158 THEORY OF NEWTONIAN FORCES. [FT. I. CH. IV. 



to the disc at its center. Let the radius be R lt thickness 6, 

 distance of P from the center h 



erdrd(f) 

 o Jo 



Jo Jo 



f* rdr r n 1 



, = 2?rep V h 2 + r 2 



J o V h 2 4- r 2 



_ _ 



= 2-Trep ! .. 1 [ . 



r + .R 2 



Attraction of circular cylinder on point in its aods. Let the 

 length be I and let the point be external, at a distance h from 

 the center. 



By the above, a disc of thickness dx at a distance x from the 

 center produces a potential at P 



- xf -(h- x)}. 

 Hence the whole is 



fl 



J - 



* 



\ 



27T/3 -i^-a- ^ 2 + (^ - ) 2 + y log ( - 



Circular cone on point in axis. 



Let R be the radius of base, a the altitude, h the height of P 

 above the vertex. 



A disc at distance x below vertex and radius r causes potential 

 at P, 



dV= Zirpdx {( + xj + r 2 - (h 



