Prof. Challis on the Dispersion of Light. 497 



the displacement of any atom of the medium in which the light is 

 propagated will necessarily bring into play the molecular forces 

 of the medium. Having found that the reasoning on this point 

 in the article just cited requires correction, I propose now to 

 determine again the acceleration of the atom due to the elasticity 

 of the medium. Suppose that by the action of the sethereal 

 waves the mean interval between consecutive atoms, estimated 

 in the direction of propagation, is diminished by a quantity (e) ex- 

 tremely small compared to that interval. Then since the result- 

 ing molecular action is proportional to the relative displacement 

 of the atoms, the acceleration of an atom due to this cause is 



de 

 — e<1 '-T-> e being considered to be a function of oc, and e 2 being 



an unknown constant. But since the movements of the atoms 

 are determined by the action of the waves, it follows that these 

 movements and the values of e are propagated through the 

 medium with the velocity (b) of the propagation of the waves. 

 Hence, just as in any case of uniform propagation, 



v = be=f(x— bt), 

 v being the velocity of any atom. Consequently 

 de e 2 dv e 2 d 2 oc , 



It should be remarked here that e 2 may be regarded as a mea- 

 sure of the force by which an atom displaced relatively to sur- 

 rounding atoms tends to return to a position of relative equili- 

 brium. On account of the small movements with which we are 

 concerned, which do not sensibly affect the density of the 

 medium, this force must be very nearly the same as that by 

 which a single atom displaced tends to return to its position of 

 absolute equilibrium ; so that e 2 may be taken as the measure 

 of molecular elasticity in the given direction of propagation. In 

 the former investigation this quantity was incorrectly stated to 

 be a measure of elasticity as inferred for a continuous body from 

 a given relation between its pressure and density, which is 

 dependent on the other measure, but not identical with it. It 

 is possible that e 2 , as resulting from the immediate action of 

 molecular forces, may be comparable in magnitude with b 2 . 



The investigation has now conducted to the following equation 

 for determining the motion of the atom : 



dt 2 ~ * 2 A ' \ dt \ W 16 ' dt 2 J + b 2 ' dt 2 ' 

 A first integration of this equation gives 



dec b 2 fv(^- ^ -?\- 3 P ^\ 



dt ~ * 2 A(6 2 -e 2 ) I \ 16/ 16 ' dt J' 



