RllOBLEMS.

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these are determinate; but x and * are indeterminate since theyare connected only by (5): for any given position, 'however,of the bodies z is known by geometry, and consequently xbecomes known by (5).

We learn from this that if 9 be chosen so as to satisfyequations (l) (2) (3) (4), the bodies will remain at rest inwhatever position they are placed, their centres of gravity re-maining in the plane of the paper : and as we give the bodiesdifferent positions z varies, consequently x and therefore thepoint of application of Q changes.

-r* ...... sin/3

y W = cos (a + - 9) '

by (3) (4) ~ =

sin acos 9 ’

W sin a cos (a+j3—9)W' sin /3 cos 9

sin asin /3

{cos (a+/3) + sin (a+/3) tan 9};

W sin /3 — W' sin a cos (a + /3)

W' sin a sin (a + /3)

(W + W') sin /3 sin (2 a + /3)

W' sin a sin (a + /3) sin a sin (a + /3) ’

sin a cos 9 sin a

cos (a — 9) cos a + sin a tan 9

W' sin a sin (a + /3)

W' {cos a sin (a+/3)-sin a cos (a+/3)} + W sin (i

IV' sin a sin (a -I- /3)

( W + IF^ sin /j ' '

The value of tan 9 gives the angle of the cone necessary forequilibrium, and the value of x gives the point of applicationof Q for any given position of the bodies.

Prob. 5. A person suspended in a balance of which thearms are equal thrusts his centre of gravity out of the verticalby means of a rod fixed to the furthest extremity of the beamof the balance, the direction of the rod passing through hiscentre of gravity : given that the rod and the line from thenearer end of the beam of the balance to his centre of gravity

tan 9

By (4) (5) =