F'g- 24.

THE

RESOLUTION

O F

Some General Problems in Mechanics, andPhysical Astronomy.

PROBLEM I.

Suppose a system of bodies A, B, C (connected together) to re-volve about a center , or axis (P), with a given angular celerity ;it is proposed to find the momentum (k) which , adding at a givendistance QP from the center , shall be jufi sufficient to slop , or takeaway the whole motion of the system.

the given angular celerity of the system, at any di-^ I ^ stance PG from the axis, be denoted by v, the cele-dties of the several bodies A, B, and C will be trulyAP RP CP

expressed by-p^xv, ^-xn, and—xi;, respectively. Hence(by the property of the Lever) it will be, as PQJs to AP, so

AP

is ( x v x A) the momentum of the body A, to „

vy.A, the momentum, which acting at Q, is a just counter-poise to the action of A. And, in the very same 'manner, themomentum, acting at Q, sufficient to take away the motion ofBP*

B, appears to be Qp-jj^ XvxB-, and so on. Whence it is

manifest, that the sum of all these , must be the true momen-

turn required ; or that k = v X--—-T-—

x PG x QP

6^ E. I.

COROLLARY I.

If the motion of the system is that which might be pro-duced by any given momentums a, b, c (or forces capable ofproducing those momentums) acting on the bodies A, B, C, in

directions

AP 1

1