1892.] as affected by Stresses in Excited Dielectrics. 61 



bubble and one in the liquid, and reckon the change in the energy 

 contained in the space originally occupied by this annulus, when it 

 receives a small displacement outwards from the axis under the action 

 of the manometer pressure P. That change is (C 2 Ci)F 2 r, where 

 F is the electric force at a distance from the meniscus. Therefore, 

 by the principle of virtual work, Pdv (C 2 d)F 2 Si; = 0, so that P = 

 (C 2 -COF 2 . 



The value of the traction between the two plates in air is given by 



rJ V 



this formula as TI = CiF 2 -f J-^ ; this mast, therefore, be the same as 



dc 



the well- ascertained experimental value F 2 /87r. Now the experiments 

 of Quincke and others on liquid dielectrics have given reason to be- 

 lieve that, within the limits of experimental uncertainty due to want 

 of purity of the materials and other causes, T 2 = P+ F 2 /8?r. It fol- 

 lows that we must have d^/dc = d^ijdc; that is, d2/dc must be the 

 same for all media, which is physically consistent only with the non- 

 existence of this surface energy, unless we can suppose it to be the 

 energy of an action at a distance which is independent of the inter- 

 vening medium altogether. 



The argument may also be expressed somewhat differently as fol- 

 lows : The plates of the condenser being supported independently, 

 the existence of an extra pressure on the dielectric when the con- 

 denser is excited shows that part, at any rate, of the electric energy 

 resides in the dielectric. That part must, on any view, either of 

 action by contact or of quasi- magnetic polarisation, be proportional 

 to the square of the electric force at the point, which is in fact con- 

 firmed by the experiments of Silow on a quadrant electrometer with 

 its needle immersed in a dielectric liquid filling the quadrants. If 

 this were the whole of the electric energy, the traction between the 

 plates would be equal to the hydrostatic pressure in the dielectric, or 

 at most differ from it by an amount which would be the same for all 

 media.* If this were only part of the electric energy, the difference 

 would depend on the other superficial part. The experiments show 

 that for a large number of liquids the difference is very nearly the 

 same, so that if, after Quincke, we suppose it to be null for air or 

 vacuum, it is null for all the others. f Hence either the superficial 

 energy must be absolutely independent of the nature of the dielectric 



* Cf. J. Hopkinson, ' Eoy. Soc. Proc.,' 1886, p. 453, for the use of a similar 

 argument in the converse manner, to show that the tension and pressure must be 

 equal ; but in it the energy of the polarisation of the medium is apparently not 

 sufficiently traced. 



f The results of Quincke are calculated so as to give values for ~Kp, the inductive 

 capacity deduced from experiments on fluid pressure, and Kg, the inductive capacity 

 deduced from experiments on the traction between the plates, on the assumption 

 that the stress is of the Faraday-Maxwell type. The following examples show the 

 order of magnitude of the discrepancies 



