216 Of the SOLIDS ‘ 
WHEN @ becomes equal to the whole angle fubtended by the 
column, the total attraétion is equal to the area of the'bafe di- 
vided by the diftance, and multiplied by the fine of the angle 
of elevation of the column. 
Ir the angle of elevation be 30°, the attraction of the co- 
lumn is juit half the attraction it would have, fuppofing it ex- 
tended to an infinite height. 
In this inveftigation, m* 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 9 to be that which 
is fubtended by the axis of the column, or by its Ase sey ba 
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. 
Ler 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 x = the angle BAD, the azimuth of D; 
v == the vertical angle fubtended by the column on DF; a= 
the 
