1873 - Old Forge Coal Mines

60 ANNUAL REPORT OF THE
and the distance between fulcrum and spring balance, or the end of lever,
equals as many times the diameter of the valve as there are square inches
in its area.
Work of
Steam used Expansively.
When steam is used expansively it is allowed to
enter the cylinder for
only part of the stroke, and for the remaining portion the piston is moved
by the expansive force of the steam ; this is the most ingenious as well as
the most economical way of employing steam power, as all the available
labor is taken out of the elastic vapor before it is condensed. It is worthy
of remark that with the increase of the volume of steam, or any elastic
fluid, its elasticity or "pressure is decreased at the same ratio, that is to say
if its volume be increased two times its pressure will be only one-half what
it was at first, and so on.
If an engine has a 3 foot 10 inch stroke, and the steam be cut off at 2
feet 4 inches, let the space through which the steam acts expansively be
divided into 6 equal parts, and each interval will be expressed by a \ foot.
Now the rule given by Simpson is generally adopted, viz. :
" To the sum
of the extreme ordinates add 4 times the sum of the even ordinates and
twice the sum of the odd ordinates, then this sum multiplied by ^ the common
distance between the ordinates will give the required area," according
to Marriotte's law.
Example 1.—In a condensing engine, the length of the stroke being 3
feet 10 inches, the steam is cut off at 2 feet 4 inches of the stroke, the pressure
of steam in the cylinder being 20 lbs., and the elasticity of the vapor
in the condenser is 4 lbs. Required, the work performed upon one inch of
the piston in one stroke.
As the 6 divisions of ordinates, designated by letters, are \ foot, or 3
inches apart, it follows that 2 feet 4 inches plus 6 times 3 inches gives 3
feet 10 inches=stroke.
Let A. B., C. D.,. E. F., &c, in figures, represent the series of ordinates,
\ foot apart ; steam being admitted into the cylinder of the elastic force of
steam at 20 lbs. to the square inch ; and if it be cut off when the piston
is at A. B., 2 feet 4 inches of the stroke, it is evident that the remaining
part of the stroke, viz : 1 foot 6 inches, will be completed by the expansion
of the steam. And, according to Marriotte's law, we have for each
interval the corresponding units of pressure indicated by the divisional
lines of figures from A. B. to M. N.
Let A. B. represent pressure of steam ;
multiply length of stroke in feet
and decimal parts to where steam is cut off. Divide A. B. plus £ foot,
equal C. D. Continue the operation and similar results will follow for each
separate ordinate.
Hence : A. B.=:20 lbs.
The following explanatory diagram is hereto subjoined for an extended
illustration, showing the system of practical calculations used by M. Marriotte
in his able treatise upon steam engines :