MECHANICS. 



The arms should be as long as possible, 

 relatively to their thickness, and the pur- 

 poses for which they are intended, as the 

 longer they are the more sensible is the 

 balance. They should also be made as 

 stiff and inflexible as possible ; for if the 

 beam be too weak, it will bend, and be- 

 come untrue. 7. The ring's, or the piece 

 on which the axis bears, should be hard 

 and well polished, parallel 1o each other, 

 and of an oval form, that the axis may 

 always keep its proper bearing 1 , or remain 

 always at the lowest point. 8. If the 

 arms of a balance be unequal, the weights 

 in equipoise will be unequal in the same 

 proportion. The equality of the arms is 

 of use, in scientific pursuits, chiefly in the 

 making of weights by bisection. A ba- 

 lance with unequal arms will weigh as ac- 

 curately as another of the same work- 

 manship with equal arms, provided the 

 standard weight itself be first counter- 

 poised, then taken out of the scale, and 

 the thing to be weighed be put into the 

 scale, and adjusted against the counter- 

 poise. Or, when proportional quantities 

 only are considered, the bodies under ex- 

 amination may be weighed against the 

 weights, taking care always to put the 

 weights in the same scale ; for then, 

 though the bodies may not be really equal 

 to the weights, yet their proportions 

 amongst each other will be the same as if 

 they had been accurately so. 9. Very 

 delicate balances are not only useful in 

 nice experiments, but are likewise much 

 more expeditious than others in common 

 weighing. If a pair of scales, with a cer- 

 tain load, be barely sensible to one-tenth 

 of a grain, it will require a considerable 

 time to ascertain the weight to that de- 

 gree of accuracy, because the turn must 

 be observed several times over, and is ve- 

 ry small. But if no greater accuracy 

 were required, and scales were used, 

 which would turn with one-hundredth of 

 a grain, a tenth of a grain more or less 

 would make so great a difference in the 

 turn, that it would be seen immediately. 

 The statera, or Roman steel-yard, is a 

 lever of the first kind, and is used for 

 finding the weights of different bodies, by 

 one single weight placed at dhTerent dis- 

 tances from the prop or centre of motion 

 D, fig. 6. _ For, the shorter arm D (i is of 

 such a weight as exactly to counterpoise 

 the longer arm D X. If this arm be divid- 

 ed into as many equal parts as it will 

 contain, each equal to G D, the single 

 weight P (which we may suppose to be 

 one pound) will serve for weighing any 

 thing as heavy as itself, or as many times 



heavier as there are divisions in the arm 

 1)X, or any quantity between its own 

 weight and that quantity. As for example, 

 if I J be one pound, and placed at the first 

 division 1 in the arm I) X, it will balance 

 one pound in the scale at W ; if it be re- 

 moved to the second di vision at 2, it will 

 balance two pounds in the scale ; if to 

 the third, three pounds ; and so on to the 

 end of the arm D X. If any of these in- 

 tegral divisions be subdividedinto as many 

 equal pans as a pound contains ounces, 

 and the weight P be placed at any of 

 ihcse subdivisions, so as to counterpoise 

 what is in the scale, the pounds and odd 

 ounces therein will by that means be as- 

 certained. In the Danish arid Swedish 

 steel-\ard, the body to be weighed, and 

 the constant weight, are fixed at the ex- 

 tremities of the steel-yard, but the point 

 oi suspension or centre of motion moves 

 along ihe lever till the equilibrium takes 

 place The centre of motion therefore 

 shews the weight of the body. 



The wheel and axle, or axis in peritro- 

 chio, is a machine much used, and is made 

 in a variety of forms. It consists of a 

 wheel witii an axle fixed to it, so as to 

 turn round with it; the power being ap- 

 plied at the circumference of the wheel, 

 the weig-Jit to be raised is fastened to a. 

 rope which coils round the axle. 



A B (fig. 7.) is a wheel, and C D an ax- 

 le fixed to it, and which moves round with 

 it. If the rope which goes round the 

 wheel be pulled, and the wheel turned 

 once round, it is evident that as much rope 

 will be drawn olV as the circumference 

 of the wheel ; but while the wheel turns 

 once round, the axle turns once round; 

 and consequent]} the rope by which the 

 weight is suspended will wind once round 

 the axis, and the weight will be raised 

 through a space equal to the circumfer- 

 ence of the axis. The velocity of the 

 power, therefore, will be to thut of th-.- 

 weight, as the circumference of the wheel 

 to that of the axis. In order, there-fore. 

 that the power and tlie weight may be in 

 equiiibrio, the power must be to the 

 weight as the circumference of the wheel 

 to that of the axis. Circles being to- 

 each other as their respective diameters, 

 the power is to the weight, as the diame- 

 ter also of the axis to that of the wheel. 

 Thus, suppose the diameter of ilie wheel 

 to be eight inches, and the diameter of 

 the axis to be one inch ; then one ounce- 

 acting as tiie power P, w 7 ill balance eight 

 ounces ;is a weight W ; and a small a 

 tional force will cause the wheel to turn 

 with its axis, and raise the weight -. 



