Theory of Galvanic Polarization. 425 



lary effect of the polarization-charge is different from that 

 used by Lippmann and by Helmholtz. In their mode of pro- 

 cedure the variation of the energy of the system is expressed 

 in terms of the variations of the surface-area and the surface- 

 density, and it is claimed that this expression is an exact 

 differential, L e. that any series of operations whereby the area 

 or density, or both, are changed so as finally to come back to 

 the original values, will also bring back the energy of the 

 system to its original value. This assumption seems to require 

 justification when it is remembered how complex such a series 

 of changes really is, and what a number of other variations 

 besides those of volume and density may enter into it. Helm- 

 holtz appeals to Lippmann's experiments on the influence of 

 extension of the surface-film on its electrification and vice versa, 

 and to his capillary engine, as pointing in a general way to 

 the truth of the assumption. 



In the method adopted above, we have proved the general 

 theorem that the mechanical action of two layers of positive 

 and negative electricity of equal amounts, spread over the 

 two faces of a flexible sheet, may be represented by a nega- 

 tive surface-tension of amount numerically measured by the 

 energy of the electrification per unit area. It follows, then, 

 on this representation of the phenomenon, that no matter 

 what other changes are taking place, the effect of the existing 

 surface-charges is to diminish the surface-tension of the sheet 

 by the amount just mentioned. 



The case contemplated in the present application of this 

 general proposition is that of a sheet of uniform thickness ; 

 but we can clearly extend the result to flexible condensers of 

 variable thickness of dielectric, provided always that the 

 thickness be small compared with any radius of curvature of 

 the surface at the place considered. In this case the mecha- 

 nical effect on the condenser of a charge to potential V is to 

 produce a negative surface-tension, numerically equal to 

 KV 2 /87r£, K being the dielectric constant and t the thickness 

 of the sheet ; this surface-tension varies from point to point 

 of the sheet, and is at any place inversely proportional to its 

 thickness. 



This result may also be at once deduced from the expres- 

 sion for the stress transverse to the lines of force in the 

 dielectric on Maxwell's well-known theory. 



4. Lippmann's original form of capillary electrometer con- 

 sists of two mercury electrodes in contact with acidulated 

 water. One of the electrodes is in an extremely fine capillary 

 glass tube, so that the surface of contact is very small ; and 

 the other is of considerable area. It follows that when a 

 battery is applied, all the polarization and consequent change 



