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 

 impossible 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, IX, 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 ; wo 

 deal with statics, not with dynamics. AVe simply take into 

 account the distance of D from ^&quot;, 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 BO OD. Placing then the particle I) at a dis- 



