324 REPORT—1890. 
osmotic pressure were really correct.’’ That the depression of the freez- 
ing-point per gram-molecule should decrease with increasing concentra- 
tion is no deduction (as Mr. Pickering seems to imagine) from the law of 
osmotic pressure; and the corresponding statement for the analogous case 
of highly compressed gases has been proved to be false by the researches 
of Regnault, Natterer, and others. . . . Besides, it is not correct that 
“‘ every known deviation ” is in the opposite direction to that expected by 
Mr. Pickering. From Beckmann’s excellent determinations (‘“‘ Zeitsch. f. 
physik. Chem.” ii. 715) it appears that in the great majority of cases the 
molecular depression does diminish with increasing concentration when 
benzene and acetic acid are the solvents. Mr. Pickering can find nume- 
rous other examples in Hykman’s observations, and I shall show below 
that it is even the case with the sulphuric acid solutions which were the 
subject of his own investigation. . . 
‘Mr. Pickering, in comparing his “theoretical” with the observed 
values for the depression of the freezing-point in dilute solutions of sul- 
phuric acid, remarks that “‘ the molecular depression, even in this extreme 
region,‘ instead of being constant, as it should be according to the theory 
of osmotic pressure, varies between 2°95 and 2°-1.”” Mr. Pickering has 
overlooked the fact that sulphuric acid is an electrolyte, and that the 
deviations may be accounted for by the theory of electrolytic dissociation. 
For the purpose of comparison with the experimental results, I have cal- 
culated the values of the depression’ for’ dilute solutions, such as Mr. 
Pickering investigated. In the calculation I have taken. the freezing- 
point of an aqueous solution of a non-electrolyte containing one gram- 
molecule per litre to be —1°-90C., in accordance with van ’t Hoff’s theory. 
I have further made the molecular conductivity of }H,SO, at infinite 
dilution (00) equal to 356/107 Siemens’ units (Kohlrausch, ‘ Wied. 
Ann.” xxvi. 196). From Kohlrausch’s numbers we then find the degree 
of dissociation— 
a for 1 SO ky cial (05:03 ‘01 ‘006 -002 normal solutions 
tobe ‘511 ‘5383 °585 ‘658 ‘707 -802 844 -910 
By interpolation we get « for other concentrations (‘“ Zeitsch. f. physik. 
Chem.”’ v. 5). From the percentage composition and the specific gravity 
(Pickering) I have calculated the number of gram-equivalents per litre 
solution. The subjoined table corresponds to that on p. 363 of the ‘Journ. 
Chem, Soc.” 
‘Under obs., are the (corrected) observed numbers obtained with 
thermometer 65,108 ; under obs., are the numbers for the same concen- 
trations interpolated from the series made with thermometer 65,561. This 
comparison affords an indication of the experimental accuracy. 
‘Tt is at once evident from the table that the observed numbers agree 
within the limits of experimental error (obs., —obs..) with the theoretical 
values so long as the concentration is less than 1 per cent. The agree- 
ment, in fact, is so extremely good as to lead one to put more faith in the 
calculated than in the observed values. In stronger solutions (1 to 4 per 
cent.) the depressions found are less than the theoretical depressions, in 
direct contradiction to Mr. Pickering’s statement that the opposite is 
always the case. On this last circumstance, however, we need not lay too 
much weight, for the theory has not yet been sufficiently advanced in this 
direction, and the deviations besides only amount here to 3°6 per cent. at 
! Mr, P.’s italics. 
