172 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
sudden opening of this valve causes a temporary reduction of temperature and 
pressure in the boiler itself. 
(49.) Composite Vapour- Engines. 
The Steam-and-Ether Engine of M. du Trembley is an example of what may be 
called a Composite Vapour- Engine, in which two fluids are employed, a less and a 
more volatile ; the heat given out during the liquefaction of the less volatile fluid 
serving to evaporate the more volatile fluid, which works an auxiliary engine, and is 
liquefied in its turn by refrigeration. 
Let the efficiency of the engine worked by the less volatile fluid be expressed in 
the form 
so that - is the fraction of the whole heat expended which is given out to the more 
volatile fluid. Let the efficiency of the engine worked by the more volatile fluid be 
then the efficiency of the combined engines will be 
1 — 
nn 
(81.) 
If both the engines are perfect thermo-dynamic engines, let r, be the absolute tem- 
perature at which the first fluid is evaporated ; r 2 that at which it is condensed, and 
the second fluid evaporated ; and r 3 that at which the second fluid is condensed ; 
then, 
being equal to the theoretical maximum efficiency of a simple thermo-dynamic 
engine working between the limits of temperature r, and r 3 . 
Composite Vapour-Engines, therefore, have the same theoretical maximum effi- 
ciency with simple vapour-engines, and other engines moved by heat, working 
between the same temperatures ; but they may, nevertheless, enable the same effi- 
ciency to be obtained with smaller engines. 
(50.) Curves of Free Expansion for Nascent Vapour. 
By Nascent V apour is to be understood, that which is in the act of rising from a 
mass of liquid. If this vapour be at once conducted to a condenser, without per- 
forming any work, and there liquefied at a temperature lower than that at which it 
was evaporated, its expansion, from the pressure of evaporation down to the pressure 
of liquefaction, will take place according to a law defined by a curve analogous in 
some respects, but not in all, to the curve of free expansion for a homogeneous sub- 
stance referred to in Proposition VI. To determine theoretically the form of this 
curve, it is necessary to know the properties of the isothermal curves and curves of 
no transmission for the fluid in question in the gaseous state, when above the tern- 
