.. the whole moving force or tension of the string is

the velocity of the chain, when quitting the quadrant, is given by

V2 = {8r+ 4 (2α-r) % — rw2 }·

4a

632.

Let y', y, be the radii of the required annulus, and the distance of its centre from the pole; also let a, b, be the semiaxis of the generating ellipse; then it may easily be shewn that

Again, if u denote the radius of any of the concentric circles which compose the ring, the attraction of any particle in its circumference upon the pole is

1

u2 + x2

and by the resolution of forces the attraction in the direction of the axis

Hence the whole force of the circle in this direction is

which gives the position of the annulus for spheroids of all eccen

tricities.

633. Let the distance of the particle attracted from the centre of the sphere be a, r the radius of the sphere, and suppose any circular section whose radius is y to be made by a plane to a, and distant from the point by the interval x; then if y' denote the radius of any concentric with the former, the attraction of any particle in the circumference of this circle is

taken between the limits of x = a + r, x = α — r.

634.

If x be the altitude of the cone, and s its slant side,

the whole attraction is (Vince, p. 142)

Again, supposing the given quantity of matter to be a3, and the density to be constant, we have

whence by substituting for r &c. &c. r may be found exactly or by approximation.

635. Let c be the distance of P from the surface of the sphere, r the radius of the sphere, then cr is the radius of the

2

Ꮖ

generated sphere. Let any circular section of the sphere be made by a plane to c or to the axis, and let y be the radius of that section, and y' that of any circle concentric with it; also let x be the distance of P from the plane of this section; then the attraction of any particle in the circumference of the circle whose radius is y', is

xdx

+ 2.x − 2.(c + r) ƒ z¿c + r) x − c(c + 2r)

and we finally obtain, after finding the correction on the supposi