
MECHANICAL ACTION OF HEAT. 161 
and consequently that 
-3 fan . udu (u,D,7)= 
0 
d d ldu pu 
+ (or. ae Ki 6D 55) af — ’ du. u?(u, D,7) 
Hence, making 
lea SON IES) 
0 
The second integral in Equation (2.) is transformed into 
1 d 
+5 (orgy + OD zp) v- 
By means of those substitutions we obtain, for the mechanical value of the 
heat developed in unity of weight of a fluid by any indefinitely small change of 
volume or of molecular distribution— 
8Q=_— = m (8D (5+ + 5p) +8752) 
or taking v=5 to denote the volume of unity of weight of 6.) 

the substance, 

dea Fah(O¥ ($38) ek 
Of this expression, the portion Cal a: PDs re ld represents the va- 
~ CxM 
riation of heat ie from wie change of volume. 
cai = “4 ave > = = i " 7 p24 aD’ U denotes the variation of heat produced by change 

of molecular distribution dependent on change of volume. 
TK 
CaM 
tribution dependent on change of temperature. 
(7.) The function U is one depending on molecular forces, the nature of 
which is as yet unknown. The only case in which it can be calculated directly is 
that of a perfect gas. Without giving the details of the integration, it may be 
sufficient to state, that in this case 

Or = expresses the variation of heat due to change of molecular dis- 
p ae | 
and therefore that SUA et!) 
LDPE SENT 9 182 
es Tt SANE Se 
In all other cases, however, the value of this function can be determined 
indirectly, by introducing into the investigation the principle of the conservation 
of vis viva. 
