MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
151 
consequently the equation of any curve of no transmission is 
O=constant ; otherwise 
(T-f- T 0 ).V N =const. ; or P.V 1+N =const. ; or 
r - • 
(T+T 0 ).P 1 + N = constant ; 
. . (43.) 
N 
in which N = 0 , 41, 1+N=1'41, j^ = 0 
2908. 
The maximum possible efficiency between any two temperatures T, and T 2 is given 
by the universal formula, 
E H x — H 2 T,-T a 
H - H t -T 1 + T 0 
(44.) 
The latent heat of expansion of unity of weight of air at a given constant tempera- 
ture T 1? from the volume V A to the volume V B , is sensibly equivalent simply to the 
expansive power developed, being given by the following formula : — 
H, = (T 1 +T,).(® B -® i ) = P 0 V..?^ 0 .hyp.log^ = f PrfV. . . (45.) 
A o v a Jy, 
Let V a and V 4 be the volumes corresponding to the points at which any isothermal 
curve intersects a given pair of curves of no transmission, or of equal transmission ; 
then the ratio of these volumes, 
r, (46.) 
is constant for every such pair of points on the given pair of curves ; because the dif- 
ference of the thermo-dynamic functions, which is proportional to the logarithm of 
this ratio, is constant. 
Hence, if in fig. 19 a, two isothermal curves, 
T,T„ T 2 T 2 , be the upper and lower boundaries of Y 
an indicator-diagram of maximum energy for an 
air-engine, AaD an arbitrary curve bounding the 
diagram at one side, and B the other limit of 
the expansion at the higher temperature; the 
fourth boundary, being a curve of equal trans- 
mission to AaD, may be described by this con- 
struction ; draw any isothermal curve tt cutting ©- 
AaD in a, and make 
Va : V B : : V a : V*, . 
then will b be a point in the curve sought, B&C. 
Fig. 19 a. 
(47.) 
