MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
143 
out again to that substance in such a manner as to be exactly sufficient for the opera- 
tion DA ; so that the whole consumption of heat in one revolution by an engine 
Fig. 18. 
Y 
whose indicator-diagram is ABCD, may be reduced simply to the latent heat of ex- 
pansion during the operation AB, which is represented by the indefinitely-prolonged 
area MABN, AdM and BcN being curves of no transmission. The efficiency of 
such an engine is represented by 
the area ABCD 
the area MABN’ ,< 
Now the maximum efficiency of an engine without a regenerator, working between 
the same limits of actual heat, is represented by 
the area AB cd Qj — Q, 2 
the area MABN (4 t ’ 
and from the mode of construction of curves of equal transmission, described in Pro- 
position IV., it is evident that 
the area ABCD=the area ABceC 
hence the maximum efficiencies, working between the given limits of actual heat, 
and Q 2 , are equal, with or without a perfect regenerator. Q.E.D. 
(30.) Advantage of a Regenerator. 
It appears from this theorem that the advantage of a regenerator is, not to increase 
the maximum efficiency of a thermo-dynamic engine between given limits of actual 
heat, but to enable that amount of efficiency to be attained with a less amount of 
expansion, and consequently with a smaller engine. 
Suppose, for instance, that to represent the isothermal curves, and the curves of 
no transmission, for a gaseous substance, we adopt the approximate equations already 
given in article 20, viz. — 
for the isothermal curve of Q, PV=NQ ; 
for a curve of no transmission ^- 2 = N = (p 3 )’ 
-1 
+ N 
( 31 .) 
