i68

Mechanics.

would answer to the Strictness of theMathematical Theory, were there no such

thing

we have AD:AE: :DO (=LO) :OK; thereforeA : P : : O L : OK.

6. If the Weight p, (equal to P) suspended by thestring N p, does at the fame Time in part rest upon the;inclined Plane p G ; let p Q_be drawn perpendicular top N, p H perpendicular to the Horizon, and H G thro'the Point N perpendicular to p G ; Then will the Ten-sion of the String PN be to that of the String /> N,as p H top N, For suppose the Body p wholly sup-ported by the two Planes p G, p Q, it will press themwith its whole Force, which may be exprefs’d by p H,and which is resolvable into the two Forces H N andp N, of which the first presses the Plane p G, and thelast the Plane p Q_; if therefore the Plane p be re-moved, the fame Force will stretch the Strings N ;,but since p ~ P, the Force with which P stretches theString PN is as p H; therefore the Tension of theString P N is to that of the String p N as p II topN.

7. Let the horce of p to move the Wheel (as sup-ported on the Plane) be called Then P : x : : p H

. T , . _ xX p II AXOK , ,

- P N j and so P = —jYf~ = - Q - j — (by 5*),

whence we have this Equation, x X p H X OL = AX O K X p N ; therefore A:*::pHXOL:pNxO K. But here it is to be observed that as the StringP N is changed into the Positions N, its nearest Dis-tance O L will become O R, so that the Analogy be-tween A and x corrected will be A : x :: p H X OR;p N x O K.

8. From what is demonstrated it follows, (1.) Thajthe Line K O L is a Lever, whose Power is always

cxprefs’d by the Ratio (2.) That the Lines M

O L, M O N, D O L, are also Levers of equal Force,because the nearest Distance of their Lines of Directionfrom the Centre O is the same in all. (3.) Wheneverthe Lever KL is moved, the Velocity of the Points

K ancf