" r 



620 



REPOKT — 1884. 



i\ 



it sball turn round the lino of propagation of tlu' waves; just as Faraday's oli- 

 servation ])rove.s to be dono by tlio line of vibration of lifrlit in u dense medium 

 between tbe poles of a powerful magnet. The case of wave front perpendiculiu- 

 to the lines of resultant moment of momentum (that is to say, tlie direction of prn- 

 pngation being parallel to tht'se lines) corresponds, in nui' meclumical model, tn 

 tlie case of light travelling in the direction of the lines of forc(^ in a magnetic Held. 



In those illustrations and models we nave ililfeient jiortions of ideal rigid 

 matter acting upon one another, by normal pressure )tt matheniatical points of 

 contact — of course no forces of friction are sup])osed. It is e.xceodingly interesting 

 to see how thus, witli no otluT postulates than inertia, rigidity, an<l mutual impe- 

 netrability, wo can tlioroughly model not oidy an elastiL- solid, and any conibinatiun 

 of elastic; solids, but so comple.v and recondite a ])heiiomenon as the passage uf 

 ])(dari/.ed liglit througli a magnetic iield. IJut now, wilii tiie view of ultimately 

 <iiscarding the postulate of rigidity from all our materials, h't us suppose some Vt 

 be absolutely destitute of rigidity, nnd to jiossess merely inertia and incouipressi- 

 bility, and mutual impenetrability with reference to the still remaining ri;.'id 

 matter, AN'ith liieso ])ostulates we can produce a ]ierfec( 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 tlirougli an interven- 

 ing medium. The law of the nnitual force in our model, liowever, is not tlu.'simpli' 

 Newtonian law, but tlie much more complex law of the iiiuliial action between twu 

 electromagnets — with this dilierence, tluu in the hy<lrokinetic model in every ca«c 

 the force is opposite in direction ti« the corresponding force in tlu* elect ronnignetic 

 analogue. luiag'ue a solid bored tlutiugh willi a liole anil ])laci'd in our idisil 

 perfect liquid, .'or u moment let the hole be stopped by a diaphragm, and let r.ii 

 impidsive pressure be apjdieil for an instant uniformly over tht> whole membranr. 

 and then instantly Id the memlirane be dissolved into li(|iii(l. 'I'liis action origi- 

 nates a motion of the liquid relatively to the soliil, of a kind to which 1 havi- 

 given the luime of 'irrota. .lal circulation,' which remains absolutely constant 

 however the solid be moved through the li(juiil. 'J'lius, at any time tlu- actiiiil 

 motion of the liquid at any point in the neighbourhood of the solid will be the 

 resultant of the motion it would have in \irtue of tbe circulation alone, were the 

 solid at rest, and the motion it would have in \irtiie of the motion of the solid 

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

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

 liquid is the sum (d'llie kinetic energies wlii<'h it would liuvi in the two cases sepa- 

 rately. Now, imagine the whole li(|ulil to be enclosed in mi inlinitely large rigid 

 containing vesstd, and in the licpiid. at an inllnilo distance from any part of the 

 containing vessel, let two perforated solids, with irrotntional circulation thriiU|.']i 

 each, be placed at rest near one another. The resultant fluid UKitioii due to tlie l\va 

 circulations will give ri-<elo fluid jiressuro on the two Ijuilies, which if unlialanctd 

 will cause them to move. The force systems— lb rce-and-tonjues, or ])airs of forces 

 — required to prevent tlu'in from moving will be mutual and opposite, and will be 

 the same as, but ojipo.-ite in direction to, the mutual force systems required tt) held 

 at rest two electromagnets fulfilling the following specilication. 'I'iie two electvn- 

 inagnets are to be of tlie samohape and si/e as the two bodies, and to be placed in 

 the same relative positions, and to consi.-'t of infinitely thin layers of electric 

 <-urrents in the surfaces of solids possessing extreme diauiagiutfic quality in other 

 words, inlinitely smad permeability. The distril)iition of electric current on each 

 body may be any whatmer which fulfils the condition that the total curnMit across 

 any closed line drawn on the surface once througli the aperture is equal to 1, Iw of 

 the circulation ' through the aperture in tbe l-.yilrukinclic anahigue. 



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

 motion could serve as a foundation for n theory of the equilibrium, aiul the 



' Tbe integral of tangential component velocity all rouml any closed curve, jias-- 

 ing once tlirou}<h the aperture, is deline'l as the 'Cyclic constant,' vr the 'circuhiti^iii ' 

 (• Vortex Motion," 4J (iU («), Trniix. li. S. E. April^'.t, KS07). It b.-isthc .same value 

 for all closed curves passing just once through the ape-turo, iind it remains constant 

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



