THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
267 
let an element SS of it sustain a di.splacement Sn along the normal, of amount very 
slight compared with the linear dimensions of 8S. If no other boundary ^Yithin the 
range of the electric field is thereby affected,—for instance if each fluid is supposed 
to be continued in a narrow tube to a great distance beyond the field and simply 
advances or recedes in the end of this tube,—the change of organized electric energy 
is merely the substitution of a volume SSS71 of energy of the one intensity for the 
same volume of the intensity on the other side of the interface. The displacement of 
SS of course affects the state of the field all over, but by hypothesis the electric field 
was in internal equilibrium, so that the change of the organized energy of any 
volume-element of the mass arising from a slight derangement is of the second order 
of small quantities, and produces no sensible effect. The above change of energy is 
thus equal to the work done by the extraneous traction over SS ; which confirms the 
result already obtained (§37) by detailed analysis of the polarization, that the 
traction is along the normal to the interface and equal in intensity to the difference 
of the densities of the organised electric energy on its two sides. 
53. It is advantageous in connexion with this subject to form a definite conception 
of the transmission of ordinary mechanical pressure in a liquid. Let us imagine an 
ideal infinitely thin interface in the fluid : what concerns the equilibrium of the fluid 
on one side of it is not the pressure which that fluid exerts on the interface, but the 
forces that are exerted on that fluid itself both by the interface and by the molecular 
attraction of the fluid on the other side of it. As the range of molecular attraction 
is very small, these forces together make up a pressure on the fluid, equa,l in 
circumstances of molecular equilibrium to the resistance of the interface against the 
impacts of the molecules diminished by the attraction exerted on these molecules 
across the interface; and this is the pressure that is transmitted by the fluid. For 
imagine a canal or tube in the fluid, with infinitely thin sides, and of diameter large 
compared with the radius of molecular action, and consider the equilibrium of the 
mass of fluid contained in it between two cross-sections A and B. There will be 
this pressure acting on the fluid just inside A, and a similar pressure acting on the 
fluid just inside B; and unless these are equal, or balance each other with the 
aid of extraneous applied forces such as gravity, the mass of fluid cannot be in 
equilibrium. This is Pascal’s principle, that the mechanical pressure is trans¬ 
mitted unchanged in amount, except in so far as it is compensated by extraneous 
mechanical forces. It is to be noticed that the argument does not assume that the 
fluid between A and B is homogeneous, all that is required is that it be in equilibrium; 
the cross-sections A and B may be in different fluids, with an interface between, and, 
provided the diameter of this ideal canal is large compared with the radius of 
molecular action, the interfacial forces will practically all be mutual ones between 
molecules inside the tube, and so will not affect the transmission of pressure. It is 
this transmitted pressure that is the subject of actual measurements : for example 
m Andeews’ experiments on the compression of carbonic acid, it is the pressure 
2 2 
