THE THERMAL EFFECTS OF FLUIDS IN MOTION. 
587 
he given by the formula 
dd I / dv \ 
where K denotes the thermal capacity, under constant pressure, of unit of mass of the 
fluid. This formula may be derived from equation (15.) of our previous communica- 
tion already referred to, by substituting j), v, and — ^ for P, V, and ^ in that equation, 
changing to jp and #, instead of v and t, as independent variables, and differentiating 
with reference to p. It is scarcely necessary to remark that a direct demonstration of 
our present formula, founded on elementary thermodynamic principles, may be readily 
obtained. 
Each experiment, of the several series recorded above, gives a value for — , which is 
found by multiplying the “corrected thermal effect” by I’educe from the 
amounts per 100 inches of mercury to the amounts per pound per square foot. Now 
by examining carefully the series of results for different temperatures, in the cases of 
atmospheric air and of carbonic acid, we And that they follow very closely the law of 
varying inversely as the square of the absolute temperature (or temperature Centigrade 
with 273-7 added). Thus for air the formula 
and for carbonic acid 
express, the former almost accurately, the latter with a deviation which we shall here- 
after investigate, the results through the whole range of temperature for which the 
investigation has been carried out. 
perature. 
Air. 
Actual coohiig effect. 
Theoretical cooling effect. 
O 
O 
O 
0 
•92 
•92 
7-1 
•88 
•87 
39-5 
•75 
•70 
92-8 
•51 
•51 
perature. 
Carbonic acid. 
Actual cooling effect. 
Theoretical cooling effect. 
O 
O 
O 
0 
4-64 
4-64 
7-4 
4-37 
4-4 
35-6 
3-41 
3-63 
54-0 
2-95 
3-23 
93-5 
2-16 
2-57 
97-5 
2-14 
2-52 
4 L 
MDCCCLXII. 
