18 FKAGMENTS OF SCIENCE. 



length, and so on. Placing then the particle D at a dis- 

 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. If D be at a very great distance from F, 

 the attraction will be very small, and the perpendicular 

 consequently 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 per- 

 pendicular to be erected, proportional in length to the 

 attraction exerted at that point; we thus obtain an in- 

 finite number of perpendiculars, 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 perpen- 

 diculars 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 

 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 ten- 

 sions. Let us fix our attention on D, at any point of 

 the path over which it is moving. Between that point 



