THE CONSTITUTION OF NATURE 23 



Uniting the ends of all these perpendiculars, we obtain a 

 curve, and between this curve and the straight line join- 

 ing F and D we have an area containing all the perpen- 

 diculars placed side by side. Each one of this infinite 

 series of perpendiculars representing an attraction, or ten- 

 sion, as it is sometimes called, the area just referred to 

 represents the sum of the tensions exerted upon the par- 

 ticle 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 in- 

 finitely 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 to- 

 ward 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 

 tensions 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 infinitely 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 

 remaining, but the greater is the vis viva ; the further D is 

 from F, the greater is the sum of the unconsumed ten- 



