In each case the basic idea and error was in supposing that by some
possibility the descent of a liquid through a given distance could be
made to deliver more energy than would be required to elevate the same
quantity of liquid the same distance. As a matter of fact, the descent
of a liquid, the same as any other weight, through a given distance
represents exactly the amount of energy necessary to elevate the same
weight of liquid through the same distance measured vertically. Some
loss by friction of the liquid in the containing tubes is inevitable as
well as from friction in the working parts of the mechanism. Therefore,
as this loss continues, some outside energy must be supplied. If all
friction could be eliminated (which is an impossibility) and if the
liquid were started in motion, the motion would be constant, but no
energy could be taken from it for running other machinery without
reducing the motion.
There have been many arguments on this subject. We select one which was
elicited by the publication in "Mechanics' Magazine" of an account of
the device of the author of the "Voice of Reason." This argument was
published in "Mechanics' Magazine" in 1831, and is as follows:
I am induced to make an attempt to demonstrate the utter
impossibility, under any circumstances, of making a water-wheel
that will supply itself instead of having any surplus power.
The accompanying drawing represents part of an overshot wheel
in section, the buckets only part filled, by which the whole of
the water expended continues to act through a greater portion of
the circumference than it otherwise would do. The area of the
vertical section of the complement of water to each bucket is
made 40 inches; and taking the breadth of the wheel at, say 28
2/3 inches, gives 40 lbs. as the weight of water in each bucket;
therefore, as there are 12 buckets containing 40 lbs. each, No.
13 30 lbs., and No. 14 only 20 lbs., altogether making a total of
530 lbs. acting on the wheel at the same time;--to show clearly
all the effect that can be expected from this, I have divided the
horizontal radius into a scale of 40 equals parts (there being
40 lbs. in each bucket); and from the gravitating centre of the
fluid contained in each is drawn a perpendicular to the scale,
where the effective force, or weight in each bucket, may be read
off as on the arm of a common steelyard. The weights will be
found as follows, viz:--
No. Lbs.
1 21½
2 26¼
3 30½
4 33¾
5 36¾
6 38¾
7 39¾
8 40
9 39½
10 38
11 35¾
12 32½
13 21
14 12
Public-domain text, read in full here on John Shaqi.
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