ON OPTICAL ROTATORY DISPERSION. 
279 
with the natural rotatory power of optically active liquids, the asymptote rarely goes 
beyond X = \ 0-024 = 0-15^ or 1500 A.U. In view of this strict limitation of 
transparency, in carbon-compounds generally as well as in water and in silica, it seemed 
improbable that the metallic tartrates could be transparent to light of excessively short 
wave-length, especially as the magnetic rotations in ethyl tartrate are controlled by an 
absorption-band in exactly the same position as in the simple alcohols. The validity of 
the simple formula, therefore, lay open to suspicion, on account of the extreme smallness 
of the dispersion-constant, and it appeared much more probable that the dispersion- 
ratios in the tartrates had been brought down into close proximity with the minimum 
value 1-570 by the influence of a second (negative) term in Drude’s equation, similar to 
that which brings the dispersion-ratios in tartaric acid down below this minimum and 
gives rise to the anomalous dispersion of the acid. 
■The evidence which first convinced us that the simple dispersion-formula, like Biot’s 
law, is merely an approximate expression of the rotatory dispersion in the tartrates, is 
shown in Tables VI. (a) and (6). In these two tables a “ simple ” formula is shown 
which has been calculated to fit the experimental values for the green and violet mercury 
lines. The average error is only a fraction of 1 per cent. ; but without exception, all 
the errors between the green and violet lines are positive in sign, whilst all those beyond 
the violet are negative ; below the green, the errors are again negative in eight out of 
ten cases. This regular distribution of the errors, which was confirmed in the case of 
ammonium tartrate, Table IX., for 14 out of 15 visual readings in one series and for 12 
out of 13 in a second series which has not been reproduced, proves clearly that the 
deviations are not accidental but systematic, calling for some further modification of 
the formula used to express the observations. 
When once it has been recognised that the dispersion curves for the alkali-tartrates 
cannot be represented by the “ simple ” formula a = ft/(A 2 — A 0 2 ), no difficulty is 
experienced in securing a satisfactory agreement between the observed and calculated 
rotations, by using a Drude equation with one positive and one negative term, as is 
shown in the last columns of Tables VI., VII., VIII. and IX., where the errors in the 
visual readings are seen to be small and for the most part distributed quite irregularly. 
On account of the smallness of the deviations from the simple law, it is difficult to deter¬ 
mine the exact magnitude of the two additional constants which serve to express them 
in the equation. The dispersion-constants selected for these calculations were 
Ai 2 = 0-038, X 2 2 = 0-06, but since the sum of these two constants 0-098 is almost 
identical with the sum of the constants 0-030+0-074 = 0-104 used in the case of 
tartaric acid, there can be little doubt that the latter pair would have given equally 
satisfactory results. 
The negative rotation-constants, k 2 , as set out in Table XIII., are larger than might 
have been expected, approaching almost to one-half of the values for the positive rotation- 
constant +. This is due to the fact that the dispersion-constant X 2 2 of the negative 
term is but little greater than the dispersion-constant Ai 2 of the positive term ; the 
