2 6i.] ATTRACTION. ^9, 



259. In many applications of the theory of attraction, in par- 

 ticular in electricity and magnetism, it is convenient to consider 

 forces of repulsion. This only requires a change of sign in the 

 expression for the force, and this sign may be regarded as 

 attaching to the mass of one of the particles ; in other words, 

 if the mass of a centre of attraction be taken as positive, that of 

 a centre of repulsion is taken to be negative, or vice versa. 



260. While according to Newton's law (i) the force is 

 inversely proportional to the square of the distance, it is often 

 convenient to use forces depending upon the distance r in a 

 different way. Thus the theory of Newtonian attraction can be 

 generalized by assuming for the force between two particles m y 

 m' the law 



F= K mm'f(r), (2) 



where /(r) represents any function of the distance r. 



When nothing is said to the contrary, we shall here always 

 assume that/(r) = i/^ 2 , as in Newton's law (i). 



261. The constant K evidently represents the force with which 

 two particles, each of mass i, attract each other when at the 

 distance i. It is a physical constant to be determined by 

 experiment, and its numerical value depends on the units of 

 measurement adopted. What can be directly observed is of 

 course not the force itself, but the acceleration it produces. 

 Dividing the force F, as given by formula (i), by the mass m' 

 of the particle on which it acts, we find for the acceleration j 

 produced by the attraction of the mass m in the mass m 1 at the 

 distance r from m : 



m / \ 



7=- 2 - (3) 



This quantity may also be regarded as the force of attraction 

 exerted by the mass m on a mass i at the distance r from m, 

 and is therefore called briefly the attraction at the point where 

 the mass i is situated. 



