22 FRAGMENTS OF SCIENCE 



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 r. 

 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 at- 

 traction might be measured by determining, with the 

 spring balance, the amount of tension just sufficient to 

 prevent D from moving toward F. Thus far we have noth- 

 ing 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 attrac- 

 tion will be very small, and the perpendicular consequently 

 very short. If the distance be practically infinite, the at- 

 traction 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 perpen- 

 diculars, of gradually increasing length, as D approaches F. 



