Mechanics.

thing as Friction or rubbing of Partsupon each other, by which means one Third

Pars

K and L will bo proportional to the Distances fromjthe Centre KO and O L. (4.) Therefore the Velo-cities also, and perpendicular Spaces pafs’d through bythe Bodies A and P, will be proportional to th? saidDistances from the Centre.

9. Since P : A : ■ KO : LO ; ’tis evident the PowerP may be in any Proportion less than the Weight A,if its Distance from the Centre of Motion OL be inthe fame Proportion greater than the Distance of thoWeight KO, and yet its Force or Momentum shall boequal to that of the Weight A. Whence the Natureof a Lever for increasing a Power sufficiently appears.

10. If the Distances from the Centre OK = OL;then will the Lever become a common Balance , becausethen, in order to an Equilibrium , the two Bodies A andP must have equal Weight.

11. If the Arms of the Balance KO and OL dif-fer but a very little in Length, there will be the fameDifference in the Weights A and P. Whence if O K: O L : : 31 : 32 : : P : A > and therefore if A is an Avcr-dupois Pound, P will want ' an Ounce of it and yet bein Equilibria. Hence the Nature of a False Balance isevident; and in order to detect it we need only inter-change the Weights, for then, in order to an Equili-brium , we must have KO : O L : : (31 : 32 : :) 32 :33 A; but of this there wants 2 5 \ half Ounces, whichwill render the Fraud very notorious.

12. The Arms of a Balance being nicely equatedin Weight and Length, and divided into an equalNumber of equal Parts, becomes the Proportional Ba-lance to be used without Scales. For any two Bodieshanging on the Arms of this Balance in Equilibria , willhave the Proportion of their Weights exprefs’d by theNumbers at the Divisions (whence they hang) alter-nately.

13. If AC the shorter Arm of a Balance be madeequal in Weight to C E the longer Arm, by the Ad-dition of the Ball A, so that the whole Beam A E

jnay

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PI. VIII.Fig- 3-