342 
DR. A. DUPRE ON THE SPECIFIC HEAT AND OTHER 
the depression of the boiling-point of this mixture below the mean is obtained. A 
similar, though less direct relation appears to exist between the compressibility of a 
mixture and the amount of contraction taking place in its formation. The numerical 
relation between these two values differs, however, in different mixtures, both being 
evidently governed by some additional factor. Lastly, it is also worthy of note that 
the compressibility of weak mixtures of methylic, as well as of ethylic alcohol and water, 
is less than that of water, rises to that of water at an alcoholic strength of about 30 per 
cent., and continues greater for all stronger mixtures. 
It has been pointed out above that an intimate relation exists between the heat 
evolved during the formation of a mixture and its specific heat. This relation may be 
formulated as follows, in accordance with the principles of the mechanical theory of 
heat, as first pointed out by Kirchhoff in 1858 (“ Ueber einen Satz der mechanischen 
Warmetheorie und einige Anwendungen desselben; von G. Kirciihoff,” Pogg. Ann. 
vol. xiii. p. 177). Relation existing between the specific heat of mixtures and the heat 
evolved during their formation : — 
1. The difference between the number of heat-units evolved during: the mixing: of 
given weights of two substances at the temperatures t and tf respectively is equal to the 
difference between the number of heat-units required to raise the mixture, and that 
required to raise the two constituents taken separately, from the lower to the higher 
temperature, provided the condition of the mixtures when they have been brought to the 
same temperature is the same in both cases. Or let U and U' be the units of heat 
evolved by mixing x and y at the temperatures t and tf respectively, S, S', and S" the 
specific heat of the mixture z and its constituents x and y respectively, then 
U - U' =2 . S(tf' - 1) ~ Rr . S \t' -t)+y.S"(t'-t)}. 
2. If more units of heat are evolved at the higher than at the lower temperature, the 
specific heat of the resulting mixture will be below the calculated mean ; on the other 
hand, the specific heat of the mixture will be above the calculated mean, if the greater 
number of heat-units be evolved at the lower temperature. 
3. The absorption of a lesser number of heat-units will be of course equivalent to the 
evolution of a greater number, while the absorption of a greater number will be equiva- 
lent to the evolution of a smaller number of heat-units. 
Ethylic Alcohol and Water. 
In the formation of 5 grms. of a 10 per cent, mixture of ethylic alcohol and water 
are evolved, at a temperature of 
17*295 C., 26*68 units of heat. 
71T5 C., 7-97 „ „ 
Difference 18*71 ., „ 
