274 ATTRACTION. CYI.INDKR. OOVE, 



<! on its axis. Suppose the cylinder divided ii,: 

 indefinitely large number of lamina; oy planes perpendicular 

 to its axis; let x be the distance of a lamina I'mm il 

 tracted particle, &/ the thieknr-s of the lamina, I tin* radius 

 of the cylinder; then the attraction of the lamina is 



Suppose the attracted particle out**' evlindT at a 



distance c from it; let A be the height of the cylinder; then 

 the resultant attraction of the cylinder 



rc+h 



H. 



' + V} 



If we suppose c = so that the particle is on the surface of 

 the cylinder the resultant attraction is 



209. To find the attraction of a uniform cone on a particle 

 at its vertex, we begin with the expression 



for the attraction of a lamina of the cone. Also, if a be the 

 semivertical angle of the cone, we have 



x 



= cos a ; 



hence, the resultant attraction 



rh 



= 27rp (1 cos a) I dx = 2?rp (1 cos a) h ; 

 'o 



where A is the height of the cone. 



I is easily seen that the same expression holds for the 

 tion of the frustum of a cone on a particle situated at 

 the vertex of the complete cone, h representing in this case 

 the height of the frustum. 



