Mr. W. Sutherland on Molecular Refraction. 149 



can write the above thus : — 



(n-l)w=m(N-l). 



But if we suppose u to become identical with U, n must 

 become identical with N, and we see that the value of Ic must 

 be 1, and 



(n-l)M=(N-l)U, (1) 



an equation which could be written down direct from the 

 consideration that the effect of the scattered molecules in re- 

 tarding the light is the same as if the molecules were gathered 

 into a continuous homogeneous mass. The corresponding 

 equation in Lorenz's theory is 



n^-1 _N2-1 



and it is important to notice the great difference in the physical 

 bearings of the two expressions. If N is large, that is if the 

 velocity of light in a molecule is small compared to that in 

 sether, then (N^ — l)(N^ + 2) approaches the limit 1, and 



U_ n^-1 

 u ~ n^ + 2' 



and this last fraction, for most liquids, has a value about one 

 fourth, so that if N could be shown to be large, we should 

 have the actual volume of an atom about one fourth of its 

 domain ; while, according to equation (1), if N is large, 

 JJ/u is a small fraction of (n — 1), and would be small for most 

 liquids. The two theories are thus in direct contradiction to 

 one another, and it would appear that the assumption previously 

 pointed out as having been made by Lorenz, is responsible 

 for the discrepancy, seeing that the greater N is, the more 

 unjustifiable is that assumption. 



The general method of proceeding in the previous proof, 

 namely, that of considering loss of time, has a certain claim to 

 be considered the correct one, if we remember that, according 

 to the wave theory of light, a ray passes from one point to 

 another by the path which makes its time of passing a 

 minimum. 



If we suppose several sorts of atoms distributed throughout 

 the same space, whether mechanically mixed or chemically 

 united into molecules, we ought, according to the above theory, 

 to have 



(/i-l)M=S(N-l)U; (2) 



but only so long as we assume that neither N nor U, for any 

 sort of atom, is altered by chemical combination ; if N or U 



