10

DETERMINATION OF THE

TRACT 21.

A 9 , is equal to the constant quantity$s; where § denotes the sin. Zbac,and $ the sin. z.bad, to the radius i.

For, first, sipce the magnitude ofthe flowing seption is every -whereas Aand the attraction of the par-ticles pf matter inversely as the same,

or as —; therefore their product or — or 1 , a copstant

quantity, is as the force of attraction of heed.

Now, to find what that quantity is. Put AB = a, andbc = x; then bd or ce, the distance between the two planesat the distance ab is = as. But the force of a particle ip

(the line ce i§ as in the direction AC, and thprefore it is as

in the direction ab ; consequently the force of the w'holeJineola ce, in the direction ab, is 5 an( i therefore the

fluxion of the force of the section bced, or f, is

AB.CZ

AC*

BC

a . as . x(« 9 + * a )J

—-■ — : and the fluent gives f —

(o a + J

•• —— —r z= s x — = ss for the attraction itself.a • + a?) ac r ■

3. Tp find now fhe attraction of the whole right-angledpuneus, on a body at a, in the direction ab. —Since theforce of each section is ss by the last article; therefore thpforce of all the sections, the number of them being ab or a,

is «ss == s . ab . the force of the whole cuneus abceda.

4. To find the attraction of the rect-angular part abcd, on a, in tlfe direc-tiop ab; abcd being ope side of thecuneus, and ad its edge.—Put ad =BC = b, and Ap = x. Then, the forceof any section, as bc, being always as

ss by Aft. 2, the fluxion of the force, or f, will be :

b bsx

S $?

aA** + *'-)

; and the fluent is

.cw