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 llU'llUL'll 

 lilt' two 



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TUAXS.VCTIONS OF SECTION A. 



621 



vibrations, of elastic solids, sind the transmission of waves like those of li<^ht 

 tlirough an extended quasi-elastic solid medium. I5ut unfortunately for this idea 

 the equilibrium is essentially unstable, both in the ease of niafrnets and, iiol- 

 withstandinfr the fact that the forces are oppositely directed, in the hydrokinetic 

 analogue also, when the vseveral movable bodies (two or any greater number) are 

 .mi placed relatively as to Ikj in equilibrium. If, however, we connect the perforated 

 bodies with circulation through them in the hydrokinetic svstem, by jointed rigid 

 connecting links, we may arrange for configurations of statjle equilibrium. Thus 

 without fly-wheels, but with fluid circulations tlirough apertures, we may make a 

 model spring balance, or a model luminiferous ether, eitiier without or with the 

 rotational quality corresponding to that of the true luminiferous ether in the 

 magnetic fluid — in short, do all by the perforated solids with circulations through 

 tliem that we saw we could do by means of linked gyrostats. IJiit something tunt 

 we cannot do by linked gyrostats we can do by tiie perforated bodies with fluid 

 circulation. We can make a model gas. The mutual action at a distance, repul- 

 sive or attractive according to tlie mutual aspect of the two boilies when passing 

 within collisional distance ' of one another, suflices to produce the change of direc- 

 tion of motion in collision, whicii essentially constitutes tiie foundation of the 

 kinetic theory of gases; and wiiich, as wo liave seen before, may as well be due to 

 attraction as to repulsion, so far as we know from any investigation hitherto made 

 in tills theory. 



There remains, however, as we have seen before, the diiliculty of providing for 

 the case of actual impacts between the solids ; which must be done by giving them 

 niiissless spring bufl'ers, or, wliich amounts to the same thing, attributing to them 

 repulsive forces sufliciently powerful at very short distances to absolutely ])revent 

 impacts between solid and solid; unless we adopt tlie equally repugnant idea of 

 infinitely small perforated solids, with infinitely great fluid circulations through 

 tlieni. Were it not for this fundamental ditliculty, the hydrokinetic model gas 

 would !>• exceedingly interesting ; and, though we couki scarcely adopt it as conceiv- 

 ably a true representation of what gases really are, it might still have some im- 

 portance as a model conliguration of solid and liquid matter, by wliich without 

 elasticity the elasticity of a true gas might bo represented. 



But lastly, since the iiydrokinetic model gas with perforated solids and fluid 

 circulations through them fails because of the impacts between the solids, let us 

 annul the solids and leave the liquid performing irrotational circulation round 

 vacancy,' in the place of the solid cores whic'? we have hitherto supposed ; cr let 

 us annul the rigidity of the soliil cores of the rings and give them molecular rota- 

 tion according to IIelmho!t/"s theory of vortex motion. For stability the molecular 

 rotation must be such as to give the same velocity at the boundary of the rotational 

 fluid core as that of the irrotal ion.ally circulating li(iuid in contact with it, 

 liecause, as I have provi'd, frictional slip between two portions of liquid in 

 contact is inconsistent with stability. There is a further condition, upon which 

 1 cannot enter in detail just now, but which may be understood in a general 

 way when I say that it is a condition of either uniform or of increasing 

 molecular rotation from the surface inwards, analogous to the condition that 

 the density of a liquid, resting for example iimler the influence of gravity, 

 must either be uniform or must be greater below than above for stability of 



' According to this view tlicre is no precise distance, or definite condition respect- 

 ing the distiince, between two molecules at which a]iparcntly they come to be in 

 collision, or when receding from one anotlier tliey cease to ho in collision. It is con- 

 venient, however, in the kinetic theory of gases, to adopt arbitrarily u precise defini- 

 tion of collision, according to which two fiodies or partit-les mutually acting' at a 

 'listance may he said to be in collision when their mutual action exceeds some 

 definite arbitrarily assigned liniif, as, for example, when tlie radius of curvature of 

 the path of either Imdy is less than a stated fraction (1, K)0, for instance) of the 

 distance between them. 



* Investigations rcsjMicting corelcss vortices will be found in a paper by the author, 

 ' Vibrations of a Columnar Vortex,' Proc. It. H. E. ilarch 1, 1880; and a paper by 

 Hicks, recently read bcfort' the Hoyal [Society. 



