THE CONSTITUTION OF NATURE. 17 



universe is as unalterable as the quantity of matter; 

 that it is alike impossible to create force and to anni- 

 hilate it. But in what sense are we to understand this 

 assertion? It would be manifestly inapplicable to the 

 force of gravity as denned by Newton; for this is a 

 force varying inversely as the square of the distance; 

 and to affirm the constancy of a varying force would be 

 self -contradictory. Yet, when the question is properly 

 understood, gravity forms no exception to the law of 

 conservation. Following the method pursued by Helm- 

 holtz, I will here attempt an elementary exposition of 

 this law. Though destined in its applications to pro- 

 duce momentous changes in human thought, it is not 

 difficult of comprehension. 



For the sake of simplicity we will consider a particle 

 of matter, which we may call F, to be perfectly fixed, 

 and a second movable particle, D, placed at a distance 

 from F. We will assume that these two particles at- 

 tract each other according to the Newtonian law. At a 

 certain distance, the attraction is of a certain definite 

 amount, which might be determined by means of a 

 spring balance. At half this distance the attraction 

 would be augmented four times; at a third of the dis- 

 tance, nine times; at one-fourth of the distance, sixteen 

 times, and so on. In every case, the attraction might 

 be measured by determining, with the spring balance, 

 the amount of tension just sufficient to prevent D from 

 moving towards F. Thus far we have nothing what- 

 ever to do with motion; we deal with statics, not with 

 dynamics. We simply take into account the distance of 

 D from F, and the pull exerted by gravity at that dis- 

 tance. 



It is customary in mechanics to represent the mag- 

 nitude of a force by a line of a certain length, a force of 

 double magnitude being represented by a line of double 



