180 MR W. J. M. RANKINE ON THE 
above quantity by the number of units of weight of water evaporated in unity of 
time. 
If this number be denoted by W, 
WS, (l—-e)=WV,(—e)s=Au .. . (48) 
will represent the cubical space traversed by the piston in unity of time, A denot- 
ing the area of the piston, and uw its mean Velocity. 
Now let the whole resistance to be overcome by the engine be reduced by the 
principles of statics to a certain equivalent pressure per unit of area of piston, 
and let this pressure be denoted by R. Then, 
Reale Wan (lse)l@) ou lies (495) 
expresses the effect of the engine in terms of the gross resistance. 
We have now the means of calculating the circumstances attending the work- 
ing of a steam-engine according to the principle of the conservation of vis viva, 
or, in other words, of the equality of power and effect, which regulates the action 
of all machines that move with an uniform or periodical velocity. 
This principle was first applied to the steam-engine by the Count pr Pam- 
BouR; and accordingly, the formule: which I am about to give only differ from 
those of his work in the expressions for the maximum pressure at a given tempe- 
rature, and for the expansive action of the steam, which are results peculiar to 
the theory of this essay. 
In the first place, the effect, as expressed in terms of the pressure, is to be 
equated to the effect as expressed in terms of the resistance, as follows :— 
1 
RAw=RWV,(1—0) s=WV, {Pi (ere #7 es) Er | me: 
This is the fundamental equation of the action of the steam-engine, and 
corresponds with Equation A. of M. pz Pamsour’s theory. 
(26.) Dividing both sides of Equation (50.) by the space traversed by the piston 
in unity of time W V, (1—c) s, and transferring the pressure of the waste steam, 
P., to the first side, we obtain this equation :— 
of AO abe ne 
ie a rug ia (si 
yy : 


1a el 
which gives the means of determining the pressure P, at which the steam must 
enter the cylinder, in order to overcome a given resistance and counter-pressure 
with a given expansion; or supposing the expansion s to be variable at pleasure, 
and the initial pressure P, fixed, the equation gives the means of finding, by 
approximation, the expansion best adapted to overcome a given resistance and 
counter-pressure. 
The next step is to determine, from Equations XV. of the Introduction and. 

