74 



III. GENERAL PRINCIPLES. WORK AND ENERGY. 



In the particular case in which the only forces acting on the 

 system are attractions or repulsions by the several particles directed 



along the lines joining them 

 and depending only on their 

 ^ mutual distances , a force - 

 function always exists. 



For let the force between 

 two particles m r and m s at a 

 distance apart r rs be 



Fig. 18. 



It will be convenient to consider 

 F positive if the force is a 

 repulsion. 

 Consider now the force F s ^ acting on m s and acting in the 



direction from m r to m s . Its direction cosines are those of the 



vector r rs . 



30) 



Z (r) 



Now since 



r? s = (x s - x r ) 2 + (y s - y r 

 differentiating partially by x t , 



31) 

 and accordingly 



^ r rs X s~ X r 



OA rs 9 ( rr <r \ 



1 1 r g ~r\ j \^s ^r ) y 



cx s 



n if y -jy fly 



dx. 



ar 



