Mechanic s.

z 3, In the Screw A B, suppose the Distance of theSpiral Threads T * B of an Inch-, and the Length of theLever F G — 16 i Inches, then will the Circles de-scribed by the Hand at F be — 16,5 X 6,3 = 103,9,or 104 Inches nearly, that is, 1040 Tenths of anInch; whence the Velocity of the Power is to that ofthe Weight, as 1040 to 1 ; therefore the Screw is agreat Mechanical Power, either for raising Weights orPressure, even though we allow the greatest Part forFriction ; but it is properly a Compound Power consist-ing of the Lever and Inclined Plane ; and therefore wecan find but four such as we can properly call SimpleMechanical Powers.

Scholium.

24. Having treated of the Simple Pendulum in thepreceding Lecture, and of the Nature of the Lever inthis; I shall here let the Reader fee how nearly thesetwo Instruments are allied, or rather shew him that theLever is in reality nothing but a Compound Pendulum-,from whence many Particulars concerning the Proper-ties of each, not hitherto mentioned, will occur worthyof Observation.

25. Let CD be a fine Rod or Wire (whose Weightis inconsiderable) and moveable about the Point C. IfA and B be two Bodies (of the same Kind) fixed atany Distance Ca, C b on the Rod ; and then the Rodpermitted to descend freely; the Bodies A and B willbegin their Motions with Velocities proportional to C aand C b, and so their respective Momenta will be A XC a and B X Cl, in the Points a and b (by AnnaUXXXVIII.)

26. Now if A : B : : tnb : m a, then will A X a m— B X b m ; and consequently the Point m will be th*common Centre of Gravity between the Bodies A andB (by Annot. XXXV.) Wherefore since the Velocityof the Point m is as C m, its Momentum will be as C m XA-j-B ; and from the Nature of the common Centreof Gravity, we have AXCu + BxCir C « X

A-j-B ; and therefore

AXC«+BxCi

A + B

——- —Cm: or

by

* 7 $

Pl.VIILFig, iL,

PI. I*.Fig. I.