BALANCE, or BALLANCE, one of the six simple powers in mechanics, principally used in determining the equality or difference of weights in heavy bodies, and consequently their masses or quantities of matter.
The balance is of two kinds; the ancient, and the modern. The ancient, or Roman, called also the statera Romana, or steel-yard, consists of a lever or beam, moveable on a centre, and suspended near one of its extremities: the bodies to be weighed are applied on one side of the centre; and their weight is shewn by the division marked on the beam, where the weight, which is moveable along the lever, keeps the steel-yard in equilibrio. This balance is still frequently used in weighing heavy bodies.
The modern balance now generally used consists of a lever or beam suspended exactly in the middle, having scales or basons hung to each extremity. The lever
Balance. is called the jugum or beam; and the two moieties thereof on each side the axis, the brachia or arms. The line on which the beam turns, or which divides its brachia, is called the axis; and, when considered with regard to the length of the brachia, is esteemed a point only, and called the centre of the balance: the handle whereby it is held, or by which the whole apparatus is suspended, is called trutina; and the slender part perpendicular to the beam, whereby either the equilibrium or preponderancy of bodies is indicated, is called the tongue of the balance. Thus in fig. 4. a b is the beam, divided into two equal brachia or arms by the white spot in the centre, which is the axis or centre of the balance, and c is the tongue. The trutina, on which the axis is suspended, is not represented in this figure, in order to render the other parts more conspicuous.
It follows, from what has been observed, therefore, that in the Roman balance, the weight used for a counterpoise is the same, but the points of application varies; in the common balance the counterpoise is various, and the point of application the same. The principle on which each is founded, may be very easily understood from the following observations, and the general properties of the lever. See LEVER.
The beam AB, fig. 7. is a lever of the first kind; but, instead of resting on a fulcrum, is suspended by something fastened to its centre of motion: consequently the mechanism of the balance depends on the same theorems as the lever.
Hence as the quantity of matter in known weight is to its distance from the centre of motion, so is the distance of the unknown weight to its quantity of matter. Hence the nature and use of the steel-yard is easily known. Let AB (fig. 7.) represent an instrument of this kind; a, the trutina or handle on which the beam turns; k, a ring on which the balance may be suspended on a nail, or hook; f, the hook on which the body to be weighed is hung; c, a collar or guard by which the hook f is fastened to the beam; g, a moveable collar; h, a swivel; i, the counterpoise. From what has been said it evidently follows, that if the body to be weighed be fastened to the hook f, and the whole suspended by the ring k, the division on which the counterpoise is placed to maintain an equilibrium in the balance, will shew the weight of the body required; provided the weight of the counterpoise i be known, and the large divisions, 1, 2, 3, &c. be equal to the distance between the centre of the balance and the screw which fastens the guard c to the shorter arm of the balance. It will also be necessary that the steel-yard itself, with its whole apparatus, exclusive of the counterpoise, be in equilibrium, when suspended on the ring k. If the body to be weighed be heavier than the divisions on the longer arm will indicate, the balance is turned the lower side upwards, and suspended on the other ring h, by which means the divisions become shorter, because the distance between the trutina d, and the screw on which the guard c moves, is less: the divisions in the figure on this side extending to 17, whereas they extend only to six on the other. It will be unnecessary perhaps to observe, that the same precaution, with regard to the centre of gravity when the balance is suspended, is also necessary when this side of the balance is used, as we before mentioned
with regard to the other.
We have already observed, that in the common scales the two brachia or arms of the balance, ef, eg, fig. 5. are equal to each other, and consequently equal weights placed in the scales d, d, will be in equilibrium when the balance is suspended on its centre e, as in the figure, where the ring at the extremity of the trutina is hung on the tapering rod a b, fixed in the foot or basis.
The Deceitful BALANCE, or that which cheats by the inequality of its brachia, is founded on the same principle as the steel-yard. Let there be, for example, a balance so constructed, that both the brachia with their scales shall equiponderate, but that the length of the one arm shall be to that of the other as 10 to 9. In this case, a weight of nine pounds put into the longest arm, will counterpoise one of ten pounds put into the shorter one: but the cheat is immediately discovered by shifting the weight from one scale to the other; in which case, the balance will no longer remain in equilibrium.