[WALKER] OUDEMANS’ LAW 115 
K. and NH, they soon reach an almost constant value of 180°, as the 
ionic theory predicts that they should, also that at the greatest dilution 
examined, the Ba. Sr. Ca. and Mg. salts have not yet reached this 
limit, a result also in conformity with the ionic theory, for these salts 
especially those of Ca. and Mg. are considerably less dissociated than 
those of the alkalies at the same concentration. According to van’t 
Hoff (loc. cit.), therefore, we should take 180° as the rotation of the 
mandelic ion in aqueous solution. Mandelic acid, even in the most 
dilute solution in which it could be examined, shows a wide departure 
from this value and this again is predicted by the ionic theory, for the 
molecular is much greater, evidently, than the ionic rotation, and 
like all the organic acids which are only half electrolytes, mandelic 
acid is but slightly dissociated at these concentrations. The progress 
of ionization with dilution is, however, clearly indicated in passing 
from a ‘/, N. to an1/,, N. solution. Even in the !/, N. solution, how- 
ever, there are some ions present as well as possibly molecular aggre- 
gates possessing a different rotatory power from the simple molecule, 
so that we are not justified in taking 243° as the value for the latter. 
If, however, a sufficiently large number of H-ions are present in the 
solution of mandelic acid they will, according to the law of mass action, 
decrease the ionization of that substance to a negligible amount. This 
condition of things has been attained by dissolving the acid in normal 
hydrochloric acid and diluting, not with water, but with normal hydro- 
chloric acid, when, as seen in the table, the molecular rotation rapidly 
falls to a constant value of 243°. This value may, therefore, be taken 
as the rotation of the simple molecule of mandelic acid. 
iN EN iN UN 
246 7° 244° 242 -7° 243-20 
Using these values, 243 for the undissociated and 180 for the 
entirely dissociated molecule, and applying Ostwald’s dilution law 
for half-electrolytes to the values found for mandelic acid in pure 
water, a fairly satisfactory constant is obtained. 
So far the results are in accordance with accepted theories, and 
seem to confirm Oudemans’ law. But a closer inspection shows that 
the explanation of them is not quite so simple, and that the full inter- 
pretation of them involves something more than the ionic theory. 
The degree of dissociation of mandelic acid, as indicated by the change 
in rotation, is much greater than that calculated from the measure- 
ments of its conductivity, being already more than 30 per cent at 
1/39 N., while the latter method gives only 27-7 per cent at 1/,,, N. 
It is evident also that not only do the salts of the alkalies approach 
a constant value of 180° but that those of Ba. Sr. and Mg. approach 
