TRANSACTIONS OF SECTION A. 689 



particles. As T decreases to T,„ fi- increases — i.e., the velocity decreases — until 

 Avh^n T =^ T,„ ij." is infinite and V zero. There is an absorption of energy, and below 

 this absorption band the velocity is very small and the refraction is abnormally 

 large. When T is slightly less than T,„ /x- is negative, the medium has the proper- 

 ties of a metal ; but as T decreases further fi" becomes positive, though less than 

 unity. The A'elocity in the medium is greater than that outside. 



Thus the sj-stem has all the properties of a medium showing anomalous dis- 

 persion. 



iij a simple tran.sformatiou the equation for fi" can be put into the form 





= cr — /c' A- + " 



x-^-V 



o» 



■where X, X,^ are the v^"ave-lengths in air of waves of periods T and T„ ; this 

 ■equation has been verified for ligbt by S. P. Langley over a long range of 

 period. For a transparent medium f„ and T^ lie outside the limits of the visible 

 ■spectrum. 



4. Note on Professor Eiert's Estimate of the Radiating Foiver of an Atom, 

 luitli Bern arks on Vibrating Systems giving Special Series of Over tunes 

 like those Given Out hj some Molecules. Bij Professoi- G. F. FiTZ- 

 Gerald, M.A., F.B.S. 



Attention was drawn to Professor Ebert's paper in ' AViedemann's Annalen ' 

 for 1893, in which he estimated that the energy radiated by a sodium atom as deter- 

 mined by Professor E. Wiedemann was approximately the same as tliat calculated 

 from Hertz's equation for the radiation from one of his oscillators, if the oscillator 

 he supposed of the diameter of the atom and electrical charge be the ionic charge 

 and the time of vibration the period of the sodium line. 



It was pointed out that the period of vibration of a simple oscillator of the size 

 of an atom would be very many times more frequent than that of the sodium line, 

 and that as the energy radiation increases inversely as tbe cube of the wave-length 

 it follows that the radiation of a simple Hertzian oscillator of tbe size of an atom 

 might be many thousands of times as great as what Wiedemann has found to be tbe 

 radiating power of a sodium atom. It follows that sodium atoms must be complex 

 Hertzian oscillators if they are Hertzian oscillators at all, and if they be complex 

 ones their radiating power might be either greater or less than that of a Hertzian ; 

 so that Professor Ebert's calculation only shows that if an atom be a Hertzian 

 oscillator its radiating power is approximately what he has calculated. It was ex- 

 plained that the fact that the vibration-frequencies of molecules were within the 

 r^nge of frequencies that might be expected if the molecules are systems of the size 

 they are known to be, and of a rigidity about that of ordinary rigid bodies, made 

 it appear that the rigidity of hard bodies may be principally the rigidity of the 

 molpcu^es.of. which they are composed. The fact that crystalline structure is gene- 

 i'ally attributed to a peculiarity in the shapes of the molecules, and that deforma- 

 tion confers a crystalline structure on solids, tends to the conclusion that the 

 molecules are deformed by strain. It is otherwise not easy to see why the liglit- 

 frequencies are so nearly those that might be expected from rigid bodies of the size 

 of tbe molecules. 



In connection with the question of the vibrations of molecules, it is to be 

 observed that vibrating systems in which tbe motion can be very simply specified 

 may produce extremely complex systems of lines, as is evident to anybody who has 

 tried to express an algebraic function in a Fourier series. A finite series of 

 discrete lines may be produced by supposing a finite vibrator to divide itself into 

 loops and nodes. If the vibrator be of such a structure that, as in an air column, 

 the velocity of propagation of a wave is independent of the wave-length, then tbe 

 system of overtones will be a system of harmonics. But if the velocity of propa- 

 gation be any other function oi the wave-length, say V =/(X), then it is easy to see 



1893. T Y 



