Mechanics.

Point in the Line joining the Centres, sosituated, that its Distance from the said

Centres

iZ3

of the Momenta 2yxx ——-—; whence the Fluenth x^

of the latter, viz. -, divided by the Fluent of the

b x 7.

3 a

former, viz. will give - .*• for the Distance of2 a 3

the Point from B in the Line B F, which has a Velo-city equal to the mean Velocity of all the Particles inthe Triangle DBF, and is therefore its Centre ofGravity. Consequently the Centre of Gravity of any Tri-angle ABC, is diflant from the Vertex B, — B G aright

3

Line drawn from the Angle B his?fling the Base A C.

10. And since the Section of a superficial or hollowCone is a Triangle, and Circles have the fame Ratio astheir Diameters, it follows that the Circle whose Planefases through the Centre of Gravity of the Cone is * of theLength of the Side diflant from the Vertex of the said Cone.

11. But in a solid Cone, which consists of an infiniteNumber of circular Areas, which therefore may beconsidered as so many Weights, the Centre of Gravitymay be found as before, by putting BE=jr, BG — a ;the circular Area D F E — y, and A G C = b; andfrom the Nature of the Cone, a % : x- : : b : y —

but x y — — Fluxion of the Weights ; and

a~ a L

yxx — --i- ~ Fluxion of the Momenta, whence

a 1

h x^

the Fluent of the latter, viz. -divided by the Fluent

4 T-j.

of the former

3

will give | a: of the Centre of

PI. vir.Fi g- 5 -

Gravity of the Part DBEF; consequently the Centre ofGravity of the Cone A B C G is dijiant from the VertexB, I of the Side B G, in a Circle parallel to the Base.

12 . If ABC D be a regular Superficies, and ABE F Fig. 6 ,

another