MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 137 
Section TIL— OF THE EFFICIENCY OF THERMO-DYNAMIC ENGINES, WORKED BY THE 
EXPANSION AND CONDENSATION OF PERMANENT GASES. 
(21.) The Efficiency of a Thermo-dynamic Engine is the proportion of the whole 
heat expended which is converted into motive power ; that is to say, the ratio of the 
motive power developed to the mechanical equivalent of the whole heat consumed. 
To determine geometrically the efficiency of a thermo-dynamic engine, it is neces- 
sary to know its true indicator-diagram ; that is to say, the curve whose co-ordinates 
represent the successive volumes and pressures which the elastic substance working 
the engine assumes during a complete revolution. This true indicator-diagram is 
not necessarily identical in figure with the diagram described by the engine on the 
indicator-card; for the abscissae representing volumes in the latter diagram, include 
not only the volumes assumed by that portion of the elastic substance, which really 
performs the work by alternately receiving heat while expanding, and emitting heat 
while contracting, in such a manner as permanently to transform heat into motive 
power, but also the volumes assumed by that portion of the elastic substance, if 
any, which acts merely as a cushion for transmitting pressure to the piston, under- 
going, during each revolution, a series of changes of pressure and volume, and then 
the same series in an order exactly the reverse of the former order, so as to transform 
no heat permanently to power. 
The thermo-dynamic engines to be considered in the present section, are those in 
which the elastic substance undergoes no change of condition. We shall in the first 
place investigate the efficiency of those which work without the aid of the contrivance 
called an “ economizer ” or “regenerator,” and afterwards, those which work with 
the aid of that piece of apparatus. 
(22.) Lemma. — Problem. To deten'mine the true from, the apparent indicator-dia- 
gram of a Thermo-dynamic Engine ; the portion of the elastic substance which acts 
as a cushion being hno wn, and the law of its changes of pressure and volume . 
Fig. 14. 
(Solution.) In fig. 14, let abed be the apparent indicator-diagram. Parallel to OX 
draw Ha and Lc, touching this diagram in a and c respectively ; then those lines 
MDCCCLIV. T 
