

1892.] as affected by Stresses in Excited Dielectrics. 59 



formal view of the phenomenon, though the dynamical machinery of 

 which it represents the action is quite unknown. But this presump- 

 tion is very much strengthened by the fact that the displacement or 

 polarisation is known to present qualitatively the properties of a true 

 current, and also that the theory of dielectric propagation developed 

 from this basis presents all the general analogies to light propagation 

 that have been experimentally confirmed by Hertz and others. 

 Taking it then that dielectric polarisation is formally of this type, 

 the absence of a sensible absolute exciting charge on the bounding 

 plates will show that it must be, so to speak, self-excited, that it is 

 of the formal character of a displacement, of something pushed across 

 from one plate towards the other like an incompressible substance, 



4. Let us confine our attention for definiteness to the case of two 

 metallic plates immersed horizontally near together in an extended 

 mass of a fluid dielectric, so as to form a condenser. The traction T 

 per unit area on the upper plate may by this arrangement be directly 

 weighed. Suppose that there is a small aperture in the centre of the 

 upper plate through which a volume of a different dielectric, say, a 

 bubble of air, may be introduced between the plates, so as to form a 

 flat cylinder co-axial with the plates and bounded above and below 

 by them. The extra pressure P in this air bubble, when the con- 

 denser is excited, may be measured by a manometer in connexion 

 with it, and it will give the means of determining the pressure in 

 the surrounding liquid dielectric. This arrangement describes in 

 fact the plan of Quincke's experiments. 



At a point in the dielectric where the electric force is F, the 

 electric pressure will be proportional to F 2 , say, A 2 F 2 for the liquid, 

 and AiF 2 for the air. The air column in the manometer tube would 

 thus be in internal equilibrium with an electric pressure AiF 2 next 

 the liquid and null at the manometer end. We might at first glance 

 infer that under these circumstances the pressure A : F 2 is not indi- 

 cated by the manometer, which would thus record simply the electric 

 pressure in the liquid. But this air pressure is an internal stress ; 

 the equilibrium of any section of the air column requires, in order to 

 maintain it, the electric pressure against it of the air on the other 

 side of that section ; therefore, the indication of the manometer really 

 gives the differential effect A 2 F 2 2 A^ 2 . 



Let now the volume energy of the electrification be C 2 F 2 in the 

 liquid, and CiF 2 in the air, each per unit volume ; and let the energies 

 of such real surface electric distributions as might exist on the plates 

 in contact with these dielectrics be 2 2 and 2 X respectively, each per 

 unit surface of both plates. These surface energies would involve in 

 their expression the electric potential as well as the force. We may 

 apply the principle of virtual work to determine the relations between 

 the quantities thus defined. 



