The deniers of this proposition, on the first view of the
subject, will say, it is true the accumulation of the weight on
the descending side thus occasioned by the capillary attraction
would produce a perpetual motion, if there were not as much power
lost on the ascending side by the change of position of the
weights, in pressing the water out of the sponge.
The point now to be established is, that the change in the
position of the weights will not cause any loss of power. For
this purpose, we must refer to the following diagram.
[Illustration]
With reference to this diagram, suppose _a a a_, etc., an endless
strap, and _b b b_, etc., an endless chain running round the
rollers; A B C not having any sponge between them, but kept
at a certain distance from each other by small and inflexible
props, _p p p_, etc., then the sides A B and C A would, in all
positions of this system, be precisely an equilibrium, so as
to require only a small increment of weight on either side to
produce motion. Now, we contend that this equilibrium would still
remain unaffected, if small springs were introduced in lieu of
the inflexible props _p p p_, so that the chain _b b b_ might
approach the lower strap _a a a_, by compressing these small
springs with its weight on the ascending side; for although
the centre of gravity of any portion of chain would move in a
different line in the latter case--for instance, in the dotted
line--still the quantity of the actual weight of every inch of
the strap and chain would remain precisely the same in the
former case, where they are kept at the same distance in all
positions, as in the latter case, where they approach on the
ascending side; and so, also, these equal portions of weights,
notwithstanding any change of distance between their several
parts which may take place in one case and not in the other,
would in both cases rise and fall, though the same perpendicular
space, and consequently the equilibrium, would be equally
preserved in both cases, though in the first case they may rise
and fall through rather more than in the second. The application
of this demonstration to the machine described in Fig. 1, is
obvious; for the compression of the sponge by the sinking of
the weights on the ascending side, in pressing out the water,
produces precisely the same effect as to the position and ascent
of the weights, as the approach of the chain to the lower strap
on the ascending side, in Fig. 2, by the compression of the
springs; and consequently, if the equilibrium is not affected in
one case--that is, in Fig. 2, as above demonstrated--it will not
be affected in the other case, Fig. 1; and, therefore, the water
would be squeezed out by the pressure of the chain without any
loss of power. The quantity of weight necessary for squeezing
dry any given quantity of sponge must be ascertained and duly
apportioned by experiment.
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