the Rotational Optical Activity. 303 



substance, diphenylbornylimidoxanthide, in a state of super- 

 fusion, in the absence of any inactive molecule. 



Lorentz's theory can, however, give an account of the 

 experimental results, for the values calculated by Mr. Livens 

 correspond to conditions widely different from those which 

 are realized. The diagrams, pages 1004 to 1006, vol. xxvii., 

 have been obtained for the values 0*1, 1, and 10 of the con- 

 stant x, which is approximately equal to the maximum value 

 of the extinction coefficient. They represent the expected 

 phenomena in the case of substances for which the absorp- 

 tion would be of the same order or' magnitude as for cyanine 

 (a = 0'75) or for silver (a. near 1). The polarimetric study 

 of such substances seems unfortunately impracticable, on 

 account of the magnitude even of the absorption. In the 

 experiments of Cotton and of 01 instead *, the extinction 

 coefficient has never exceeded 2 . 10~ 5 ; for the most absorbing 

 compound which I could study, it is at the maximum 4.10 -3 . 

 If we give to a the corresponding values, the expected 

 anomaly, according to the formula? of Mr. Livens, becomes 



negligible : it is, in the case of solutions, lower than A 



/a) 1 \ 1UUU0 



of the mean rotation ( — < ) f. 



\<*i 10000/ 



If the calculations pointed out page 1007 are made in the 

 same way, by neglecting a term which, in the case of solu- 

 tions, never attains -fk™. of the expected anomaly, the same 



formula? are found as in Drude's theory, multiplied by 

 (e 2 — 1) (e 2 + 2): the variation of this factor as the fre- 

 quency of the light varies is never great enough to introduce 

 between the two theories any discrepancy experimentally 

 appreciable. 



The two theories are then quite equivalent from the point 

 of view of the observable phenomena of anomalous rotatory 

 dispersion and circular dichroism, and their comparison can 

 be made only by the results expected for the dependence of 

 the rotation on the concentration and on the nature of the 

 solvent. Whereas Drude's theory points out that the rota- 

 tory power is independent of these two factors, Lorentz's 



* L. B. Olmstead. Phys. Rev. xxxv. p. 31 (1912). 



t Similar remarks apply to the formulae obtained for the magnetic 

 rotatory dispersion. It is known indeed that the attempts with aniline 

 dyes have not given any result : those obtained by Schmauss are due to 

 experimental error (F. Bates, Ann. der Phys. xii. 1903, p. 1080). The 

 magnetic rotatory dispersion is moreover not necessarily similar to the 

 natural rotatory dispersion (E. Darmois, Ann. de Chim. et de Phi/s. (8) 

 xxii. p. 247, 1911). 



