5(^ 



NA TUKE 



[NOVEMHEK 17, 1898 



CONTINUITY OF WAVE THEORIES} 



CONSIDER the following three analogous cases :— I. 

 mechanical, II. electrical, III. electromagnetic. 



I. Imagine an ideally rigid globe of solid platinum of 

 12 centim. diameter, hung inside an ideal rigid massless 

 spherical shell of 13 centim. internal diameter, and of 

 any convenient thickness. Let this shell be hung in air 

 or under water by a very long cord, or let it be em- 

 bedded in a great block of glass, or rock, or other elastic 

 solid, electrically conductive or non-conductive, trans- 

 parent or non-transparent for light. 



I. (i) By proper application of force between the 

 shell and the nucleus cause the shell and nucleus to 

 vibrate in opposite directions with simple harmonic 

 motion through a relative total range of 10""' of a cen- 

 timetre. We shall first suppose the shell to be in air. 

 In this case, because of the small density of air com- 

 pared with that of platmum, the relative total range 

 will be practically that of the shell, and the nucleus may 

 be considered as almost absolutely fixed. If the period 

 is ;,\t of a second, frequency 32 according to Lord 

 Rayleigh's designation, a humming sound will be heard, 

 certainly not excessively loud, but probably amply audible 

 to an ear within a metre or half a metre of the shell. 

 Increase the frequency to 256, and a very loud sound of 

 the well-known musical character (Co^,;) will be heard.- 



Increase the frequency now to 32 tmies this, that is to 

 8192 periods per second, and an exceedingly loud note 5 

 octaves higher will be heard. It may be too loud a 

 shriek to be tolerable ; if so, diminish the range till the 

 sound is not too loud. Increase the frequency now suc- 

 cessively according to the ratios of the diatonic scale, 

 and the well-known musical notes will be each clearly 

 and perfectly perceived through the whole of this octave. 

 To some or all ears the musical notes will still be clear 

 up to the G (24756 periods per second) of the octave 

 above, but we do not know from experience what kind 

 of sound the ear would perceive for higher frequencies 

 than 25000. We can scarcely believe that it would hear 

 nothing, if the amplitude of the motion is suitable. 



To produce such relative motions of shell and nucleus 

 as we have been considering, whether the shell is em- 

 bedded in air, or water, or glass, or rock, or metal, a 

 certain amount of work, not extravagantly great, must 

 be done to supply the energy for the waves (both con- 

 densational and rarefactional), which are caused to pro- 

 ceed outwards in all directions. .Suppose now, for 

 example, we find how much work per second is required 

 to maintain vibration with a frequency of 1000 periods 

 per second, through total relative motion of lo'' of a 

 centimetre. Keeping to the same rate of doing work, 

 raise the frequency to lo^ lO", 10'', 10'', 10'-, 500 x 10'-. 

 We now hear nothing ; and we see nothing from any 

 point of view in the line ol the vibration of the centre 

 of the shell which I shall call the axial line. Hut from 

 all points of view, not in this line, we see a luminous 

 point of homogeneous polarised yellow light, as it were 

 in the centre of the shell, with increasing brilliance as 

 we pass from any point of the axial line to the equatorial 

 plane, keeping at equal distances from the centre. The 

 line of vibration is everywhere in the meridional plane, 

 and perpendicular to the line drawn to the centre. 



1 "Continuity in unduUtory tlicory of condensational-rarcfactionai waves 

 in gases, liquids, and solids, of distortional waves in solids, of electric waves 

 in all substances capable of transmitting them, and of radiant heat, visible 

 light, ultra-violet light." Communicated by l^rd Kelvin, G.C.V.O., being 

 the substance of a communication to Section A of the British Association 

 at its recent meeting in Bristol. 



- Lord Rayleigh has found that with frequency 256, periodic condensation 

 and rarefaction of the marvellously small amount 6 x io"f of an atmosphere, 

 or "addition and subtraction of densities far less than those to be found in 

 our highest vacua," gives a perfectly audible sound. The amplitude of the 

 aerial vibration, on each side of zero, corresponding to this is I's; x io~7 of 

 a centimetre.— " Sound," vol. ii. p. 439 (second edition). 



NO. I 5 16, VOL. 59] 



When the vibrating shell is surrounded by air, 01 

 water, or other fluid, and when the vibrations are ol 

 moderate frequency, or of anything less than a few 

 hundred thousand periods per second, the waves pro- 

 ceeding outwards are condensational-rarefactional, with 

 zero of alternate condensation and rarefaction at every 

 point of the equatorial plane and maximum in the axial 

 line. When the vibrating shell is embedded in an elastic 

 solid extending to vast distances in all directions from it, 

 two sets of waves, distortional and condensational-rare- 

 factional, according respectively to the two descriptions 

 which have been before us, proceed outwards with 

 different velocities, that of the former essentially less 

 than that of the latter in all known elastic solids.^ Each of 

 these propagational velocities is certainly independent 

 of the frequency up to io\ 10^, or 10", and probably up 

 to any frequency not so high but that the wave-length is 

 a large multiple of the distance from molecule to mole- 

 cule of the solid. When we rise to frequencies of 

 4 X 10'-, 400 X 10'-, 800 X 10'-, and 3000 x 10'-. cor» 

 responding to the already known range of long-i)eriod 

 invisible radiant heat, of visible light, and of ultra-violet 

 light, what becomes of the condensational-rarefactional 

 waves which we have been considering ? How and 

 about what range do w^e pass from the propagational 

 velocities of 3 kilometres per second for distortional 

 waves in glass, or 5 kilometres per second for the con- 

 densational waves in glass, to the 200,000 kilometres per 

 second for light in glass, and, perhaps, no condensational 

 wave ? Of one thing we may be quitej sure ; the tran* 

 sition is continuous. Is it probable (if aether is abso* 

 lutely incompressible, it is certainly possible) that ih^ 

 condensational-rarefactional wave becomes less and less 

 with frequencies of from lo" to 4 x 10'-, and that there 

 is absolutely none of it for periodic disturbances of fre- 1 

 quencies of from 4 x 10'-' to 3000 x 10'-? There is 

 nothing unnatural or fruitlessly ideal in our ideal shell, 

 and in giving it so high a frequency as the 500 x 10'- of 

 yellow light. It is absolutely certain that there is a 

 definite dynamical theory for waves of light, to be 

 enriched, not abolished, by electromagnetic theory ; and 

 it is interesting to find one certain line of transition from 

 our distortional waves in glass, or metal, or rock, to our 

 still better known waves of light. 



1. (2) Here is another still simpler transition from the 

 distortional waves in an elastic solid to waves of light. 

 Still think of our massless rigid spherical shell, 13 

 centim. internal diameter, with our solid globe of 

 platinum, 12 centim. diameter, hung in its interior. 

 Instead of as formerly applying simple forces to pro- 

 duce to-and-fro rectilinear vibrations of shell and nucleus, 

 apply now a proper mutual forcive between shell and 

 nucleus to give them oscillatory rotations in contrary 

 directions. If the shell is hung in air or water, we should 

 have a propagation outwards of liisturbance due to 

 viscosity, very interesting in itself ; but we should have 

 no motion that we know of appropriate to our present 

 subject until we rise to frequencies of 10", 10 x 10'-, 

 400 X 12'-, 800 X 10'-, or 3000 X 10'-', when we should 

 have radiant heat, or visible light, or ultra-violet light 

 proceeding from the outer surface of the shell, as it were 

 from a point-source of light at the centre, with a character 

 of polarisation which we shall thoroughly consider a 

 little later. Hut now let our massless shell be embedded 

 far in the interior of a vast mass of glass, or metal, or 

 rock, or of any hoiinigeneous elastic solid, firmly att.ached 

 to it all round, so that neither splitting away nor tangential 

 slip shall be possible. Purely distortional waves will 

 spread out in all directions except the axial. Suppose, to 

 fix our ideas, we begin with vibrations of one-second 

 period, and let the elastic solid be either glass or iron. 

 At distances of hundreds of kilometres (that is to say, 

 distances great in comparison with the wave-length and 



* "Math, and I'hys. I*apcrs," vol. iii.,nrt. civ. p. 522. 



