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
expenditure of a quarter of a cylinder full of steam, we get an amount of
power represented by 69, without any expenditure of steam at all, merely by
permitting the steam first used to expand into four times its original
volume.

181. _Q._--Then by working an engine expansively, the power of the steam is
increased, but the power of the engine is diminished?

_A._--Yes. The efficacy of a given quantity of steam is more than doubled
by expanding the steam four times, while the efficacy of each stroke is
made nearly one-half less. And, therefore, to carry out the expansive
principle in practice, the cylinder requires to be larger than usual, or
the piston faster than usual, in the proportion in which the expansion is
carried out. Every one who is acquainted with simple arithmetic, can
compute the terminal pressure of steam in a cylinder, when he knows the
initial pressure and the point at which the steam is cut off; and he can
also find, by the same process, any pressure intermediate between the first
and the last. By setting down these pressures in a table, and taking their
mean, he can determine the effect, with tolerable accuracy, of any
particular measure of expansion. It is necessary to remark, that it is the
total pressure of the steam that he must take; not the pressure above the
atmosphere, but the pressure above a perfect vacuum.

182. _Q._--Can you give any rule for ascertaining at one operation the
amount of benefit derivable from expansion?

_A._--Divide the length of stroke through which the steam expands, by the