OPALESCENCE 343 



that the smallest particles which are capable of scattering light are 

 from fifty to a hundred times smaller than the mean wave length 

 of light at 0.5 /*, the diameter of such particles could be not less 

 than from 5 to 10 MM- Now we have seen in Chaps. VIII and IX, 

 that the molecular weight of casein in solutions containing 11.4 X 

 10~ 5 equivalents of base per gram of protein, is probably about 

 17,600 (estimated from electrochemical data). From the analysis 

 of Hammarsten (39) it appears that if casein be possessed of this 

 molecular weight, then its empirical formula must be, approxi- 

 mately: 



Now it has been shown by Kopp (54) that the relative molecular 

 volumes of organic substances can, with certain marked exceptions, 

 be calculated as an additive function of their constituent atoms.* 

 The mode in which the valencies of the atoms are distributed 

 affects their contribution to the total volume, however, "carbonyl" 

 oxygen contributing an amount differing from that contributed by 

 hydroxyl oxygen. From the analysis of Abderhalden and others it 

 would appear that if casein possesses the above molecular weight 

 it must contain about four molecules of tyrosin, and one each of the 

 other hydroxy-acids which it is known to contain, namely, serin 

 and caseinic acid, or in all, neglecting the necessarily few terminal 

 COOH groups (Cf. Chap. I) it would appear to contain only 

 about 8 atoms of hydroxyl oxygen out of the 250 atoms of oxygen 

 which are present. But it will be recollected (Chap. I) that there 

 is strong reason to suspect that in many of the COHN groups 

 within the protein molecule the oxygen is in the hydroxy condition. 

 We must, therefore, make two estimates of the molecular volume, 

 one on the supposition that the molecule contains only carbonyl 

 oxygen and the other on the supposition that it contains only 

 hydroxyl oxygen. The true volume will, it is probable, lie be- 

 tween the two. Now the difference in molecular volume due to 

 carbon is 11, that due to hydrogen is 5.5, to nitrogen (as in am- 

 monia) 2.3, to carbonyl oxygen 12.2, to sulphur 22.6, to phos- 

 phorus 25.5, yielding, for the first estimate of the relative molecular 

 volume of casein: 



777 X 11 + 1241 X 5.5 + 197 X 2.3 + 250 X 12.2 + 4 X 22.6 

 + 5 X 25.5 = 19,060; 



* The figures employed in the calculation which follows are cited after 

 Ostwald (77). 



