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ON THE THEORY OF SOLUTION. 321 
come which the solution would have to be further cooled. The necessary 
cooling may be estimated in the following way: Supposing the solution 
to be a mixture and to be cooled below its normal freezing point; then, 
on solidification, the temperature would rise to this point; but if this 
solidification involved a chemical decomposition which absorbed « cal. 
the rise of temperature would be thereby. reduced, the reduction thus 
caused amounting to e — the heat capacity of the solution. As the heat 
absorbed in the decomposition of the various hydrates of sulphuric acid 
is known, we can calculate the lowering produced by their presence. 
Taste I].—Freezing Points of Solutions of Sulphuric Acid. 
L Calculated VL Next hydrate 
raSO.. Il. Ill. IV. v. me vi. | vim. 
Mech. Phys. Chem. Total Cale. | Found 
Per cent.|Per cent. 
068 0:0209 0 0110 0:0347 } 00354 0:37 0°36 
362 Or1114 0004 0248 01508? 0°1582 1:43 1:06 
1:06 0°3276 0014 0589 0:4314! 0-4272 3°54 4:02 
4:02 1:285 ‘071 ‘O77 1582! 1:59 8-40 8:59 
8:59 2°879 +388 “189. | 38151 3°80 18:17 | 1849 
18-49 6:96 3°23 1:59 11°78 11°83 29-7 29°5 
29°53 12°85 18°82 3°50 | 34:17 34:00 37°5 37°7 
In Cols, IT., IIT., and IV., Table II., Ihave given the depression due to 
the three above-mentioned causes in the case of certain solutions, Col. V. 
containing their sum ; and it will be seen what a small proportion of this 
total lowering can be attributed to purely chemical causes. With most 
_ solutions it does not exceed 10 per cent. of the total, and with weak 
solutions, such as are generally used in freezing-point determinations— 
say 5 per cent.—it amounts to considerably less than 0°:1; this, too, in 
the case of sulphuric acid, where the heat of formation of the higher 
hydrates is greater than with any other known substance. 
The reason, therefore, why the deviations from constancy are so 
small as to have escaped detection hitherto, and the reason why solutions 
behave almost as if their chemical nature was’ non-existent, becomes. 
apparent ; but this near approach to constancy and regularity, instead of 
proving the correctness of the physical theory and giving a death-blow 
to the chemical theory, is really one of the strongest arguments which 
can be adduced in favour of the latter. If the hydrate theory is right, 
the influence of hydrates must often be nearly inappreciable. 
But it is not only a general concordance between the found and 
Calculated magnitude of the irregularities which the hydrate theory’is 
capable of affording, but a concordance so exact that the precise value of 
the deviation at any point may be calculated. In Col. VI. of Table II. 
are given the observed freezing points of the solutions, and these show 
an average difference of but 0°:004 for the three weaker solutions, and 
0°06 for the four stronger solutions, from those calculated (Col. V.). 
The last two columns exhibit this concordance in a different manner ; 
‘ The actual total has been increased by 10-4 per cent. of its value to give the 
figures quoted in these five cases, for reasons which will be given elsewhere. Some 
of the numbers in this table may be subject to slight corrections, as they have been 
quoted 90 the absence of the original calculations. 
ve 
