568 MR W. J. M. RANKINE ON THE 
increase of total heat dQ, while the volume remains constant, is: expressed as 
follows :— 
751a=(9 Fpav+ H@}aQ Me ee ci 
the heat Q being treated as a constant in the integration. 
If we now investigate the entire quantity of heat, both sensible and latent, 
which is consumed by a body during a simultaneous small change of total heat 
dQ and volume dV, we find the following results :— 
Sensible heat (which retains its condition) . é : : =dQ 
Latent heat, or heat which disappears in overcoming 
molecular action ; ; i : F ; J : ZQ sy Q + av Sav 
Latent heat equivalent to the visible mechanical effect. : Pav 
The amount being 
dQ+d.8+PaV= (1 +55) dQ+ (y+?) dV= 
(72.) 
(1+ of Fp 4v+9'Q) aQ+Q. 5:2 age Ve 18 
This formula expresses completely the relations between heat, molecular 
action, and expansion, in all those cases in which the expansive power developed, 
P ZV, is entirely communicated to the bodies enclosing the substance which ex- 
pands. 
(49.) The following coefficients are contained in, or deducible from it. 
The ratio of the specie Ba at constant volume to the real specific heat :— 
Ky Tae 
Ha1+5q=14 +Q ae 7V+¥@ Pee 50) 
The coefficient of latent heat of expansion at constant heat :— 
d8 dP 
The ratio of the specific heat at constant pressure to the real specific heat is 
found as follows. To have the pressure constant, we must have 



ae 
dP dP aN or idQ 
ge sae 0; dO nae 
a 
consequently the ratio in question is 
dP 
ae ane fa dQ _ P é 
%=1+ 797 oy tP) Sb H1+ Oa -4vt+9@ 
Se 75 
Sah (75.) 
dQ 
aa dP 
