12 FRAGMENTS OF SCIENCE. 



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 de- 

 fined 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 excep- 

 tion to the law of conservation. Following the method 

 pursued by Helmholtz, I will here attempt an elementary 

 exposition of this law. Though destined in its applica- 

 tions to produce 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 attract each 

 other according to the Newtonian law. At a certain dis- 

 tance, 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 toward F. Thus 

 far we have nothing whatever to do with motion; we deal 

 with statics, not with dynamics. We simply take into ac- 

 count the distance of D from F, and the pull exerted by 

 gravity at that distance. 



It is customary in mechanics to represent the magnitude 

 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 distance 

 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 attraction will 

 be very small, and the perpendicular consequently very 

 short. If the distance be practically infinite, the attrac- 

 tion is practically nil. Let us now suppose at every point 

 in the line joining F and D, a perpendicular to be erected, 

 proportional in length to the attraction exerted at that 

 point; we thus obtain an infinite number of perpendicu- 



