EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 331 



surface of the tube multiplied by 9", the superficial tension of liquid 

 water in contact with the tube at the pressure at which the water 

 and its vapor would be in equilibrium at a plane surface. In this 

 sense, the total weight of water which can be supported by the tube 

 per unit of the perimeter of its surface is directly measured by the 

 value of ? for water in contact with the tube. 



Modification of the Conditions of Equilibrium by Electromotive 

 Force. Theory of a Perfect Electro-Chemical Apparatus. 



We know by experience that in certain fluids (electrolytic con- 

 ductors) there is a connection between the fluxes of the component 

 substances and that of electricity. The quantitative relation between 

 these fluxes may be expressed by an equation of the form 



~ Dm. , Dm*. , Dm* Dm^ 



De = - -H -- -+etc. --- * -etc., (682) 



a b g a h 



where De, Dm & , etc. denote the infinitesimal quantities of electricity 

 and of the components of the fluid which pass simultaneously through 

 any same surface, which may be either at rest or in motion, and 

 a a , b> etc., a g , a h , etc. denote positive constants. We may evidently 

 regard Dm a , Drn^, etc., Dm g , .Z)ra h , etc. as independent of one another. 

 For, if they were not so, one or more could be expressed in terms of 

 the others, and we could reduce the equation to a shorter form in 

 which all the terms of this kind would be independent. 



Since the motion of the fluid as a whole will not involve any 

 electrical current, the densities of the components specified by the 

 suffixes must satisfy the relation 



(683) 



a b g h 



These densities, therefore, are not independently variable, like the 

 densities of the components which we have employed in other cases. 



We may account for the relation (682) by supposing that electricity 

 (positive or negative) is inseparably attached to the different kinds of 

 molecules, so long as they remain in the interior of the fluid, in such a 

 way that the quantities a a , a b , etc. of the substances specified are each 

 charged with a unit of positive electricity, and the quantities a g , a h , 

 etc. of the substances specified by these suffixes are each charged with 

 a unit of negative electricity. The relation (683) is accounted for by 

 the fact that the constants a a , a g , etc. are so small that the electrical 

 charge of any sensible portion j the fluid varying sensibly from 

 the law expressed in (683) would be enormously great, so that 

 the formation of such a mass would be resisted by a very great 

 force. 



