140 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
the limits of actual heat, and, laterally, by any pair of curves of no transmission. 
The efficiency in this case, as has been already proved in various ways, is represented 
by 
E Q.]— /qq \ 
Hj“ 5 v ' 
being the maximum efficiency possible between the limits of actual heat, Qj and Qa. 
( 25 .) Second Corollary . — Problem. To draw the diagram of greatest efficiency of 
a Thermo-dynamic Engine without a Regenerator, when the extent of variation of 
volume is limited, as well as that of the variation of actual heat. 
(Solution.) In fig. 16 , let QjQ,, Q 2 Q 2 be the iso- Fig. 16 . 
thermal curves denoting the limits of actual heat ; 
"V a, V B the limits of volume. Draw the ordinates 
VJDA, V b CB, intersecting the isothermal curves 
in the points A, B, C, D. Through A and C re- 
spectively draw the curves of no transmission, 
AM cutting Q 2 Qo in d , and CN cutting QjQj in b. 
Then will AbCd be the diagram required. An 
analogous construction would give the diagram 
of greatest efficiency when the variations of press- 
ure and of actual heat are limited ; as in the Air-Engine proposed by Mr. Joule. 
( 26 .) Of the use of the Economizer or Regenerator in Thermo-dynamic Engines. 
As the actual heat of the elastic substance which works a Thermo-dynamic Engine 
requires to be alternately raised and lowered, it is obvious that unless these opera- 
tions are performed entirely by compression and expansion, without reception or 
emission of heat (as in the case of maximum efficiency described in the first corol- 
lary of Proposition IX.), part, at least, of the heat emitted during the lowering of 
the actual heat may be stored up, by being communicated to some solid conducting 
substance, and used again by being communicated back to the elastic substance, 
when its actual heat is being raised. The apparatus used for this purpose is called 
an Economizer or Regenerator, and was first invented, about 1816, by the Rev. 
Robert Stirling. In the Air-Engine proposed by him, it consisted of a sheet-metal 
plunger surrounded by a wire grating or network ; in that of Mr. James Stirling, 
it is composed of thin parallel plates of metal or glass through which the air passes 
longitudinally, and in the engine of Captain Ericsson, of several sheets of wire 
gauze. 
A regenerator may be regarded as consisting of an indefinite number of strata, 
with which the elastic substance is successively brought into contact ; each stratum 
serving to store up and give out the heat required to produce one particular inde- 
finitely small variation of the actual heat of the working substance. 
A perfect regenerator is an ideal apparatus of this kind, in which the mass of ma- 
terial is so large, the surface exposed so extensive, and the conducting powers so 
