along and S be the retarding force upon B arising from the

Aa2 + Ag2

.(1)

the equation to the curve, which is therefore one of Cotes' Spirals.

573.

Let w be the given weight of the cylinder; then the accelerating force down the plane is

R being the distance of the centre of gyration from the axis of rotation, and the inclination of the plane.

574.

Let W be the weight of the cylinder, r the radius of

575.

Supposing m' not equal to m, and putting cm' = x, ac

cb= a, then since the efficacy of m in opposing the motion of m', is measured by

But at the time the velocity is a maximum, the accelerating

577. Let r be the radius of either globe, M its mass, k, k' the distances of their centres of gravity from the axis of rotation l, l' the distances of their centres of oscillation from the same, when the bodies are unconnected; then since (Creswell's Translat. of Venturoli, p. 141), the length of the compound pendulum is Mkl+Mk'l kl+k'l'

L=

Mk + Mk'

and by the question

=

k+k

Let a be the length of the rod; then supposing ge

the distance of the point of suspension from its extre

mity, the length of the pendulum is (see Venturoli)

579.

Since the centre of Initial Rotation is distant from that point of impact by the same interval as the centre of oscillation, considering that point as the point of suspension, the distance required is (Venturoli)

A, B being the masses, and a, b the lengths of the arms of the

lever.

580. Generally, if P denote the power moving the system, whose weight is w, acting at the distance r from the axis of rotation, then the force which accelerates P is

F=

Pr2
Pre+W.R

R being the distance of the centre of gynation from the axis. But s denoting the space described in the time t, we have s = gFt

6.32". 6173 nearly.