Prof. Larmor, On Kundt's law of selective dispersion. 21 



On the dynamical significance of Kundt's law of selective dis- 

 persion, in connexion with the transmission of the energy of trains 

 of dispersive waves*. By J. Larmor, M.A., St John's College, 

 Lucasian Professor of Mathematics. 



[Read 14 November 1904.] 



1. This subject has been treated by the writer, Phil. Trans. 

 1897a, p. 243. If we are content with a naive theory of an inde- 

 pendent vibrator for each line of the spectrum, or even with a 

 conception of a molecule as a connected dynamical system vibrating 

 about a position of rest, it is readily inferred that the index of 

 refraction always trends upward with increasing frequency, so as 

 to be abnormally great on the lower side of an absorption band and 

 abnormally small on the upper side of it, as was originally remarked 

 by Kundt to be actually the case in anomalously dispersive media. 

 But when the molecule is considered, as it must be, notwithstanding 

 analytical difficulties, to be a dynamical system vibrating about a 

 permanent state of steady cyclic motion, the gyrostatic terms in 

 the equations of its vibrations render a theoretical discussion of 

 Kundt's law difficult, and it was not then completely effected ; 

 though it was easy to see that the law should be connected with 

 the necessarily positive quality of the vibratory energy. A recent 

 paper by Prof. Lamb, in Proc. Math. Soc, consequent upon a 

 remark by Prof. Schuster, seems to afford a key to the matter. 



When we speak in optics of wave-length X , we can only mean 

 light of wave-lengths comprehended within a small interval SX 

 around \ , — that is a train of undulations of wave-length uncertain 

 from point to point within this interval BX, which is itself a 

 measure of the defect of purity of the beam. There is no such 

 thing as an absolutely homogeneous train of wave-length exactly 

 X . Now Sir George Stokes has explained (Smith's Prize Ex- 

 amination Questions, 1876) how in such an undamped train, nearly 

 homogeneous, the velocity of propagation, considered as the rate 

 at which the actual disturbance travels onwards, is in a dispersive 

 medium not the wave-length X of the wave-form divided by its 

 periodic time t, but is 



* The first section of this note was communicated to the British Association at 

 the meeting in Cambridge last August. 



