effect--forces convertible into each other--two different forms of one
and the same object. For example, a weight resting on the ground is not
a force: it is neither the cause of motion nor of the lifting of another
weight. It becomes so, however, in proportion as it is raised above the
ground. The cause--that is, the distance between a weight and the earth,
and the effect, or the quantity of motion produced, bear to each other,
as shown by mechanics, a constant relation.

"Gravity being regarded as the cause of the falling of bodies, a
gravitating force is spoken of; and thus the ideas of PROPERTY and
of FORCE are confounded with each other. Precisely that which is
the essential attribute of every force--that is, the UNION of
indestructibility with convertibility--is wanting in every property:
between a property and a force, between gravity and motion, it is
therefore impossible to establish the equation required for a rightly
conceived causal relation. If gravity be called a force, a cause
is supposed which produces effects without itself diminishing, and
incorrect conceptions of the causal connections of things are thereby
fostered. In order that a body may fall, it is just as necessary that it
be lifted up as that it should be heavy or possess gravity. The fall of
bodies, therefore, ought not to be ascribed to their gravity alone. The
problem of mechanics is to develop the equations which subsist between
falling force and motion, motion and falling force, and between
different motions. Here is a case in point: The magnitude of the falling
force v is directly proportional (the earth's radius being assumed--oo)
to the magnitude of the mass m, and the height d, to which it is
raised--that is, v = md. If the height d = l, to which the mass m is
raised, is transformed into the final velocity c = l of this mass, we
have also v = mc; but from the known relations existing between d and c,
it results that, for other values of d or of c, the measure of the
force v is mc squared; accordingly v = md = mcsquared. The law of the
conservation of vis viva is thus found to be based on the general law of
the indestructibility of causes.

"In many cases we see motion cease without having caused another motion
or the lifting of a weight. But a force once in existence cannot be
annihilated--it can only change its form. And the question therefore
arises, what other forms is force, which we have become acquainted with
as falling force