158 STATICS. [257. 



VIII. Theory of Attractive Forces. 



I. ATTRACTION. 



257. Among the various kinds of forces introduced in physics 

 for describing and interpreting natural phenomena, forces of 

 attraction and repulsion occupy a most prominent place. 



According to Neivtons law (the law of universal or cosmical 

 gravitation, the law of nature), every particle of matter attracts 

 every other such particle with a force proportional to the masses 

 and inversely proportional to the square of the distance of the| 

 particles. 



If m, m 1 be the masses of the two particles, r their distance, 

 and K a constant, the mathematical expression for the force oH 

 mutual attraction exerted by each particle on the other, or for 

 the stress between them, is, therefore, 



*=**. ( i; 



258. Each particle is here regarded as a mathematk 

 point at which its mass is concentrated. The attractive forc< 

 would, therefore, approach the limit oo as the distance betweei 

 the points approaches the value o. To prevent the introductioi 

 of infinite forces, we may in such limiting cases regard the par- 

 ticles as very small homogeneous spheres formed of an impene- 

 trable substance. If r, r* be the radii, p, p 1 the densities of th< 

 spheres, the attraction reaches a finite maximum value 

 when the spheres are in contact, viz. 



tw" 



which is very small of the fourth order if r, r 1 be very small of 

 the first order. Thus, for r=r l , 



