350 



NA TURE 



\_August 23, 1888 



above is more than a kind of parody of the truth ; never- 

 theless, supposing it only a parody, supposing what we call 

 electromotive elasticity and inertia are things capable of 

 clearer conception and more adequate statement, yet, 

 inasmuch as they correspond to and represent a real 

 analogy, and inasmuch as we find that a medium so con- 

 structed would behave in a very electrical manner, and 

 might in conjunction with matter be capable of giving rise 

 to all known electrical phenomena, we are bound to follow- 

 out the conception into other regions, and see whether any 

 other abstruse phenomena, not commonly recognized as 

 electrical, will not also fall into the dominion of this hypo- 

 thetical substance and be equally explained by it. This is 

 what we shall now proceed to do. 



Before beginning, however, let me just say what I mean 

 by " electromotive elasticity." It might be called chemical 

 elasticity, or molecular elasticity. There is a well-known 

 distinction between electromotive force and ordinary 

 matter-moving force. The one acts upon electricity, 

 straining or moving or, in general, "displacing" it ; the 

 other acts upon matter, displacing it. The nature of 

 neither force can be considered known, but crudely we 

 may say that as electricity is to matter so is electromotive 

 force to common mechanical force : so also is electro- 

 motive elasticity to the common shape-elasticity or 

 rigidity of ordinary matter : so perhaps, once more, may 

 electrical inertia be to ordinary inertia. 



Inertia is defined as the ratio of force to acceleration ; 

 similarly electric inertia is the ratio of electromotive force 

 to the acceleration of electric displacement. It is quite 

 possible that electric inertia and ordinary inertia are the 

 same thing, just as electric energy is the same with 

 mechanical energy. If this were known to be so, it 

 would be a step upward towards a mechanical explana- 

 tion ; but it is by no means necessarily or certainly so ; 

 and, whether it be so or not, the analogy undoubtedly 

 holds, and may be fruitfully pursued. 



And as to " electromotive elasticity,'' one may say that 

 pure water or gas is electromotively elastic, though 

 mechanically limpid ; each resists electric forces up to a 

 certain limit of tenacity, beyond which it is broken ; and 

 it recoils when they are withdrawn. Glass acts in the 

 same way, but that happens to be mechanically elastic 

 too. Its mechanical elasticity and tenacity have, 

 however, nothing to do with its electric^ elasticity and 

 tenacity. 



One perceives in a general way why fluids can be 

 electrically, or chemically, or molecularly elastic : it 

 is because their molecules are doubly or multiply com- 

 posed, and the constituent atoms cling together, while 

 the several molecules are free of one another. Mechan- 

 ical forces deal with the molecule as a whole, and to 

 them the substance is fluid ; electrical or chemical forces 

 deal with the constituents of the molecule, setting up 

 between them a shearing strain and endeavouring to tear 

 them asunder. To such forces, therefore, the fluid is 

 elastic and tenacious up to a certain limit. Extend this 

 view of things to the constitution of the ether, and one has 

 at least a definite position whence to further proceed. 



It may be convenient and not impertinent here to say 

 that a student might find it a help to re-read Parts I. and 

 II. in the light of what has just been said: remembering 

 that, for the sake of simplicity, only the simple fact of an 

 elastic medium was at first contemplated and insisted 

 on ; no attempt being made to devise a mechanism for its 

 elasticity by considering it as composed of two con- 

 stituents. Hence the manifest artificiality of such figures 

 as Fig. 6 (Nature, vol. xxxvi. p. 559), where fixed beams 

 are introduced to serve as the support of the elastic con- 

 nections. But it is pretty obvious now, and it has been 

 said in Part III., that a closer analogy will be obtained 

 by considering two ^ets of beads arranged in alternate 

 parallel rows connected by elastic threads, and displaced 

 simultaneously in opposite directions. 



Recovery of the Medium from Strain. 

 We have now to consider the behaviour of a medium 

 endowed with an elastic rigidity, k, and a density, /*, 

 subject to displacements or strains. One obvious fact is 

 that when the distorting force is removed the medium 

 will spring back to its old position, overshoot it on the 

 other side, spring back again, and thus continue oscillating 

 till the original energy is rubbed away by viscosity or 

 internal friction. If the viscosity is very considerable, it 

 will not be able so to oscillate ; it will then merely slide 

 back in a dead-beat manner towards its unstrained state, 

 taking a theoretically infinite time to get completely back, 

 but practically restoring itself to something very near its 

 original state in what may be quite a short time. The 

 recovery may in fact be either a brisk recoil or a leak of 

 any degree of slowness, according to the amount of 

 viscosity as compared with the inertia and elasticity. 



The matter is one of simple mechanics. It is a case 

 of simple harmonic motion modified by a friction pro- 

 portional to the speed. The electrical case is simpler 

 than any mechanical one, for two reasons : first, because 

 so long as capacity is constant (and no variation has 

 yet been discovered) Hooke's law will be accurately 

 obeyed — restoring force will be accurately proportional 

 to displacement ; secondly, because for all conductors 

 which obey Ohm's law (and no true conductor is known 

 to disobey it) the friction force is accurately proportional 

 to the first power of velocity. 



There are two, or perhaps one may say three, main 

 cases. First, where the friction is great. In that case 

 the recovery is of the nature of a slow leak, according to 

 a decreasing geometrical progression or a logarithmic 

 curve ; the logarithmic decrement being independent of the 

 inertia, and being equal to the quotient of the elasticity 

 and the resistance coefficients. 



As the resistance is made less, the recovery becomes 

 quicker and quicker until inertia begins to prominently 

 assert its effect and to once more lengthen out the time of 

 final recovery by carrying the recoiling matter beyond its 

 natural position, and so prolonging the disturbance by 

 oscillations. The quickest recovery possible is obtained 

 just before these oscillations begin ; and it can be shown 

 that this is when the resistance coefficient is equal to 

 twice the geometric mean of the elasticity and the inertia. 

 One may consider this to be the second main case. 



The third principal case is when the resistance is quite 

 small, and when the recovery is therefore distinctly oscilla- 

 tory. If the viscosity were really zero, the motion would 

 be simply harmonic for ever, unless some other mode of 

 dissipating energy were provided ; but if some such mode 

 were provided, or if the viscosity had a finite value, 

 then the vibrations would be simply harmonic with a 

 dying out amplitude, the extremities of all the swings 

 lying on a logarithmic curve. In such a case as this, the 

 rate of swing is practically independent of friction ; it 

 depends only on elasticity and inertia ; and, as is well 

 known for simple harmonic motion, the time of a complete 

 swing is 27r times the square root of the ratio of inertia 

 and elasticity coefficients. 



Making the statement more electrically concrete, we 

 may consider a circuit with a certain amount of stored-up 

 potential energy or electrical strain in it:, for instance, a 

 charged Leyden jar provided with a nearly complete 

 discharge circuit. The main elastic coefficient here is 

 the reciprocal of the capacity of the jar: the more 

 capacious the jar the more "pliable" it is — the less force 

 of recoil for a given displacement, — so that capacity is the 

 inverse of rigidity. The main inertia coefficient is that 

 which is known electrically as the " self-induction " of the 

 circuit : it involves the inertia of all the displaced matter 

 and ether, of everything which will be moved or disturbed 

 when the jar is discharged. It is not a very simple thing 

 I to calculate its value in any given case ; still it can be 

 I done, and the general idea is plain enough without under- 



