TRANSACTIONS OF SECTION A. 785 



wave becomes less and less with frequencies of from 10® to 4 x W, and that there 

 is absolutely none of it for periodic disturbances of frequencies 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 abso- 

 lutely certain that there is a definite dynamical theory for waves of light, to be 

 enriclied, 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. 



I. {:i) 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 

 produce 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 disturbance 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 l:^''^, 800 x 10'=, or 3000 x lO''^, 

 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. But now let our massless shell be embedded far in the interior of a vast 

 mass of glass, or metal, or rock, or of any homogeneous elastic sohd, firmly 

 attached to it all round, so that neither splitting away nor tangential slip shall be 

 possible. Purely distortional waves will spread out in all directions excejrt the 

 axial. Suppose, to fi.x our ideas, we begin with vibrations of one-secoud period,, 

 and let the elastic solid be either glass or iron. At distances of hundreds of kilo- 

 metres (that is to say, distances great in comparison with the wave-lengtli and 

 great in comparison with the radius of the shell), the wave-length will be approxi- 

 mately 3 kilometres.' Increa.se the frequency now to 1000 period? per second : at 

 distances of hundreds of metres the wave-length will be about 3 metres. Increase 

 now the frequency of 10'' periods per second : the wave-length will be 3 millim.,. 

 and this not only at distances of several times the radius of the shell, but through- 

 out the elastic medium from close to the outer surface of the shell ; because the 

 wave-length now is a small fraction of the radius of the shell. Increase the frequency 

 further to 1000 x lO""' periods per second; the wave-length will be 3 x 10~^ of a 

 millimetre, or 3 mikroms,- if, as in all probability is the case, the distance between 

 the centres of contiguous molecules in glass and in iron is less than a five-hundredth 

 of a mikrom. But it is probable that the distance between centres of contiguous 

 molecules in glass and in iron is greater than 1U~'^ of a mikrom, and therefore it is 



' Math, and PJiys. Papers, vol. iii. art. civ. p. 552. 



* For a small unit of length Langley, fourteen years ago, used with great advan- 

 tage and convenience the word 'mikron ' to denote the millionth of a metre. The 

 letter n has no place in the metrical system, and I venture to suggest a change of 

 spelling to 'mikrom ' for the millionth of a metre, after the analogy of the English 

 usage for millionths (mikrohm, mikro-ampere, mikrovolt). For a conveniently small 

 corresponding unit of time I further venture to suggest ' michron ' to denote the 

 period of vibration of light whose wave-length in jether is 1 mikrom. Thus, the 

 velocity of light in asther being 3 x 10^ metres per second, the michron is i x 10~'* 

 of a second, and the velocity of light is 1 mikrom of space per michron of time. 

 Thus the frequency of the highest ultra-violet light investigated by Schumann (-1 of 

 a mikrom wave-length, Sitzunciiher. d. k. Gesellscli.d. Wisseiisch. zu Wien,c\\. pp. 415 

 k. (525, 189.3) is 10 periods per michron of time. The period of sodium light (mean 

 of lines D) is -589212 of a michron; the periods of the ' Keststrahlen ' of rocksalt 

 and sylvin found by Rubens and Aschkinass (Wied. Ann. Ixv. (1898) p. 211) are 

 512 and (51-1 michrons respectively. 



No practical inconvenience can ever arise from any possible confusion or momen- 

 tary forgetfulness in respect to the similarity of sound between michrons o£ time 

 and mikroms of. space. — K. 



1898. .<?P,. 



