EFFORT, ACCELERATION, AND VELOCITY DIAGRAMS 293 
957. The Bull Engine.—Towards the end of the eighteenth century 
“William Bull invented a simple form of pumping-engine, which was 
developed and improved by his son Edward Bull and Richard Trevithick. 
“This engine is now antiquated, but in its working it presents an exceed- 
‘ingly interesting problem in mechanics, which will now be considered. 
The engine has an inverted cylinder ab (Fig. 458) placed directly over 
the pump well, and this piston-rod is attached directly to the pump rods 
or “pitwork.” The up stroke is performed by the steam acting on the 
- under side of the piston, but during this stroke no water is pumped, the 
_ work done by the steam, over and above that required to overcome the 
friction appearing’ in the energy of the raised heavy pitwork. During 
the down stroke the steam is led from the lower to the upper end of the 
cylinder, thus produc- Hs SEES 
ing equilibrium on the 
piston, and the descent 
of the heavy pitwork 
raises the water. 
During the up 
stroke the steam is 
used expansively, and 
the end of the stroke 
is reached when the r 
work done by the 
steam is equal to 
Ky 
_ «the work done on the K, 1” 
resistance. The dia- 
gram ACDEFB to the 
right in Fig. 458 shows 
the effective pressure 
per square inch on the piston during the up stroke, AB being the 
4 fength of the stroke. AH represents the total resistance, per square 
inch of piston, due to the weight of the piston, piston-rod, and pitwork, 
and the resistance of friction. HEK, the resistance line, is parallel 
to AB, and cuts the expansion curve at E. When the piston has 
moved to N, the effective pressure on the piston exactly balances the 
resistance, and from A to N the work done by the steam is represented 
by the area ACDEN, while the work done on the resistance is repre- 
sented by the area AHEN. The excess work, represented by the area 
HCDE, is stored in the rising masses as kinetic energy, and the 
speed of the piston increases as it moves from A to N. Above N the 
effective pressure on the piston will continue to diminish as the piston 
rises, until the position B is reached, when it comes to rest. 
* The velocity curve ALB may be constructed as in the second example 
of the preceding Article, and the point B where this curve cuts the line 
of stroke AB determines the end of the up stroke. 
A similar problem is presented during the down stroke of the piston. 
Referring to the diagram to the left of Fig. 458, the effort A,C, is the 
weight of the pitwork, etc. (per square inch of piston), and the effort line 
C,E,F, is parallel to A,B,, the line of stroke. The resistance A,H,, at 
the beginning of the stroke, is due to the head of water, the size of the 
pump, and the resistance of the valves. As the speed increases the 
] 
2 
Down stroke 
<== 
Fig. 458. 
a 
