138

MODERN STEAM PRACTICE.

divided into ten parts on the atmospheric line; the tenth spaceis subdivided, having one-half at each end, thus having ten ordinatesas shown; so by measuring each Ordinate by the scale adopted, thesum of the ordinates divided by io gives the mean pressure in thecylinder. The power is run out by the usual formula—

Area of cylinder in square inches x mean pressure x speed of piston in feet pcrminute' " 33ÖOO

thus the real or indicated power of the engine is obtained.

The theoretical line of expansion of the steam in the cylinder isonly useful to show how nearly the diagram as taken by the, indi-cator approaches it. Without comparing the theoretical measurewith the diagram illustrated, we will explain how the theoreticalline of expansion is obtained. It is based on the natural law thatgoverns pneumatics, namely, that the pressure of an elastic fluidvaries inversely as the space into which it is expanded or com-pressed. Thus if the steam in the cylinder is cut off at one-fourth ofthe stroke of the piston, the space it occupies at the end of the

stroke will be four times the volume ofthe steam admitted into the cylinder; ithas expanded into four times its bulk,and the pressure at the end of the strokewill be only one-fourth of the originalvolume admitted into the cylinder. To_find the pressure of the steam at the endof the stroke, or at any intermediatepart of the stroke of the piston, multiplyc the number of inches the piston hastravelled when the steam is cut off bythe pressure, dividing the result by thetotal length of the stroke in inches, or, by that portion of it that is required.Thus, supposing AB in the figure repre-sented one-fourth of the stroke, B being the point of cut-off, and thestroke of the piston is 36 inches, with a steam pressure of 20 Ibs. persquare inch, we would have—

S lbs. steam pressure at the end of the stroke,

6'66 lbs. steam pressure at three-quarters of the stroke,

10 lbs. steam pressure at one-half of the stroke.

9 X 20 _

~~¥~ ~~9 X 20 __~27 —

9 X 20 _

Stroke

Fig. 84.—Theoretical