150 Mr. W. Sutherland on Molecular Refraction. 



is altered, then in this last equation it must have its value 

 proper to the compound. 



Thus we have the theoretical view of the application of 

 Gladstone's empirical law to mixtures and chemical com- 

 pounds. 



But so far the reasoning by which equations (1) and (2) 

 have been established is only a first approximation to an 

 accurate argument, as we have left out of count the effect of 

 the atoms in producing delay, not only when the wave is 

 passing through their actual substance, but in the inter- 

 mediate gether by breaking up the wave-front ; in other 

 words no ray can get through in a straight line, it is bent now 

 this way, now that, by the successive atoms. The mean ray, 

 therefore, has its time of traversing the aather thus increased. 

 A more definite idea of this efifict of the atoms can be ob- 

 tained if we imagine them spread out in successive planes 

 parallel to the plane of an incident wave. At each encounter 

 with a layer of atoms the plane wave-front, after getting just 

 through, is a curved sui'face that tends to recover its plane 

 form before encountering the next layer ; during this process 

 of recovering the mean velocity of the wave-front must be 

 less than the velocity of a plane wave in pure sether. The 

 amount of delay thus produced must be proportional to the 

 length of path and a function of the density, and as it vanishes 

 with the density we may assume that it is expressible by 

 s (bd + ccP) + , where h and c are constants^ which may depend 

 on the arrangement of the atoms in a molecule. Adding this 

 to the right-hand side of our original equation, we get 



s s slad /I 1 \ ,, , „ . 

 -- = [^-~)+{hd^-cd^^)s, 



whence we get 



(n-l)J = Za(N-l) + ^(6 + cc^ + ). ... (3) 



This would make the refraction-equivalent of the molecule 

 equal to a constant term plus a term proportional to the 

 density if the series can be arrested at the second term. The 

 terms nib and iiicd must be small compared to la (N — 1), as 

 is seen from the nature of the argument by which they were 

 introduced, and it is to be noticed that they may vary with 

 the structure of the molecule. 



To test the last formula (3) the only experiments suitable 

 are those of Lorenz (Wiedemann, xi.), who determines the 

 values of the index and density of six liquids at the tempera- 



