﻿On the Theory of Dispersion. 4G5 



from which we have 



p _ A(a 2 log a 2 - h 2 log b 2 + a 2 - tf ) 

 2{a 2 -b 2 ) 

 Aa 2 /> 2 (loga 2 -log6 2 ) 

 °~ d'-b 2 



If Q denotes the volume of fluid which flows through the 

 canal per unit depth in unit time, it is equal to the difference 

 of the value of yjr for r=a, b. 



Q = A{b 2 logb-a 2 \oga) + B(b 2 -a 2 ) + C()ogb-loga) 



P r 2 4a 2 /> 2 /. «Vh 



If a, & tend to infinity in such a way that a — b ->d and 

 aa~>l _^ Fd s 



^ 12fiV 



which agrees with the known result for the flow between 

 parallel planes. 



LT. Theory of Dispersion. 

 By Prof. D. N. Mallik, Sc.D., F.R.S.E* 



1. TT is well-known that the electromagnetic theory, as 

 J. expressed by the equations of Maxwell and Hertz, 

 cannot account for aberration, dispersion, and allied pheno- 

 mena. In analysing the reason for this, we note that the 

 theory is based on the following postulates : — 



(1) The energy of the electromagnetic field is that of the 



dielectric medium alone, arising from a certain 

 strained condition of the medium. 



(2) The conductors having static charges serve only to 



limit the dielectric region so that no part of the 

 energy resides on them. 



(3) The strained condition of a dielectric is due to electric 



displacement or polarization /, g, A, subject to the 

 condition 



3* + By + B* () 



This displacement is apparently held to involve 

 motion of the aether in the medium, subject to a pro- 

 perty akin to elasticity (due to inter-action of matter 



* Communicated by the Author. First appeared as a Bulletin of the 

 " Indian Association for the Cultivation of Science," Calcutta. 



Phil Mag. S. 6. Vol. 29. No. 172. April 1915. 2 H 



