se 
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( 195 ) 
IX.—On the Power and Economy of Single-Acting Expansive Steam-Engines, 
being a Supplement to the Fourth Section of a Paper On the Mechanical Action 
of Heat. By Witttam Joun Macquorn Ranxine, Civil Engineer, F.R.S.E., 
F.R.S.S.A., &c. 
(Read 21st April 1851.) 
(34.) The objects of this paper are twofold: First, To compare the results of 
the formulze and tables relative to the power of the steam-engine, which have 
been deduced from the Dynamical Theory of Heat, with those of experiments on 
the actual duty of a large Cornish engine at various rates of expansion ; and, 
Secondly, To investigate and explain the method of determining the rate of expan- 
sion, and, consequently, the dimensions and proportions of a Cornish engine, 
which, with a given maximum pressure of steam in the cylinder, at a given 
velocity, shall perform a given amount of work at the least possible pecuniary 
cost, taking into account the expense of fuel, and the interest of the capital re- 
quired for the construction of the engine. 
This problem is solved with the aid of the tables already printed, by drawing 
two straight lines on a diagram annexed to this paper. 
The merit of first proposing the question of the economy of expansive en- 
gines in this definite shape, belongs, I believe, to the Artizan Club, who have 
offered premiums for its solution; having done so (to use their own words), 
‘© with a view to enable those who, from their position, cannot take part in the 
discussions of the various scientific Societies to give the profession the benefit of 
their studies and experience.” The 5th of April is the latest day fixed by them 
for receiving papers; and as this communication cannot possibly be read to a 
meeting before the 7th April, nor published until some months afterwards, I trust 
I may feel confident that it will not be considered as interfering with their design. 
Formule applicable to the Cornish Engine. 
(35.) The equations of motion of the steam-engine, in this and the original 
paper, are the same in their general form with those of M. p—E Pamgour. The 
differences consist in the expressions for the pressure and volume of steam, and 
for the mechanical effect of its expansion; the former of which were deduced 
from a formula suggested by peculiar hypothetical views, and the latter from the 
dynamical theory of heat. 
Those equations are Nos. (50) and (51) of the original paper. I shall now 
VOL. XX. PART II. 3F 
