This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

**Balance**. A simple machine, in which the lever is employed to determine the equality or difference of two given weights. Balances are of various kinds, differing in their form, and in the perfection of their construction, according to the nature of the objects for which they are employed. The common balance or scales are well known to consist of a lever or beam a b, turning on its axis in a vertical plane, and having two dishes or scale-pans d e suspended at its two ends. The distances between the centre of the beam and the extremities a and b are made as nearly equal as possible: hence it is clear, from the nature of the lever, that the weights placed in the two scales will be equal to each other when the beam rests in a horizontal position. Although, theoretically speaking, the balance is exceedingly simple, consisting merely of a right line turning on its centre, yet in practice it becomes a matter of considerable difficulty to approximate its construction to that perfection which theory points out, and which the nicer operations of philosophical research demand.

Although it is not necessary on all occasions to use a balance capable of detecting differences in weight equivalent to the 1/2000 of a grain, yet the more perfect our model is, and the nearer we approach to it, the greater chance there is of obtaining the object of our search, viz. an exact indication of the weight of any given substance. In the most perfect balances, one of which is represented in the annexed engraving, the beam L L is a bar of tempered steel, so strong as not sensibly to bend with the weights usually placed in it If G is the centre of gravity of the beam, the arms G L G L should be of precisely the same length. At the extremities, silk cords of the same length and weight support the scale-pans A A, which are also equal. That the slightest motion of the beam may be distinguished, an index S C is attached to the beam exactly perpendicular to it, and in the same plane with the centre of gravity.

The whole is sustained on an axis perpendicular to the beam at C; and in order that the line around which the beam turns may not change its place, and thus vary the lengths of the arms, the axis is formed below into a sharp knife edge of hardened steel, and moves on planes of polished crystal, agate, or other hard substance. Now if a perfect equality were established between the parts of the balance on each side the centre G, an equilibrium would naturally occur when the beam L L' was in a horizontal position; for the centre of gravity of the whole would then be in the same vertical line as the point C; hence if weights were placed in the scale, and the beam retained its horizontal position, we might infer their equality. But an experiment of this kind may be possible or not, according to the position in the vertical line of the points C and G. If the centre of gravity G coincided with the centre of motion C, the beam would rest in any position into which it might be thrown. Or if the centre G were above the centre C, the beam would remain horizontal when placed so, but its equilibrium would be unstable, and the least additional weight to either side would cause that side to descend indefinitely.

But if the centre of gravity be below the centre of support, then, if the horizontality of the beam be deranged, it will be recovered after a succession of oscillations of continually diminishing amplitude. The delicacy, or stability, of the beam, will depend, in a great measure, on the distance between these two points. Thus, if G be much below C, a considerable weight will be required to turn the beam, but it will soon regain its state of rest. On the other hand, if the point G be only a short distance below C, a slight additional weight will cause the arm to descend, but it will be longer in regaining its quiescent position.

The sensibility is increased by lengthening the arms, diminishing the distance between the centre of support and centre of gravity, and lessening the weight of the beam, and the quantity of matter to be weighed. The stability also increases with the weight, and the distance between the two centres. As another step towards the perfection of the balance, we must be careful that the centre C and the knife edges that support the scale-pans at L L, be in the same right line. If this be neglected, the beam becomes a bent lever, and the weight of the body will appear to vary with the position of the beam. The great difficulty of attaining an exact equality in the length of the arms of a balance, renders it almost hopeless to attempt to obtain the exact weight of any mass of matter by this means. It is fortunate, therefore, that there is a method of weighing which will enable us to dispense with one of these, and not the least difficult of attainment. The method of double weighing, introduced by Borda, renders the equality in the length of the arms a matter of indifference.

To ascertain the weight of a body by his method, we place the body in one scale, as A, for example, then exactly counterbalance it by small shot, sand, etc. placed in the other scale A, till the index points to O on the scale at the foot of the pillar supporting the beam. The body is next carefully removed from the scale A, and its place supplied by known weights, until the beam again stands horizontal. The weights then in the scale will indicate the weight of the body. As the weights, and the body to be weighed, have both been placed in the same scale, and, consequently, at the same distance from the centre, it is manifest, whatever may be the length of the arms, or their weight, that the true weight of the body has been ascertained. That this method may be completely efficient, only two conditions are required to be fulfilled. The one is, that the distances between the centre C, and the points L L, continue the same during the operation of weighing; and the second is, that the balance be exceedingly sensible, i. e. that it turn with the smallest possible quantity of matter.

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