27$ Mr. Knight on the Attraction of such Solids 
A = 4 (x + x ) arc (tang. = ~=) + 4 v/Ir — 2 *tt. 
Cor. 3. If ct = y k , the attraction of the solid in the propo- 
sition equals that of a sphere whose radius is k ; for by sub- 
stituting for x, in the expression 2 tt [y/ %kx + V* — a), it 
becomes the action of a sphere whose radius is k on a 
point in its surface. 
The attractions of cylinders of finite length, in directions 
perpendicular to their axes, are to be found after the manner 
of this last proposition ; but there are not many cases in which 
they can be expressed by circular arcs and logarithms. 
Prop. 28. 
Let fig. 16 represent a circle, C the centre, ab, cd two pa- 
rallel chords ; conceive a right cylinder, whose section is the 
portion abed of the circle, terminated by the chords ab, cd, to 
be extended to the distance d above and below the plane of the 
figure. 
It is required to determine the action of this cylinder on a 
point at C. 
Put k for the radius of the circle, and let x be the distance 
from C of a chord parallel to ab. Then, using the same for- 
mula as in the last Prop, we have b = d, b' = V k* — x z , and 
for the action of the solid, A = 4 fx arc (tang. 
d d IC-—X 1 \ qy 
x v' 
A = 4* arc (tang. == ||==) - 4 fx arc (tang. = 
= 4-r arc (tang. — ~ V ~ { 
Vd*+k 7 
- 4<fL . 
dep+k 1 ". f Vk 2 
vV-f* 2 
X >/d*+k*l 
f. 
■ + corr. 
If the fluent is to begin when x = o } the correction is 
