THE CONSTITUTION OF NATURE. 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 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 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. 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 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 unconsumed 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. 



