272 
MESSRS. THOMAS MARTIN LOWRY AND PERCY CORLETT AUSTIN 
cases the series was extended to wave-length about 4150, by the inclusion of photo¬ 
graphic readings, and in the case of two of the strongest solutions, readings were taken 
for 21 and 26 lines, extending to wave-lengths 4005 and 3941 respectively. 
These solutions were filtered, in order to facilitate the reading of the more difficult 
blue and violet lines. The concentrations, as well as the specific and molecular rotations 
derived from them, were therefore less certain than those set out in the preceding section, 
and, when the latter had been completed, the earlier observations were regarded as 
obsolete, with the exception of the two long series which covered a very wide range of 
the spectrum, and were specially well adapted for testing the form of the dispersion- 
curves. The rotations for these two solutions are set out in Table III. (a) and ( b ). In 
order to bring them into line with the standard series of readings of Table I. the true 
concentrations of these two solutions were found by interpolation from the standard 
series, the concentrations deduced in this way being e = 0-4590 and 0-5875, or 69-90 
and 49-96 grams of tartaric acid in 100 c.c. of solution, as compared with the nominal 
values of 70 and 50 per cent. After making these very small corrections, the specific 
and molecular rotations of the two long series were included with the shorter standard 
series of Table I. amongst the data used in discussing the relation between rotatory 
power and wave-length. 
The calculated rotations shown in Tables III. and IV. are derived from an equation 
of the Drude type containing one positive and one negative term, thus 
~k'2 
But whereas in the case of quartz the data are now so extensive and so accurate that 
five arbitrary constants can be determined exactly, the range and accuracy of the data 
in the case of tartaric acid and other optically-active organic compounds are only suffi¬ 
cient for the exact determination of three arbitrary constants ; in other words, the 
effect of a small alteration in any one of four constants can be eliminated almost entirely 
by suitable alterations in the other three. This limitation has already been discussed 
in the case of ethyl tartrate, the rotatory-dispersion of which can be calculated almost 
equally well from formulae in which the dispersion-constants are :— 
(i) v 2 = 0-035, X 2 2 = 0'065, 
(ii) X x 2 = 0-030, X 2 2 = 0-070. 
(iii) V 2 = 0-025, X 2 2 = 0-080, 
where the sum of the dispersion-constants Xff and X 2 2 is almost constant (Lowry and 
Dickson, ‘ Trans. Chem. Soc.,’ 1915, vol. 107, p. 1186). The best results are therefore 
obtained by assuming a steady value for one of the two dispersion-constants in a series 
of related compounds ; thus, in 22 independent series of observations of tartaric acid 
and its esters, the value Xff = 0-030 may be maintained for the smaller of the two 
