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.2 2 FRAGMEN TS OF SCIENCE.

of force asserts that the quantity of force in the universe is
as unalterable as the quantity of matter; that it is alike
impossible to create force and to annihilate it. But in
what sense are we to understand this assertion ? . It would
be manifestly inapplicable to the force of gravity as N ew-
ton defined it ; for this is a force varying inversely as the
square of the distance, and to affirm the constancy of a
varying force would be self-contradictory. Yet, when the
question is properly understood, gravity forms no exception
to the law of conservation. Following the method pur—
sued by Helmholtz, I will here attempt an elementary ex-
position of this law, which, though destined in its applica-
tions to produce momentous changes in human thought, is
not difficult of comprehension.

For the sake of simplicity we will consider a particle of
matter, which we may call F, to be perfectly fixed, and a
second movable particle, D, placed at a distance from F.
We will assume that these two particles attract each other
according to the Newtonian law. At a certain distance, the
attraction is of a certain definite amount, which might be
determined by means of a spring-balance. At half this dis-
tance the attraction would be' augmented four times ; at a
third of the distance it would be augmented nine times ; at
one-fourth of the distance sixteen times, and so on. In
every case the attraction might be measured by determin-
ing, with the spring-balance, the amount of tension which
is just sufficient to prevent D from moving toward F.
Thus far we have nothing whatever to do. with motion; we
deal with statics, not with dynamics. We simply take into
account the distance of D from F, and the pull exerted by
gravity at that distance.

It is customary in mechanics to represent the magni-
tude of a. force by a line of a certain length, a force of
double magnitude being represented by a line of double
length, ’and so on. Placing then the particle D at a dis-

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