784 REPORT— 1898. 



the nucleus may be considered as almost absolutely fixed. If tbe period is ^ of a 

 second, frequency 32 according to Lord Rayleijjh'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 2oG, and a 

 very loud sound of the well-known musical cliaracter (C-f;) will be heard.' 



Increase the frequency now to 32 times this, that is to 8192 periods per second, 

 and an exceedinglj' 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 successively according to the ratios of the diatonic 

 scale, and the well-known musical notes will be each clearly and perfectly per- 

 ceived 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 no- 

 thing, if the amplitude of the motion is suitable. 



To produce such relative motions of shell and nucleus as we have been con- 

 Mdering, whether the shell is embedded 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 condensational and rarefactional), which are caused 

 to proceed outwards in all directions. Suppose now, for example, we find liow 

 much work per second is required to maintain vibration with a frequency of 1000 

 j)eriods per second, through total relative motion of 10"^ of a centimetre. Keeping 

 to the same rate of doing work, raise the frequency to 10*, 10'^, 10", 10", 10''^, 

 500 X 10''^. "We now hear nothing ; and we see nothing from any point of view 

 in the line of the vibration of the centre of the shell, which I shall call the axial 

 line. But 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 every- 

 where in the meridional plane, and perpendicular to the line drawn to the centi-e. 



When the vibrating shell is surrounded by air, or water, or other fluid, and 

 when the vibrations are of moderate frequency, or of anything less than a few 

 hundred thousand periods per second, the waves proceeding outwards are conden- 

 sational-rarefactional, with zero of alternate condensation and rarefaction at every 

 point of the equatorial plane and maximimi 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-rarefactional, according 

 respectively to the two descriptions which have been before ns, 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 10', 10"', or 10'^, and probably up to any 

 frequency not so high but that the wave-length is a large multiple of the distance 

 fi'om molecule to molecule of the solid. When we rise to frequencies of 4 x lO'-, 

 400 X 10", 800 X 10l^ and 3000 x 10'==, corresponding to the already known rane-e 

 of long-period 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 we pass from the propagational 

 velocities of 3 kilometres per second for distortional waves in glass, or 5 kilometres 

 per second for the condensational 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 quite sure ; the transition is continuous. Is it probable (if ether is abso- 

 lutely incompressible, it is certainly possible) that the condensational-rarefactional 



' Lord Rayleigh has found that with frequency 25G, periodic condensation and 

 rarefaction of the marvellously small amount, G x 10-" 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 1-27 x 10-' of a centimetre. Sound, vol. ii. p. 439 

 (2nd edition). 



' Math, and Pltys. Papers, vol. iii. art. civ. p. 522. 



