ON OPTICAL ROTATORY DISPERSION. 
271 
is in the wrong direction, but also for more concentrated solutions, as may be seen by 
comparing Bruhat’s experimental values for the anhydrous acid, e = 0, on the one 
hand, with the values of A t in the linear equation, which showed deviations amounting, 
on the average, to 1-5°, and on the other hand, with the values of A, in the parabolic 
equation, which gives errors as follows :— 
3-3, 2-9, 4-1, 4-5, 5-1, 4-5, 4-5, 4-3, Mean 4-1°. 
The complete course of the curve of rotatory power against concentration is shown, 
for the violet mercury line, by the heavy curve a in fig. 3. The ordinates of curve b 
represent the errors of a linear formula which is correct at 55 and 85 per cent, of water ; 
the curve c shows the errors of a parabolic formula which is correct at 55, 70 and 85 per 
cent, of water. The error (-(-0-6 degrees) in extrapolating by means of the linear 
formula to the anhydrous condition is shown on the left-hand side of the diagram, 
where a broken line is used to cover the interval between 0 and 45 per cent, of water 
in which no experimental values are available. A similar prolongation of the curve of 
errors on the right-hand side of the diagram indicates the most probable value for infinite 
dilution. If the aqueous solutions contained only an anhydrous acid and a fully- 
hydrated acid, both of constant specific rotatory power, the relationship between rotatory 
power and concentration should be expressed from end to end, if not by the straight 
line d, at least by a simple uninflected curve. The actual deviations from this ideal 
straight line are shown in fig. 3 by measuring the ordinates downwards from d instead 
of from the horizontal axis of zero rotation. It will be seen that this curve of 
deviations (which are all negative in sign) shows one minimum and two maxima, so 
that the exact relationship between rotation and concentration could only be expressed 
by an equation containing at least five arbitrary constants. 
In view of the complexity disclosed by this preliminary analysis, we have not thought 
it worth while to pursue the subject further, except to point out that in the case of 
each wave-length it is possible to use a linear formula (as indicated by the straight 
line e, and the curve of errors c, in fig. 3), which is substantially correct both for the 
anhydrous acid and for aqueous solutions from, say, e = 0*6 to 0-9, but widely 
divergent outside these limits. A series of values calculated from such a linear 
formula, for the mercury violet line, is given under [a,,] in Table II. ; this formula is 
correct for the anhydrous acid e = 0, and gives a ± error at three other points lying- 
near e — 0-63, e — 0*80 and e = 0*91. 
6. Rotatory Dispersion in Aqueous Solutions op Tartaric Acid. 
In order to determine the exact form of the curves of rotatory dispersion in aqueous 
solutions of tartaric acid, eight solutions were originally prepared and examined, con¬ 
taining from 5 up to 70 grams of tartaric acid in 100 c.c. of solution. In two cases the 
readings were confined to the seven visible cadmium and mercury lines ; in four other 
