301 
MOVING FORCE. 
Respecting the maximum of effect produced by machines, I Cases of d.ffi- 
•wish to observe, that in the actual construction of machines it joctriues'of 
is necessary to aim at a maximum quite different from that moving torcc. 
which is usually proposed in books on the theory of mechanics. 
This will perhaps be best explained by examining the simple 
case where a given weight P, (fig. 20) connected with another 
W, by a string passing over the pulley F, descends vertically 
and raises W, without friction, from the horizontal line AC 
along the inclined plane AB. If we make AB : BC : : 2\V : P, 
W will be raised to B in the least time* ; and upon this princi- 
ple, the maximum of effect in machines is usually deraonstrat- 
red in theory. In practice, however, the object is not merely to 
:raise W to B in the leait time, but to raise it with the least 
texpenditure of moving force. When it i.s raised in the least 
ttime, P must descend through a space = AB, but when it is 
rraised with the least moving force, P descends through a space 
= |AB only. For, if we make BD = 4^B, and let W 
aascend along any concave surface DEB, of which BD is the 
cchord, it will be raised to B by the descent of P through a space 
= BD, and it will be at rest when it arrives at B. This is so 
lobvious, that it would be superfluous to give a demonstration of 
iit. It appears then, that twice the quantity of moving force 
vwbich is absolutely necessary to raise W to B, must be expend- 
fed if it is to be raised by P in the least time. To determine the 
C 2 urve by which W will ascend from D to B in the least time, is 
ssn intricate problem, and I do not know that it has ever been 
ssolved i but a practical approximation to it in any particular 
cease m.iy be easily found. A well constructed steam-engine 
ffor raising water exhibits in every stroke a practical example of 
^he same problem. At the commencement of the stroke, a very 
kjreal pressure of steam is thrown upon the piston, and this 
[pressure is gradually diminished, so that at the end of the 
(■stroke there is a considerable preponderance in the opposite 
i.iirection. la consequence of this regulated pressure of the 
• Ifthc ascent be mailc iu the least possible time, W must asccud not 
Mlong the plane AB, but along a concave surface AGB. 
steam, 
