314 APPLIED MECHANICS 
The upper part of Fig. 488 shows a pair of indicator diagrams from 
the cylinder of a vertical steam-engine. The full line diagram is from 
the top end, while the dotted line diagram is from the bottom end of the 
cylinder. 
The effective pressure on the piston at any point of the sixoks is 
shown by the vertical distance between the top of one diagram and the 
bottom of the other at that point. If this vertical distance be plotted on 
a straight base for a sufficient number of points in the stroke, a diagram is 
obtained which shows more clearly the effort on the piston during the 
stroke. In Fig. 488 the full line diagram on the base XX is the effort 
diagram for the down stroke, while the dotted line diagram is the effort 
diagram for the up stroke. Where the effort is negative, the diagram is 
below the base XX. 
272. Reduction of Indicator Diagrams to same Effort Scale —It 
was stated in the preceding Article, in referring to the indicator diagrams 
given in Fig. 488, that the effective pressure on the piston at any point of 
the stroke is shown by the vertical distance between the top of one 
diagram and the bottom of the other at that point. This, however, is 
only true when the effective areas of the top and bottom of the piston- 
are equal, and when the pressure scales of the two diagrams are the 
same, If the pressure scales are the same, but the areas are unequal, 
then either the ordinates of the diagram for the smaller area of piston 
must be reduced in the ratio of the smaller to the larger area, or the 
ordinates of the diagram for the larger area of piston must be enlarged 
in the ratio of the larger to the smaller area. 
The diagrams of Fig. 488 are repeated in Fig. 489, and the diagram 
for the bottom of the piston is shown cor- 
rected to the thicker dotted line diagram 
to allow for the area of the piston-rod on 
the under side. The effective force on the 
piston at any point of the down stroke is 
now represented by the vertical distance 
between the top of the full line diagram 
and the bottom of the thicker dotted line 
diagram at that point, and the effective 
force at any point of the up stroke is represented by the vertical distance 
between the top of the thicker dotted line diagram and the bottom of the 
full line diagram at that point. If the original indicator diagrams are not 
to the same pressure scale, it will of course be necessary to bring them to 
the same scale, in addition to correcting one of them for the difference 
between the areas of the top and bottom of the piston. 
The indicator diagrams from the different cylinders of a compound 
or triple expansion engine are generally to different pressure scales ; also 
Fig. 489. 
when the strokes of the different pistons are the same, which is generally 
the case, their areas are different. Hence it is evident that in order that 
the effort diagram for one piston may be comparable with the effort 
diagram for another piston, the pressure scales must be the same, and 
their ordinates ‘must be such as to give equivalent pressures on pistons of 
the same area, 
Let A be an indicator diagram for one side of a piston, the effective 
area of that side being a,, and let », be the pressure scale of this diagram 
CO EE ———<— 
