2i5 Of the SOLIDS 



When <p becomes equal to the whole angle fubtended by the 

 column, the total attraction is equal to the area of the bafe di- 

 vided by the diftance, and multiplied by the line of the angle 

 of elevation of the column. 



If the angle of elevation be 30 °, the attraction of the co- 

 lumn is juft half the attraction it "would have, fuppofing it ex- 

 tended to an infinite height. 



In this inveftigation, nt is fuppofed an infinitefimal ; but if 

 it be of a finite magnitude, provided it be fmall, this theorem 

 will afford a fufficient approximation to the attraction of the- 

 column, fuppofing the diftance AD to be meafured from the 

 centre of gravity of the bafe, and the angle <p to be that which 

 is fubtended by the axis of the column, or by its perpendicular 

 height above the bafe. 



XV. 



Let the femicircle CBG (Fig. 9.), having the centre A, be the 

 bafe of a half cylinder ftanding perpendicular to the horizon, 

 AB a line in the plane of the bafe, bifecting the femicircle, and 

 reprefenting the direction of the meridian ; it is required to 

 find the force with which the cylinder attracts a particle at A, in 

 the direction AB, fuppofing the radius of the bafe, and the alti- 

 tude of the cylinder to be given. 



Let DF be an indefinitely fmall quadrilateral, contained be- 

 tween two arches of circles defcribed from the centre A, and 

 two radii drawn to A ; and let a column ftand on it of the fame 

 height with the half cylinder, of which the bafe is the femi- 

 circle CBG. Let z = the angle BAD, the azimuth of D ; 

 v zz the vertical angle fubtended by the column on DF ? azz 



the 



