22 FRAGMENTS OF SCIENCE. 



of force asserts that the quantity of force in the universe is 

 as unalterable as the quantity of matter ; that it is alike 

 imjDossible to create force and to annihilate it. But in 

 what sense are we to understand this assertion ? It would 

 be manifestly inapplicable to the force of gravity as New- 

 ton defined it ; 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 pur- 

 sued by Helmholtz, I will here attempt an elementary ex- 

 position of this law, which, though destined in its applica- 

 tions to produce momentous changes in human thought, 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 attract 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 dis- 

 tance the attraction would be augmented four times ; at a 

 third of the distance it would be augmented nine times ; at 

 one-fourth of the distance sixteen times, and so on. In 

 every case the attraction might be measured by determin- 

 ing, with the spring-balance, the amount of tension which 

 is just sufficient to prevent D from moving toward F. 

 Thus far we have nothing whatever 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 distance. 



It is customary in mechanics to represent the magni- 

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

 double magnitude being represented by a line of double 

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



