THE CONTINUITY OF MOTION. 189 



absent) the slowly-diminished motion of the carriage over a 

 certain space, is the equivalent of the constant backward 

 strain put upon the carriage while it is travelling through 

 that space. Carrying with us the conception thus reached, 

 we will now consider a case which makes it more definite. 



When used as a plaything by boys, a ball fastened to 

 the end of an india-rubber string yields a clear idea of 

 the correlation between perceptible activity and latent ac- 

 tivity. If, retaining one end of the string, a boy throws the 

 ball from him horizontally, its motion is resisted by the 

 increasing strain on the string; and the string, stretched 

 more and more as the ball recedes, presently brings it to 

 rest. Where now exists the principle of activity which 

 the moving ball displayed? It exists in the strained thread 

 of india-rubber. Under what form of changed molecu- 

 lar state it exists we need not ask. It suffices that the string 

 is the seat of a tension generated by the motion of the 

 ball, and equivalent to it. When the ball has been arrested, 

 the stretched string begins to generate in it an opposite mo- 

 tion; and continues to accelerate that motion until the ball 

 comes back to the point at which the stretching of the 

 string commenced — a point at which, but for loss by atmos- 

 pheric resistance and molecular redistribution, its velocity 

 would be equal to the original velocity. Here the truth that 

 the principle of activity, alternating between visible and 

 invisible modes, does not cease to exist when the translation 

 through space ceases to exist, is readily comprehensible; 

 and it becomes easy to understand the corollary that at each 

 point in the path of the ball, the quantity of its perceptible 

 activity, plus the quantity which is latent in the stretched 

 string, yield a constant sum. 



Aided by this illustration we can, in a general way, con- 

 ceive wdiat happens between bodies connected with one 

 another, not by a stretched string, but by a traction exer- 

 cised through what seems empty space. It matters not 

 to our general conception that the intensity of this traction 



