18 FRAGMENTS OF SCIENCE. 



attraction will be very small, and the perpendicular conse- 

 quently 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 ap- 

 proaches 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 attrac- 

 tion, 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 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 

 towards 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 pre- 

 viously in store at that point disappears, but not with- 



