But some will ask, in regard to the vertical movement, is it only in
the descent of the water from P′ to P that work is performed? Water
cannot descend from P′ to P, it will be urged, unless the entire column
P O underneath descend also. But the column P O descends by means of
gravity. Why, then, it will be asked, is not the descent of the column
a motive power as real as the descent of the mass of water P′ P?
That neither force nor energy can be derived from the mere descent of
the polar column P O is demonstrable thus:—The reason why the column P
O descends is because, in consequence of the mass of water P′ P resting
on it, its weight is in excess of the equatorial column E Q. But the
force with which the column descends is equal, not to the weight of
the column, but to the weight of the mass P′ P; consequently as much
work would be performed by gravity in the descent of the mass P′ P (the
one foot of water) alone as in the descent of the entire column P′ O,
10,000 feet in height. Suppose a ton weight is placed in each scale of
a balance: the two scales balance each other. Place a pound weight in
one of the scales along with the ton weight and the scale will descend.
But it descends, not with the pressure of a ton and a pound, but with
the pressure of the pound weight only. In the descent of the scale,
say, one foot, gravity can perform only one foot-pound of work. In like
manner, in the descent of the polar column, the only work available is
the work of the mass P′ P laid on the top of the column. But it must be
observed that in the descent of the column from P′ to P, a distance of
one foot, each pound of water of the mass P′ P does not perform one
foot-pound of work; for the moment that a molecule of water reaches P,
it then ceases to perform further work. The molecules at the surface P′
descend one foot before reaching P; the molecules midway between P′ and
P descend only half a foot before reaching P, and the molecules at the
bottom of the mass are already at P, and therefore cannot perform any
work. The mean distance through which the entire mass performs work is
therefore half a foot. One foot-pound per pound of water represents in
this case the amount of work derived from the vertical movement.
Public-domain text, read in full here on John Shaqi.
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