MR. MACQUORN RANKINE ON THERMO DYNAMICS. 
149 
where K v = k +/'•’•+ (r—x) • dX. 
The expression for the Thenno-dynainic function denoted by F takes the form 
but a more convenient thermo-dynamic function, bearing 1 the same relation to tem- 
perature as reckoned from the point of absolute cold, which the function F does to 
actual heat, is formed by multiplying the latter by the real specific heat ft, thus : — 
(40.) 
which, being introduced into the general equation, transforms it to 
A.'F^^r— x)dQ — jPf/V (40 a.) 
(33.) Of the Numerical Computation of the Efficiency of Air-Engines, with or with- 
out a perfect Regenerator. 
The relation between temperature and heat being known, the preceding proposi- 
tions can be applied to determine the efficiency, and other circumstances relative to the 
working of Thermo-dynamic engines. To exemplify this application of the theory, let 
the substance working the engine be atmospheric air, and let the real indicator-diagram 
be such as to develope the maximum efficiency between two given absolute tempera- 
tures t 1 and r 2 , being a quadrilateral, as in fig. 19, of which two sides are portions 
of the isothermal curves of those temperatures, and the other two, portions of a pair 
of curves of equal transmission, of such a form as may be best suited to the easy 
working of the engine. Should these curves be curves of no transmission, a regenerator 
may be dispensed with. In every other case a regenerator is necessary, to prevent 
waste of heat ; and for the present its action will be assumed to be perfect, as the 
loss which occurs from its imperfect action cannot be ascertained except by direct 
experiment. 
In this investigation it is unnecessary to use formulae of minute accuracy; and for 
practical purposes, those will be found sufficient which treat air as a perfect gas, 
whose thermometric zero of pressure coincides with the point of absolute cold, viz. — 
272 °^ Centigrade, or] 
> below melting ice ;* 
490°! Fahrenheit, J 
* This estimate of the position of the point of absolute cold is to be considered as merely approximate, 
recent experiments and calculations having shown that it may possibly be too high by about 1^° Centigrade. 
It is, however, sufficiently correct for all practical purposes. — W. J. M. R., June 1854. 
