ON OPTICAL ROTATORY DISPERSION. 
251 
represented by a line inclined at an arbitrary angle, instead of at 45 degrees, to the 
horizontal axis ; the anomalous dispersion in concentrated solutions is shown by the 
intersection of the lines showing the rotatory power of the acid for light of different 
colours, and the removal of some of the more obvious anomalies on diluting the solutions 
is shown by the gradual separation of the lines until they follow the normal sequence 
of the primary colours of the visible spectrum. 
( b ) Rotatory Power of Amorphous Tartaric Acid. 
Our own investigations (pp. 266 to 271) have shown that Biot’s linear law is only 
an approximation, and that an equation with five arbitrary constants would probably 
be required to express completely the relationship between rotatory power and concen¬ 
tration. With the help of his diagram and formula, Biot was, however, able to calculate 
by extrapolation the rotatory power of pure anhydrous tartaric acid at different tem¬ 
peratures and for light of different colours. In particular, he concluded that the rotatory 
power A of the anhydrous acid for the red light transmitted through glass coloured by 
cuprous oxide would change sign at 23° C., being positive above this temperature and 
negative below it (‘ Mem. Acad. Sci.,’ 1838, vol. 16, p. 269). This prediction was verified 
dramatically some years later when Laurent in 1849 discovered a method by which 
moistened tartaric acid could be fused and cooled to a transparent glass in thicknesses up 
to 76 mm. (‘ Ann. Chim. Phys.,’ 1850, vol. 28, p. 353). Biot then found that the hot, 
pasty acid produced a strong dextrorotation, which became negative on cooling. A 
70 mm. column of the acid at + 3*5° C. gave a red = —3*28°, when [a] r8d — —2 , 787°, 
agreeing very closely with the value [a] red = —2*752° calculated by extrapolation 
from the rotatory power of concentrated aqueous solutions of the acid {ibid., p. 366). 
(c) Rotatory Power of the Tartrates. 
Whilst his first long memoir on tartaric acid (“ Methodes mathematiques et experi- 
mentales, pour discerner les Melanges et les Combinaisons, definies ou non definies, qui 
agissent sur la Lumiere Polarisee ; suivies d’applications aux combinaisons de l’acide 
tartrique avec l’eau, l’alcool, et l’esprit de bois,” ‘ Mem. Acad. Sci.,’ 1838, vol. 15, 
pp. 93-279) dealt with solutions of the acid in water, alcohol, and wood spirit, his second 
memoir (“ Memoire sur plusieurs Points Fondamentaux de Mecanique Chimique”; 
‘ Mem. Acad. Sci.,’ 1838, vol. 16, pp. 229-396) described the changes which are produced 
in the rotatory power of tartaric acid by adding other acids (sulphuric, hydrochloric and 
citric, loc. cit., 271-304), alkalis (potash, soda and ammonia, loc. cit., 307-377) and earths 
(alumina and beryllia, loc. cit., 377-385). The action of alkalis was of special interest in 
that the tartrates derived from them showed none of the anomalies of the acid, their 
rotatory dispersion conforming approximately to the law of inverse squares and agreeing 
generally with that of quartz. Our own measurements have shown that this conclusion 
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