MECHANICS. 



of the first kind, and is so contrived, 

 that a power applied at the point JL of the 

 lever C, may sustain a weight at the point 

 S of the lever A, the power must here be 

 to tiie weight, in a ratio, or proportion, 

 compounded of the several ratios, which 

 those powers that can sustain the weight 

 by the help of each lever, when used 

 singly and apart from the rest, have to the 

 weight. For instance, if the power 

 which can sustain the weight W by the 

 help of the lever A, be to the weight as 

 1 to 5 ; and if the power which can sus- 

 tain the same weight, by the lever B 

 alone, be to the weight as 1 to 4; and if the 

 power which could sustain the same 

 weight by the lever C, be to the weight 

 as 1 to 5 ; then the power which will sus- 

 tain the weight by help of the three le- 

 vers joined together, will be to the 

 weight in a proportion consisting of the 

 several proportions multiplied together, 

 of 1 to 5, 1 to 4, and 1 to 5 ; that is as 1 : 

 3 X4 X 5, or of 1 : 100. For since, in 

 the lever A, a power equal to one-fifth of 

 the weight W, pressing down the lever at 

 L, is sufficient to balance the weight, and 

 since it is the same thing whether that 

 power be applied to the lever A at L, or 

 the lever B at S, the point S bearing on 

 the point L, a power equal to one-fifth of 

 the weight P, being applied to the point 

 S of the lever B, will support the weight ; 

 but one-fourth of the same power being 

 applied to the point L of the lever B, 

 and pushing the same upward, will as ef- 

 fectually depress the point S of the same 

 Jever, as if the whole power were ap- 

 plied at S ; consequently a power equal 

 to one-fourth of one-fifth, that is one-twen- 

 tieth of the weight P, being applied to 

 the point L of the lever B, and pushing 

 up the same, will support the weight : in 

 like manner, it matters not whether that 

 force be applied to the point L of the le- 

 ver B, or to the point S of the lever C, 

 since, if S be raised, L, which rests on it, 

 must be raised also ; but one-fifth of the 

 power applied at the point L of the lever 

 C, and pressing it downwards, will as ef- 

 fectually raise the point S of the same 

 lever, as if the whole power were appli- 

 ed at S, and pushed up the same; conse- 

 quently a power equal to one-fifth of one- 

 twentieth, that is, one hundredth part of 

 the weight P, being applied to the point 

 L of the lever C, will balance the weight 

 at the point S of the lever A. This me- 

 thod of combining levers is frequently 

 used in machines and instruments, and is 

 of great service, either in obtaining a 

 VOL. IV. 



greater power, or in applying it with 

 more convenience. 



The balance, an instrument of very 

 extensive use in comparing the weights 

 of bodies, is a lever of the first kind, 

 whose arms are of equal length. The 

 points from which the weights are suspen- 

 ded being equally distant from the cen- 

 tre of motion, will move witli equal velo- 

 city ; consequently if equal weights be 

 applied, their momenta will be equal, and 

 the balance will remain in equilibrio. In 

 order to have a balance as perfect as possi- 

 ble, it is necessary to attend to the follow- 

 ing circumstances : 1. The arms of the 

 beam ought to be exactly equal, both as 

 to weight and length. 2. The points from 

 which the scales are suspended, should 

 be in a right line, passing through the 

 centre of gravity of the beam ; for by this, 

 the weights will act directly against each 

 other, and no part of either will be lost, 

 on account of any oblique direction. 3. 

 If the fulcrum be placed in the centre of 

 gravity of the beam, and if the fulcrum 

 and the points of suspension be in the 

 same right line, the balance will have no 

 tendency to one position more than ano- 

 ther, but will rest in any position it may be 

 placed in, whether the scales be on or off, 

 empty or loaded. If the centre of gravi- 

 ty of the beam, when level, be immedi- 

 ately above the fulcrum, it will overset by 

 the smallest action ; that is, the end which 

 is lowest will descend ; and it will do this 

 with more swiftness, the higher the cen- 

 tre of gravity be, and the less the points 

 of suspension be loaded. But if the cen- 

 tre of gravity of the beam be'immediate- 

 ly below the fulcrum, the beam will not 

 rest in any position but when level ; and 

 if disturbed from that position and then 

 left at liberty, it will vibrate, and at last 

 come to rest on the level. In a balance, 

 therefore, the fulcrum ought always to be 

 placed a little above the centre of gravity. 

 Its vibrations will be quicker, and its ho- 

 rizontal tendency stronger, the lower the 

 centre of gravity, and the less the weight 

 upon the points of suspension. 4. The 

 friction of the beam upon the axis ought 

 to be as little as possible ; because, should 

 the friction be great, it will require a con- 

 siderable force to overcome it; upon 

 which account, though one weight should 

 a little exceed the other, it will not pre- 

 ponderate, the excess not being sufficient 

 to overcome the friction, and bear down 

 the beam. 5. The pivots, which form 

 the axis or fulcrum, should be in a straight 

 line, and at right angles to the beam. 6, 



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