between 68 and 70 per cent. ; this last difference taken by itself, with-
out consideration of the alteration of /z, is not very marked. The
greatest differences between the observed and calculated results
amount in two cases only to 33 parts per 10,000, but in the large
majority of cases to 5 parts per 10,000, or even less, which is within
the limits of experimental error.
The observed points of alteration are in accordance with the points noticed in Section I, though the last point, viz., at 78 per cent., is not here apparent. It is, of course, to be noticed that the density enters as a factor alike into the contractions and Lorentz's formula, though the refractivity for light is a wholly independent property. As pre- viously shown, the maximum value for contraction is at 54 per cent., while that of the refractive index is at 70 per cent. ; it would not, therefore, appear probable that Pulfrich's formula (vide supra), which expresses the relation between /A and the contraction in terms of a constant, would be applicable in this particular case. It was found by examples selected from various data that though the formula is applicable approximately for results differing by small percentage concentrations, yet such is far from the case when these differences are considerable.
Refractive Indices Curve.
For obtaining the curve showing the changes in the refractive indices, the value for /x for 2'1 9 per cent, acid was taken as unity ; and in order to keep the curve within moderate limits the differences in the successive values of ft were divided by 3. (See next page.)
It will be observed that the observations from 2 per cent, to about 20 per cent, lie upon one straight line, and those from 20 per cent, to about 33 per cent, are upon a second, while those from 40 per cent, to 70 per cent., the maximum, and beyond apparently lie upon some form of regular curve. The observations, however, are too few in number, and the scale too small to decide as to whether this curve could be resolved into two or more straight lines.
The general contour of the curve is very similar to those given by v. d. Willigen for /A (A ... H) in the case of sulphuric acid ; he draws special attention to the maximum value at 83'20 per cent., and while admitting that his observations are insufficient to show whether the results from per cent, to 80 per cent, are on one or several straight lines, yet alludes to the regularity of curvature in the vicinity of the maximum.
General Conclusions.
In both the physical properties of nitric acid solutions herein studied, namely, densities or contractions and refractive indices, the various sources of error and their possible magnitude are
