es 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
distance the attraction would be augmented four times; at a third of
the distance, nine times; at one-fourth of the distance, sixteen
times, and so on. In every case, the attraction might be measured by
determining, with the spring balance, the amount of tension just
sufficient to prevent D from moving towards 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 magnitude 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 distance from F, we can, in imagination, draw a
straight line from D to F, and at D erect a perpendicular to this
line, which shall represent the amount of the attraction exerted on D.
If D be at a very great distance from F, the attraction will be very
small, and the perpendicular consequently very short. If the distance
be practically infinite, the attraction is practically _nil_. Let us
now suppose at every point in the line joining F and D a perpendicular
to be erected, proportional in length to the attraction exerted at
that point; we thus obtain an infinite number of perpendiculars, of
gradually increasing length, as D approaches F. Uniting the ends of
all these perpendiculars, we obtain a curve, and between this curve
and the straight line joining F and D we have an area containing all
the perpendiculars placed side by side. Each one of this infinite
series of perpendiculars representing an attraction, or tension, as it
is sometimes called, the area just referred to represents the sum of
the tensions exerted upon the particle D, during its passage from its
first position to F.

Up to the present point we have been dealing with tensions, not with
motion. Thus far _vis viva_ has been entirely foreign to our
contemplation of D and F. Let us now suppose D placed at a
practically infinite distance from F; here, as stated, the pull of
gravity would be infinitely small, and the perpendicular representing
it would dwindle almost to a point. In this position the sum of the
tensions capable of bein