THE CONSTITUTION OF NATURE. 17 



as defined by Newton ; for this is a force varying inversely 

 as the square of the distance ; and to affirm the con- 

 stancy of a varying force would be self-contradictory. 

 Yet, when the question is properly understood, gravity 

 forms no exception to the law of conservation. Follow- 

 ing the method pursued by Helmholtz, I will here at- 

 tempt an elementary exposition of this law. Though 

 destined in its applications to produce momentous 

 changes in human thought, it is not difficult of compre- 

 hension. 



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 distance the attraction would be augmented 

 four times ; at a third of the distance, nine times ; at 

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

 every case, the attraction might be measured by deter- 

 mining, with the spring balance, the amount of tension 

 just sufficient to prevent D from moving towards 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- 

 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 



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