September 5, 1884.] 



scie: e 



205 



of an elastic body, this would be at least a finger-post, 

 pointing a way which we may hope will lead to a ki- 

 netic theory of matter. Any ideal system of material 

 particles, acting on one another mutually through 

 mass-less connecting springs, may be perfectly imi- 

 tated in a model consisting of rigid links jointed to- 

 gether, and having rapidly rotating fly-wheels pivoted 

 on some or on all of the links. The drawings (figs. 1 

 and 2) illustrate two such material systems. The di- 

 rections of rotation of the fly-wheels in the gyrostatic 



Fig. l. 



Fig. 2. 



system (fig. 2) are indicated by directional ellipses, 

 which show in perspective the direction of rotation of 

 the fly-wheel of each gyrostat. The gyrostatic system 

 (fig. 2) might have been constituted of two gyrostatic 

 members, but four are shown for symmetry. The 

 enclosing circle represents in each case, in section, an 

 enclosing spherical shell to prevent the interior from 

 being seen. In the inside of one there are fly-wheels ; 

 in the inside of the other, a massless spring. The 

 projecting hooked rods seem as if they are connected 

 by a spring in each case. If we hang any one of the 

 systems up by the hook on one of its projecting rods, 

 and hang a weight to the hook of the other projecting 

 rod, the weight, when first put on, will oscillate up and 

 down, and will go on doing so forever, if the system 

 be absolutely unfrictional. If we check the vibration 

 by hand, the weight will hang down at rest, the pin 

 drawn out to a certain degree ; and the distance drawn 

 out will be simply proportional to the weight hung on, 

 as in an ordinary spring-balance. 



Here, then, out of matter possessing rigidity, but 

 absolutely devoid of elasticity, we have made a per- 

 fect model of a spring in the form of a spring-balance. 

 Connect millions of millions of particles by pairs of 

 rods such as these of this spring-balance, and we 

 have a group of particles constituting an elastic solid. 



The gyrostatic model spring-balance is arranged to 

 have zero moment of momentum as a whole, and 

 therefore to contribute nothing to the Faraday rota- 

 tion. With this arrangement, the model illustrates the 

 luminiferous ether in a field unaffected by magnetic 

 force. But now let there be a different rotational ve- 

 locity imparted to the jointed square, round the axis 

 of the two projecting hooked rods, such as to give a 

 resultant moment of momentum round any given line 

 through the centre of inertia of the system, and let 

 pairs of the hooked rods in the model thus altered, 



which is no longer 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 propaga- 

 tion 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 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 condi- 

 tion, so keenly desired by Newton and Faraday, of 

 being explained by continuous action through an in- 

 tervening medium. 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 impulsive pressure be applied for an instant 

 uniformly over the whole membrane, and then in- 

 stantly let the membrane be dissolved into liquid. 

 This action originates a motion of the liquid relatively 

 to the solid, of a kind to which has been given the 

 name of ' irrotational circulation,' which remains ab- 

 solutely 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 through the aperture. It is interesting 

 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 be 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 irro- 

 tational circulation through each, be placed at rest 

 near one another. The resultant fluid motion due to 

 the two circulations will give rise to fluid pressure on 

 the two bodies, which, if unbalanced, will cause them 

 to move. 



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 

 vibrations of elastic solids, and the transmission of 

 waves like those of light through an extended quasi- 

 elastic solid medium. But, unfortunately, the equi- 

 librium is essentially unstable. If, however, we 

 connect the perforated bodies, with circulation through 



