REFRACTIVE INDICES 363 



of the dissolved protein itself be d (Cf. Chap. XIII, section 11) 

 the refractive index of the mixture should be given by: 



, ^. (N: - 1) (100 - c) , (N - 1) c 1 



100 ' 100 d 



whence 



100 (w - 1) = 100 (iVi - 1) - c f 1 - ^ - iVi + ^ 



and Ar I ^ /i 1 Ar I -^ 



^ = ^^ + 100 i-rf-^^+d 



or 



„_^, = (i_i_^. + ^)_£_, (i) 



which is identical with the relation n — ni = a X C which, as we 

 have alreadj^ seen, subsists between the refractive index of a pro- 

 tein solution and its percentage concentration.* Hence we may 

 conclude that for solutions of proteins in aqueous solvents Gladstone's 

 law of mixtures holds good. The constant a is obviously given by 



-ttt; 1 1 T — Ni -\ — t] . For solutions of casein containing be- 



100 V d d) 



tween 0.25 and 6.00 per cent the average value of a is 0.00125. 

 Hence, by exterpolation, the refractive index of the pure protein 

 should be 1.675, taking the refractive index of water as 1.333 and 

 the density of dissolved casein as 1.39 (Cf. Chap. XIII, section 11). 

 For serum globuhn this constant is 1.774. The refractive index 

 of the pure protein does not readily admit of direct determination 

 in these cases. The protamin salts, clupein sulphate and salmin 

 sulphate can, however, readily be obtained in a fluid (oily) con- 

 dition. Kossel (24) has determined the refractive indices of these 

 fluids and finds them to be, respectively, 1.443 and 1.442, figures 

 which are of the same order of magnitude as the above estimates. 

 If the density of the solvent be d' instead of 1 and c be small, so 

 that the density of the solution is very nearly that of the solvent, 

 then equation (i) becomes: 



* From this it would appear that the value of a should vary with the re- 

 fractive index even of a dUute solution of a base or acid which is not exactly 

 the same as that of water, that is, with the nature and concentration of the 

 (dilute) acid or base employed as a solvent. It will be observed, however, 

 that in the experimental values of a only a one-hundredth part of the difference 

 between the refractive index of the acid or alkali solution and that of water 

 appears. This quantity, for the solutions employed, is far too small to be 

 detectable. 



