a model of a mere spring balance, be applied as connections between millions of pairs of particles as before, with the lines of resultant moment of momentum all similarly directed.  We now have a model elastic solid which will have the property that the direction of vibration in waves of rectilinear vibrations propagated through it shall turn round the line of propagation of the waves, just as Faraday’s observation proves to be done by the line of vibration of light in a dense medium between the poles of a powerful magnet.  The case of wave front perpendicular to the lines of resultant moment of momentum (that is to say, the direction of propagation being parallel to these lines) corresponds, in our mechanical model, to the case of light traveling in the direction of the lines of force in a magnetic field.

In these illustrations and models we have different portions of ideal rigid matter acting upon one another, by normal pressure at mathematical points of contact—­of course no forces of friction are supposed.  It is exceedingly interesting to see how thus, with no other postulates than inertia, rigidity, and mutual impenetrability, we can thoroughly model not only an elastic solid, and any combination of elastic solids, but so complex and recondite a phenomenon as the passage of polarized light through a magnetic field.  But now, with the view of ultimately discarding the postulate of rigidity from all our materials, let us suppose some to be absolutely destitute of rigidity, and to possess merely inertia and incompressibility, and mutual impenetrability with reference to the still remaining rigid matter.  With these postulates we can produce a perfect model of mutual action at a distance between solid particles, fulfilling the condition, so keenly desired by Newton and Faraday, of being explained by continuous action through an intervening medium.  The law of the mutual force in our model, however, is not the simple Newtonian law, but the much more complex law of the mutual action between electro magnets—­with this difference, that in the hydro-kinetic model in every case the force is opposite in direction to the corresponding force in the electro-magnetic analogue.  Imagine a solid bored through with a hole, and placed in our ideal perfect liquid.  For a moment let the hole be stopped by a diaphragm, and let an impulsure pressure be applied for an instant uniformly over the whole membrane, and then instantly let the membrane be dissolved into liquid.  This action originates a motion of the liquid relatively to the solid, of a kind to which I have given the name of “irrotational circulation,” which remains absolutely constant however the solid be moved through the liquid.  Thus, at any time the actual motion of the liquid at any point in the neighborhood of the solid will be the resultant of the motion it would have in virtue of the circulation alone, were the solid at rest, and the motion it would have in virtue of the motion of the solid itself, had there been no circulation established