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tance 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 in this position. If D be at a very great distance
from F the attraction will be very small, and the perpendic-
ular consequently very short. Let us now suppose that at
every point in the line joining F and D a perpendicular is
erected prOportional in length to the attraction exerted at
that point; we should thus obtain an infinite number of
perpendiculars of gradually increasing length as D ap-
proaches F. Uniting the ends of all these perpendiculars,
we should obtain a curve, and between this curve and the
straight line joining F and D we should have an area con-
taining 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 total effort capable of being ex-
erted by the tensions upon the particle D, during its pas-
sage from its first position up to F.

Up to the present point we have been dealing with ten-
sions, and 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 the pull of gravity would be nothing, and the per-
pendicular representing it would dwindle to a point. In
this position the sum of the tensions capable of being ex-
erted on D would be a maximum. Let D now begin to
move in obedience to the attraction exerted upon it. Mo-
tion being once set up, the idea of “vie viva arises. In
moving toward F'the particle D cons’mes, as it were, the
tensions. Let us fix our attention on D at any point of the
path over which it is moving. Between that " point and F
there is a quantity of unused tensions; beyond that point
the’tensions have been all consumed, but we have in their
place an equivalent quantity of vis viva. After D has

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