THE CONSTITUTION OF NA TURE. 13 
lars, 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 i) 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 dur- 
ing, its passage from its first position to F. 
Up to the present point we have been dealing with ten- 
sions, not with motion. Thug 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 being exerted on D would be a 
maximum. Let D now begin to move in obedience to the 
infinitesimal attraction exerted upon it. Motion being 
once set up, the idea of vis viva arises. In moving toward 
F the particle D consumes, 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 ten- 
sions have been all consumed, but we have in their place 
an equivalent quantity of vis viva. After D has passed 
any point, the tension previously in store at that point 
disappears, but not without having added, during the in- 
finitely small duration of its action, a due amount of 
motion to that previously possessed by D. The nearer D 
approaches to F, the smaller is the sum of the tensions re- 
maining, but the greater is the vis viva; the farther D is 
from F, the greater is the sum of the unconsurned ten- 
sions, and the less is the living force. Now the principle 
of conservation affirms not the constancy of the value of 
the tensions of gravity, nor yet the constancy of the vis 
viva, taken separately, but the absolute constancy of the 
value of both taken together. At the beginning the vis 
viva was zero, and the tension area was a maximum; close 
to F the vis viva is a maximum, while the tension area is 
zero. At every other point the work-producing power of 
the particle D consists in part of vis viva, and in part of 
tensions. 
