A Catechism of the Steam Engine by Bourne

*Computed according to the laws of pneumatics*

179.

_A._--If the steam be shut off at half stroke, the pressure of the steam, reckoning the total pressure both below and above the atmosphere, will just be one-half of what it was at the beginning of the stroke. It is a well known law of pneumatics, that the pressure of elastic fluids varies inversely as the spaces into which they are expanded or compressed. For example, if a cubic foot of air of the atmospheric density be compressed into the compass of half a cubic foot, its elasticity will be increased from 15 lbs. on the square inch to 30 lbs. on the square inch; whereas, 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

_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 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.