduced precisely as much as 

 the volume of the inner sphere is increased. Proceeding in 

 the same way, the inner sphere could be expanded until 

 r 2 — ?'i ? which originally might be as large as we pleased, was 

 reduced to an insignificant amount; the aether between r x 

 and r 2 retaining all the while a radial tension which is nowhere 

 less than e/?' 2 2 , and being ultimately made to occupy only a 

 minute fraction of its original volume. 



7. Let us now contrast two interpretations of the virtual 

 work corresponding to a small change of configuration of an 

 electrified system ; one interpretation being that of the 

 Faraday-Maxwell mechanical stress, the other that of the 

 electronic theory. Let the system consist of any number of 

 bodies carrying surface charges, the intervening spaces, for 

 simplicity of illustration, being supposed vacuous; and con- 

 sider the virtual work of the electrostatic forces when the 

 system suffers a determinate change of configuration 80, 

 specifiable in terms of the geometrical coordinates. If, 

 without making any other change, we increase the charge 



