CHAPTER IV. 



s 



NEWTONIAN POTENTIAL FUNCTION. 



73. Definition and fundamental properties of Poten- 

 tial. We have seen in 59, (29), (31), that if we have any 

 number of material particles m repelling according to the New- 

 tonian Law of the inverse square of the distance, the function 



TT _ g 2s 



MS 1 r ...... -\ 



r, r 



where r 1} r 2 ...... r n are the distances from the repelling points, is 



the force-function for all the forces acting upon the particle m s . 

 If we put the mass m s equal to unity the function 



(i) 



is called the potential function of the field of force due to the 

 repulsions of the particles m lt m 2 ...... m n , and its negative vector 



parameter is the strength of the field, that is, the force experienced 

 by unit of mass concentrated at the point in question. Since any 



term - - possesses the same properties as the function - , 39, 

 we have for every term, for points where r is not equal to zero, 

 A f-J = 0, and consequently 



(2) AF-W.A (1) + m 2 A (I 



Vl/ V 2 



= 0. 



74. Potential of Continuous Distribution. Suppose now 

 that the repelling masses, instead of being in discrete points, 

 form a continuously extended body K. 



Let the limit of the ratio of the mass to the volume of any 



infinitely small part be p = lim - , which is called the density. 



A T =O AT 



