29a Mr. landen’s new Theory of 
Therefore, writing 2 ^]y L -w L inftead of p, it follows that 
*mnxx — -x 2 y\ the whole fluent of K 
£ 4 s 
/ • “ 
mnxxw 2 -x 2 xw, generated w ( = k p — kp ) from o becomes 
equal to the radius y (both x and y being confidered as 
invariable) will exprefs the value of the force which, 
acting on the line oco_at the diftance g from c, would be 
equivalent to the force of all the particles in the faid fec- 
tion, whofe thicknefs is denoted by the indefinitely fmall 
/ 
quantity x ; the diftance c k being denoted by x, and a 
being put for (.78539.) the area of a quadrant of a circle 
whofe radius is 1. 
4. Fig. 1 1 . In the cylinder whofe length is 2 b and dia- 
4 . yZ 
meter 2 r ; y being - r ->g_ - x'y 1 will be = r x — —x 2 : con- 
r i 
fequently, the fluent of —~x 2 xx, generated whilft x 
from o becomes = b, being ~ , we have —p— xmnx 
~ - b — - x 3 r ~ — 4 b 2 x M for the force which, acting 
as above at the diftance g from (c) the center of gravity 
of the cylinder, would be equivalent to the efficacy of the 
forces ailing as above on all the particles of the cylinder 
to turn it about a diameter paffing through c, M being 
the mafs or content of the cylinder. 
7 
5- Fig- 
