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 satura 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 equilibrium. 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 bacons hung to each extremity. The lever is called the jum 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. 1. Plate LXXXIV. 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,

PLATE LXXXIV.

BALISTA. Fig. 6.

COMMON BALANCE. Fig. 3.

ROMAN BALANCE. Fig. 2.

ASSAY BALANCE. Fig. 5.

HYDROSTATIC BALANCE. Fig. 4.

E. Mitchell sculp. that in the Roman balance, the weight used for a counterpoise is the same, but the point 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. 2.), 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 a 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. 2.) 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 twivel; i, the counterpoise. From what has been said it evidently follows, that if the body to be weighed is 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 b; 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 6 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. 3. 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 c.

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 equilibrio.

Assay-Balance, a very nice balance used in docimastical operations, to determine exactly the weight of minute bodies; see fig. 4. This balance should be made of the best steel, and of the hardest kind; because that metal is not so easily spoiled with rust as iron; and it is more apt than any other to take a perfect polish, which at the same time prevents the rust.

The structure of the assayer's scale is little different from that of common scales, otherwise than by its nicety and smallness. The longer the beam of it is, the more exact may the weight of a body be found; however, 10 or 12 inches are sufficient length. Let the thickness of it be so little, that two drachms may hardly be hung at either of its extremities without its bending; for the largest weight put upon it seldom exceeds one drachm. The whole surface of this beam must be altogether without ornaments, which only increase the weight and gather dust, &c. The beam is suspended in a fork, the two legs of which are steel springs joined at top, but kept together below with a brafs pliant clasp, parallel, and two lines and a half distant from each other. This clasp being taken off, and the legs of the fork being stretched out, the axis of the beam may be put into two holes made for that purpose at the ends of the legs, or be taken away from them. Let a very sharp needle be fixed in the head of the fork, standing perpendicularly downwards, if the fork is suspended, and so long, as that it may almost touch the top of the tongue of the beam put into the fork when in equilibrium. This needle is the mark of the equilibrium; and that the artist may be able to observe this, the legs of the fork must be broader in that place, and have an opening two or three lines wide; this fork may be adorned at pleasure, provided the motion of the balance is not hindered by such ornaments: then take two scales made of thin plate of silver, one inch and a half in diameter, hanging on three small silk strings, almost as long as the beam, tied together at top, with a silver hook in form of an S, and hang them to the extremities of the beam: a smaller silver dish or blood steel, somewhat less than one inch in diameter, belongs to each of these scales. You first put into these dishes, with a pair of pincers, the bodies to be weighed, or with a spoon or a small shovel, when they are pounded, and then you put them into the scales; therefore the small dishes must be perfectly equal in weight. We use them, that bodies may be more conveniently put into and taken out of the scales, and that these which are vastly thin may not be bent or foiled, and thence rendered false by wiping.

This balance is suspended on a moveable brafs or copper support, which consists of a pedestal, and of a column set upon it about 20 inches high, at the top of which comes out at right angles an arm one inch long. At the extremity of this arm, put a small pulley three lines in diameter, another at the top of the column, and a third near the bottom of it; all which pulleys must turn very easily on their axes. At the distance of one inch and a half below the upper arm, let another arm one inch and a half long come out of the column at right angles, having a hole through it two lines long, a quarter of a line broad, and placed perpendicularly. Balance. pendicularly below the pulley of the upper arm, to receive a small plate, one inch and a half long; and of such breadth and thickness, as that it may freely move up and down, and yet not have too much play within the hole. This plate must also have a small hook at each extremity.

And as such a balance will hardly stand still in the open air, and becomes false when foiled with dust, it must be put, together with its support, into a small case as represented in fig. 4, having glaases, a, a, at top, and all round it, that you may see what is within.

Manner of using the Assay-Balance.—Puts a silk string over the three pulleys of the support, and tie it at its upper extremity to the small hook introduced into the hole of the inferior arm; then put the support in the middle of the small case, and puts the other extremity of the silk string below, through a hole bored in the middle of the lower part of the frame, containing the window in the fore-part of the case, and fasten it to a small weight of a cubic form. Suspend the fork of the balance on the inferior hook of the plate. By this means if you move backwards and forwards the weight fastened to the string, placed upon the top of the drawer jutting out beyond the fore-part of the case, the balance within is either lifted up or let down. But you must put the bodies to be weighed, and the weights themselves, into the small silver dishes; and these, when loaded, into the scales, through the side-windows, which must be opened for that purpose. When any thing is to be added or taken out of them, you do it with the small pincers; or, if it is powder, with the small shovel or spoon: but you must let the balance down every time any thing is to be added or taken away, that the scales may rest upon the bottom of the case; and that the windows before the balance is lifted up again, especially if the air is not perfectly calm.

Hydrostatic Balance, an instrument contrived to determine accurately the specific gravity of both solid and fluid bodies. It is constructed in various forms; but we shall content ourselves here with describing that which appears of all others the most accurate.

VCG (fig. 5.) is the stand or pillar of this hydrostatic balance, which is to be fixed in a table. From the top A hangs, by two silk strings, the horizontal bar BB, from which it is suspended by a ring i, the fine beam of a balance b; which is prevented from descending too low on either side by the gently springing piece t x y z, fixed on the support M. The barrels is annulated at o, to show distinctly the perpendicular position of the examen, by the small pointed index fixed above it.

The strings by which the balance is suspended, passing over two pulleys, one on each side the piece at A, go down to the bottom on the other side, and are hung over the hook at v; which hook, by means of a screw P, is moveable about one inch and a quarter, backward and forward, and therefore the balance may be raised or depressed so much. But if a greater elevation or depression be required, the sliding piece S, which carries the screw P, is readily moved to any part of the square brafs rod VK, and fixed by means of a screw.

The motion of the balance being thus adjusted, the rest of the apparatus is as follows. HH is a small board, fixed upon the piece D, under the scales d and e, and is moveable up and down in a low slit in the pillar above C, and fastened at any part by a screw behind. From the point in the middle of the bottom of each scale hangs, by a fine hook, a brafs wire a d and a c. These pass through two holes mm in the table. To the wire a d is suspending a curious cylindric wire r s, perforated at each end for that purpose: this wire r s is covered with paper, graduated by equal divisions, and is about five inches long.

In the corner of the board at E, is fixed a brafs tube, on which a round wire h l is so adapted as to move neither too tight nor too free, by its flat head I. Upon the lower part of this moves another tube Q, which has sufficient friction to make it remain in any position required: to this is fixed an index T, moving horizontally when the wire h l is turned about, and therefore may be easily set to the graduated wire r s. To the lower end of the wire r s hangs a weight L; and to that a wire p n, with a small brafs ball g about one-fourth of an inch diameter. On the other side, to the wire a c, hangs a large glass bubble R, by a horse hair.

Let us first suppose the weight L taken away, and the wire p n suspended from S: and, on the other side, let the bubble R be taken away, and the weight F, suspended at c, in its room. This weight F we suppose to be sufficient to keep the several parts hanging to the other scale in equilibrium; at the same time that the middle point of the wire p n is at the surface of the water in the vessel N. The wire p n is to be of such a size, that the length of one inch shall weigh four grains.

Now it is evident, since brafs is eight times heavier than water, that for every inch the wire sinks in the water it will become half a grain lighter, and half a grain heavier for every inch it rises out of the water: consequently, by sinking two inches below the middle point, or rising two inches above it, the wire will become one grain lighter or heavier. Therefore, if, when the middle point is at the surface of the water in equilibrium, the index T be set to the middle point a of the graduated wire r s, and the distance on each side a r and a s contains 100 equal parts: then, if in weighing bodies the weight is required to the hundredth part of a grain, it may be easily had by proceeding in the following manner.

Let the body to be weighed be placed in the scale d. Put the weight X in the scale e; and let this be so determined, that one grain more shall be too much, and one grain less too little. Then the balance being moved gently up or down, by the screw P, till the equilibrium be nicely thrown at o; if the index T be at the middle point a of the wire r s, it shows that the weights put into the scale e are just equal to the weight of the body. By this method we find the absolute weight of the body; the relative weight is found by weighing it hydrostatically in water, as follows.

Instead of putting the body into the scale e, as before, let it hang with the weight F, at the hook c, by a horse hair, as at R, supposing the vessel O of water were away. The equilibrium being then made, the index T standing between a and r, at the 36 division, sion, shows the weight of the body put in to be 195.36 grains. As it thus hangs, let it be immersed in the water of the vessel O, and it will become much lighter: the scale e will descend till the beam of the balance rest on the support x. Then suppose 100 grains put into the scale d before the equilibrium precisely, so that the index T stand at the 36 division above a; it is evident that the weight of an equal bulk of water would, in this case, be exactly 100 grains.

After a like manner this balance may be applied to find the specific gravity of liquids, as is easy to conceive from what has been said.

BALANCE of Trade. That which is commonly meant by the balance of trade, is the equal importing of foreign commodities with the exporting of the native. And it is reckoned that nation has the advantage in the balance of trade, which exports more of the native commodities, and imports less of the foreign. The reason of this is, that, if the native commodities be of a greater value than are imported, the balance of that account must be made up in bullion or money; and the nation grows so much richer, as the balance of that account amounts to.

BALANCE of a Clock, or Watch, is that part which regulates the beats. See CLOCK-Making.

BALANCE-Fish. See SQUALUS, Ichthyology Index.