Page:Reflections on the Motive Power of Heat.djvu/215

Hence the total quantity added is equal to

$A\tau +{\tfrac {E^{2}p}{\mu (1+Et)^{2}}}\tau .$

But, since B denotes the specific heat under constant pressure, the quantity of heat requisite to bring the gas into this state, from its primitive condition, is equal to Bτ; and hence we have

$B=A+{\tfrac {E^{2}p}{\mu (1+Et)^{2}}}.$

(12)

IV. Comparison of the Relative Advantages of the Air-engine and Steam-engine.

54. In the use of water-wheels for motive power, the economy of the engine depends not only upon the excellence of its adaptation for actually transmitting any given quantity of water through it, and producing the equivalent of work, but upon turning to account the entire available fall; so, as we are taught by Carnot, the object of a thermodynamic engine is to economize in the best possible way the transference of all the heat evolved, from bodies at the temperature of the source, to bodies at the lowest temperature at which the heat can be discharged. With reference, then, to any engine of the kind, there will be two points to be considered:

(1) The extent of the fall utilized.