fee Sie aia 

MECHANICAL ACTION OF HEAT. 579 
in which, if we substitute the symbol of real specific heat, 
k= Nr, 5 A i A : : = (96.) 
~ we obtain the formula already given (86) for the relation between heat and tem- 
perature.* 
(59.) The introduction of the value given above of the quantity of heat in 
terms of temperature, into the formula 67, gives for the latent heat of a small 
expansion d V at constant temperature 
ee ae Ut te Cae en) 
The formule: 79 and 82, for the proportion of heat rendered available by an 
expansive engine working to the greatest advantage, becomes 
T —T. 
Nei Oil: touukh neato feeutntils dn wire eD 
or the ratio of the difference between the temperatures of receiving and emitting 
heat, to the elevation of the former temperature above that of total privation of heat. 
This is the law already arrived at by a different process in Section V. of this 
paper. 
When the same substitution is made in Equation 80, which represents the 
total energy, whether as heat or as compressive power, which must be applied to 
unity of weight of a substance to produce given changes of heat and volume, the 
following result is obtained :— 

d.v=dQtd.8={k+/@+0-" J av jar 
+{ (r—«) $ ——-—P me 
wn {wr+s(7)+ pena Daa (905) 
As it cannot be simplified, it is unnecessary here to recapitulate the investi- 
gation, which leads to the conclusion that the functions /(7) and /’ (7) have the 
following values :— 
f(r)=K N (hyp. log. t + ) sf =kn (SS 2 (99 A) 
We have thus reproduced Equation 26 of the paper formerly referred to, on the 
Centrifugal Theory of Elasticity. 
The coefficient of the variation of temperature in the first form of Equation 99 
is the specific heat of the substance at constant volume. Denoting this by Ky, 
the formula becomes 
d.v=K,.dr+{ (r- K) 52 -P hav a 100.) 
* See Appendix, Note A. 
