

88, 89] 



NEWTONIAN POTENTIAL FUNCTION. 



175 



e 



The force in the direction of p is inversely proportiona 

 first power of p. 



We may verify this by direct calculation. Let us consider the 



FIG. 43. 



cylinder as infinitely thin, with cross-section r. We will find the 

 component of force in the direction of p. 



The action of dm at z on P at distance p (Fig. 43) is 

 dm dm 



The component parallel to p is 

 dm 



Now since, calling the density 8, dm = Sixdz, we have for the 

 total force in direction p 



F=^r ^P dz 

 Jo 



Put 



z = p tan 0, 

 z = /osec 2 Qd6. 



o /> 



C 

 -- = as before. 



P P 



89. Logarithmic Potential. We may state the above 

 result in terms of the following two-dimensional problem. Sup- 

 pose that on a plane there be distributed a layer of mass in such 

 a way that a point of mass m repels a point of unit mass in 



