620 report— 1884. 



it shall turn round the line of propagation of the waves: just as Faraday's ob- 

 servation proves to he 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 pro- 

 pagation being parallel to these lines) corresponds, in our mechanical model, to 

 the case of light travelling in the direction of the lines of force in a magnetic held. 



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 impe- 

 netrability, 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 incompressi- 

 bility, 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 interven- 

 ing 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 two 

 electromagnets — with this difference, that in the hydrokinetic model in every case 

 the force is opposite in direction to the corresponding force in the electromagnetic 

 analogue. Imagine a solid bored through with a hole ami placed in our ideal 

 perfect liquid. For a moment let the hole be stopped by a diaphragm, and let an 

 impulsive pressure be applied for an instant uniformly over the whole membrane, 

 and then instantly let the membrane be dissolved into liquid. This action origi- 

 nates 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 neighbourhood 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 iu virtue of the motion of the solid 

 itself, had there been no circulation established through the aperture. It is inter- 

 esting and important to remark in passing' that the whole kinetic energy of the 

 liquid is the sum of the kinetic energies which it would have in the two cases sepa- 

 rately. Now, imagine the whole liquid to he enclosed in an infinitely large rigid 

 containing vessel, and in the liquid, at an infinite distance from any part of the 

 containing vessel, let two perforated solids, with irrotational circulation through 

 each, be placed at rest near one another. The resultant thud motion due to the two 

 circulations will give rise to fluid pressure on the two bodies, which if unbalanced 

 will cause them to move. The force systems — force-and-torques, or pairs of forces 

 — required to prevent them from moving will be mutual and opposite, and will he 

 the same as, but opposite in direction to, the mutual force systems required to hold 

 at rest two electromagnets fulfilling the following specification. The two electro- 

 magnets are to he of the same shape and size as the two bodies, and to be placed in 

 the same relative positions, and to consist of infinitely thin layers of electric 

 currents in the surfaces of solids possessing extreme diamagnetic quality — in other 

 words, infinitely small permeability. The distribution of electric current on each 

 body may be any whatever which fulfils the condition that the total current across 

 any closed line drawn on the surface once through the aperture is equal to l/47r of 

 the circulation 1 through the aperture in the hydrokinetic analogue. 



It might be imagined that the action at a distance thus provided for by fluid 

 motion could serve as a foundation for a theory^ of the equilibrium, and the 



1 The integral of tangential component velocity all round any closed curve, pass- 

 ing once through the aperture, is defined as the 'Cyclic constant,' or the 'circulation ' 

 (' Vortex Motion,' § GO (a). Trans. I?. 8. E. April* 29, 1867). It has the same value 

 for all closed curves passing just once through the aperture, and it remains constant 

 through all time whether the solid body be in motion or at rest. 





