268 
MESSRS. THOMAS MARTIN LOWRY AND PERCY CORLETT AUSTIN 
molecular rotatory power of the acid is plotted against the percentage by weight of 
water in the solution, the curves are seen to be inflected, but the deviations from the 
linear law, though quite real, are by no means conspicuous. More remarkable still is 
the fact, which Biot discovered in 1850, that extrapolation by means of the linear law 
leads to substantially correct values for the specific rotatory power of the anhydrous 
glassy or amorphous acid. In our own calculations we have used,- for each of a series 
of nine wave-lengths, a linear formula based on the values for the specific rotatory powers 
of the acid in solutions containing 55 and 85 per cent, of water ; the rotatory powers 
of the anhydrous acid, as shown under e = 0 in Table II., are derived by interpolation 
from the observations of Bruhat (‘ Trans. Faraday Soc.,’ 1914, vol. 10, p. 89), and 
the differences between the observed and calculated values are :— 
1-2, 1-5, 1-6, 1-7, 1-7, 1-7, 1-8, 0-6°, Mean 1-5°. 
This agreement is remarkably close, having regard to the facts that (i.) the linear law 
is only an approximation, (ii.) the extrapolation covers nearly half of the total range of 
concentration, and amounts in the case of the violet mercury line to an extension of 
over 12 degrees in the range of rotatory powers. 
In view of the fact that the linear law is valid to this extent over the wide gap between 
the anhydrous acid and its saturated solutions in water, we were prepared to find that, 
although closer examination would show marked deviations in the values for dilute 
solutions, no substantial errors would occur in the case of the more concentrated solu¬ 
tions. This anticipation was, however, by no means correct. Basing the linear formula 
again on the rotatory powers of the acid in solutions containing 55 and 85 per cent, of 
water, we find that the deviations which are produced by increasing the concentration 
to ivater 45 per cent., acid 55 per cent., are even greater than those which result from 
diluting to ivater 95 per cent., acid 5 per cent. ; and this is true, not only for one wave¬ 
length, but for the whole range of wave-lengths shown in Table II. The linear law is 
thus shown to be even less exact in concentrated than in dilute solutions. 
A natural sequel to the recognition of the fact that the linear law is inexact, is the 
introduction of a third term into the equation, which thus changes from 
= Aj + BjC to : Ao + BjC + . 
This method of expressing the specific rotatory powers of the acid was adopted by 
Winther in 1902. Its application to the data now recorded is shown in Table II. 
The parabolic formulae were all based on the readings for solutions containing 55, 70 
and 85 per cent, of water ; in a few cases these readings may have been less exact than 
others that might have been selected ; but no great advantage would have been obtained 
from any laborious attempt to smooth the values or to adjust the curves, since the 
general results were perfectly obvious when the errors were examined over the whole of 
the series of nine wave-lengths. Within the range from 55 to 85 per cent, of water, the 
