ON OPTICAL ROTATORY DISPERSION. 
255 
and invert-sugar gave, on the other hand, a very exact compensation (‘ Ann. Chim. 
Phys.,’ 1844, vol. 10, p. 35). After Biot’s death the law of inverse squares was generally 
abandoned, even as a first approximation. The result was most unfortunate, since the 
experimenters who proved the inaccuracy of Biot’s formula did not possess the 
mathematical skill that was required to replace it by another formula that was more 
exact. There can be little doubt that, as more exact methods of measurement were 
developed, Biot himself would have investigated the deviations from this law, and might 
well have discovered the small but important correction which Drude introduced 
many years later when he wrote a = k/(\ 2 —\ 2 ) instead of a — k/\ 2 . 
This discovery was extremely likely in view of the fact that, as early as 1817, Biot, 
in applying the law of inverse squares to the rotatory power of quartz, had used a 
graphical method in which virtually the reciprocal of the rotatory power was plotted 
against the square of the wave-length* (‘Mem. Acad. Sci.,’ 1817, vol. 2, plate 3 facing 
p. 136). This device of plotting 1/a against X 2 is, however, the simplest method of 
checking the validity of Drude’s formula, and has been used extensively in recent years 
as a convenient test for this purpose (Lowry and Dickson, ‘ Trans. Chem. Soc.,’ 1913, 
vol. 103, p. 1075 ; Lowry and Abram, ‘ Trans. Faraday Soc., 5 1914, vol. 10, p. 104 ; 
compare also Frankland and Garner, ‘ Trans. Chem. Soc.,’ 1919, vol. 15, p. 640, 
footnote, and Rupe and Akermann, ‘ Ann. der Chem.,’ 1920, vol. 420, p. 12). The 
mere, plotting out on Biot's original plan of a series of accurate experimental data 
would therefore have disclosed to him both the existence arid the magnitude of Drude’s 
correction. 
In the absence of Biot’s mathematical genius, however, nearly all the work on rotatory 
dispersion during the next half-century became semi-qualitative in character, the data 
being represented by curves of unknown form, instead of by mathematical equations. 
This fact affords an explanation of the exaggerated importance which was attached to 
the more conspicuous anomalies, as well as of the utter confusion into which all attempts 
to classify rotatory dispersion fell. Thus, in the absence of any precise knowledge of 
the real form of the dispersion curves, Krecke seized upon “ the anomaly that, in con¬ 
centrated solutions of tartaric acid, the green rays are turned more than the red and 
violet rays ” (‘ Arch. Neerlandaises,’ 1872, vol. 7, p. 114). Landolt in 1877 recognised 
two anomalies, namely, (i.) that in aqueous solutions of tartaric acid “ if one increases 
the concentration, the maximum rotation wanders [from the violet] towards the red 
end of the spectrum, and in solutions containing 50 per cent, tartaric acid, the green 
rays are most strongly deflected,” (ii) “ that tartaric acid in the anhydrous state must 
deflect the rays C D E to the right, b F e to the left, and that for a certain kind of light, 
whose wave-length lies between the lines E and C, there can be no rotation at all ” 
(‘ Liebig’s Ann. der Chem.,’ 1877, vol. 189, p. 274). 
* The lengths of the columns of quartz required to produce a rotation of n-j 2 were plotted against the 
square of the wave-length as a series of straight lines diverging from the origin where l = 1/a = 0 and 
A 2 = 0 ; Drude’s equation gives straight lines diverging from 1 /a = 0, A 2 = Ao 1 . 
