, if
its volume be enlarged to two cubic feet, its elasticity will be reduced to
7-1/2 lbs. on the square inch, being just half its original pressure. The
same law holds in all other proportions, and with all other gases and
vapors, provided their temperature remains unchanged; and if the steam
valve of an engine be closed, when the piston has descended through
one- fourth of the stroke, the steam within the cylinder will, at the end
of the stroke, just exert one-fourth of its initial pressure.

180. _Q._--Then by computing the varying pressure at a number of stages,
the average or mean pressure throughout the stroke may be approximately
determined?

[Illustration: Fig. 32. Diagram showing law of expansion of steam in a
cylinder.]

_A._--Precisely so. Thus in the accompanying figure, (fig. 32), let E be a
cylinder, J the piston, _a_ the steam pipe, _c_ the upper port, _f_ the
lower port, _d_ the steam pipe, prolonged to _e_ the equilibrium valve, _g_
the eduction valve, M the steam jacket, N the cylinder cover, O stuffing
box, _n_ piston rod, P cylinder bottom; let the cylinder be supposed to be
divided in the direction of its length into any number of equal parts, say
twenty, and let the diameter of the cylinder represent the pressure of the
steam, which, for the sake of simplicity, we may take at 10 lbs., so that
we may divide the cylinder, in the direction of its diameter, into ten
equal parts. If now the piston be supposed to descend through five of the
divisions, and the steam valve then be shut, the pressure at each
subsequent position of the piston will be represented by a series, computed
according to the laws of pneumatics, and which, if the initial pressure be
represented by 1, will give a pressure of .5 at the middle of the stroke,
and .25 at the end of it.

If this series be set off on the horizontal lines, it will mark out a
hyperbolic curve--the area of the part exterior to which represents the
total efficacy of the stroke, and the interior area, therefore, represents
the diminution in the power of a stroke, when the steam is cut off at
one- fourth of the descent. If the squares above the point, where the steam
is cut off, be counted, they will be found to amount to 50; and if those
beneath that point be counted or estimated, they will be found to amount to
about 69. These squares are representative of the power exerted; so that
while an amount of power represented by 50 has been obtained by the
expend