Balance, an instrument intended to measure different amounts or masses of matter by the determination of their weight, using as standards of comparison certain fixed units, as the gramme, the pound, the ton, etc. The instrument is founded on the law that gravitation acts in a direct ratio to the mass, and on the mechanical principle that when a solid body is suspended on one point, the centre of gravity will place itself always perpendicularly under that point. If therefore a beam, ab, fig. 1, is supported in the middle at c, and movable around this point, its centre of gravity, s, will place itself under the point c; and if disturbed from that position, this centre will oscillate like a pendulum, and the beam will finally come to rest only with the centre of gravity in the perpendicular passing through the point of support. It is evident that when the distances from a to c and from b to c are equal, the two sides of the beam equal, and the whole made of homogeneous material, the horizontal position will be arrived at, and also when at a and b equal weights pp are suspended; the gravity of such scales and weights must be considered concentrated in the points of suspension a and b, and their common centre of gravity will be either in, under, or above the point of support, according as the line ab uniting them passes through, under, or above the support c.

But suppose we place an additional weight r in one of the scales, then the common centre of gravity of the weights in the scales will be shifted toward the side of that additional weight. Suppose it to be in rf, then the centre of gravity of the whole balance will be in the line ds, uniting the centre of gravity d of the weights with that of the balance s; if then it is somewhere at m, it is evident that the balance can no longer maintain the horizontal position, but will only come to rest when m is under c, or the line cm has attained a perpendicular position. It is evident that the angle which the beam in this case makes with a horizontal line is equal to the angle scm. If the centre of gravity is in the point of support, the balance is indifferent; that is, it will, when charged with equal weights, remain at rest in any position. And if the centre of gravity is above the point of support, we have a case of so-called unstable equilibrium; the balance will with equal ease tip over to the right or left, and the beam can never be brought into the horizontal position.

In either case the balance is useless, and it follows from this that the centre of gravity must be under the point of support, and the sensitiveness of the instrument depends to a great extent on the distance between these two points. This derived degree of sensitiveness varies with the purposes for which balances are to be used. The most delicate balances are those used for physical and chemical investigation; and in order to secure the greatest possible degree of sensitiveness the conditions are as follows:

Common Balance.

1. The centre of gravity of the beam must lie as near as possible under the point of suspension; it is evident that when this centre of gravity s is raised, the point m will be raised also, and the angle scm will become larger, which results in a greater deflection of the beam in case there is no proper equilibrium. Fine balances are provided with an upright rod above their point of suspension, on which a small weight may be screwed up or down, in order to raise or lower the centre of gravity, and so to increase or diminish the delicacy of the instrument. In tig. 1 this rod is represented below, which is only admissible when no great degree of sensitiveness is required, as in this case the centre of gravity is lowered too much.

2. The beam should be as long as compatible with strength. As the distance cd becomes greater in proportion to the length of the arms, any difference in the two weights with which the balance is charged will be the more perceptible the longer the arms are. 3. The beam should also be as light as compatible with strength; the smaller the weight of the balance itself, the greater the influence of minute differences in the load will be to shift the position of the point d from the centre. Therefore the beams of chemical balances are made like an elongated frame, with large openings between, on the same principle as the walking beams of steam engines are constructed. 4. The points of suspension of the two scales must be such that the line uniting them passes exactly through the point of support; if this line passes under that point, the sensitiveness of the balance will diminish too much when the load is increased. This takes place in any case to a small degree, as no beam is so perfectly inelastic that a slight flexion will not take place under the maximum load. 5. The distances of the points of suspension of the scales a and b from the centre c should be perfectly equal; this is best verified by changing the weights in the two scales, when if the equilibrium remains unchanged their distances are equal.

Some balances have screw arrangements to correct small differences in this respect. In fig. 2 a chemical balance is represented as used, in a glass case, which serves to protect it not only from dust, but also against air currents which might prevent a truly sensitive balance from ever coming to rest, and thus make correct weighings impossible. The turning point of the beam, in order to reduce the friction to the least amount, is a knife-edge or triangular prism of hardened steel passing at right angles through the beam, and resting when in use upon polished plates of agate (one each side of the beam), which are set exactly upon the same horizontal plane. This knife-edge is polished and brought to an angle of 30°. The points of suspension are also knife-edtres, one set across each extremity of the beam. Great care is required that the line connecting them shall be precisely at right angles with the line passing through the centres of motion and of gravity. The index or pointer is sometimes a long needle, its line passing through the centre, and extending either above or below the beam, or it is a needle extended from each extremity of the beam. In either case it vibrates with the motion of the beam over a graduated arc, and rests upon the zero point when the beam is horizontal.

The degrees upon each side of the zero of the scale indicate, as the needle oscillates past them, the intermediate point at which this will stop, thus rendering it unnecessary to wait its coming to rest. In order to save the knife-edges from wear, the beam is made, in delicate balances, to rest when not in use upon a forked arm, and the pans upon the floor of the case in which the instrument stands. The agate surfaces, being lifted by means of a cam or lever, raise the beam off its supports and put it in action; or the supports, by a similar contrivance, are let down from the beam, leaving it to rest upon the agate; the pans in the latter case must always remain suspended. - However perfectly a balance may be made, there is always great care to be exercised in its use. Errors are easily made in the estimation of the nice quantities it is used to determine. The sources of some are avoided by a simple and ingenious method of weighing suggested by Borda. The body to be weighed is exactly counterpoised, and then taken out of the pan and replaced by known weights, added till they produce the same effect. A false balance must by this method produce correct results.

The weights employed for delicate balances are either troy grains, one of each of the units, one of each of the tens, and the same of the hundreds and thousands, as also of the tenths, hundredths, and thousandths of a grain; or they are the French gramme weights, with their decimal parts. The latter are the most commonly used in chemical assays and analyses. The larger weights are of brass, the smaller of platinum, and these are always handled by means of a pair of forceps. The beam of the balance is, according to the method introduced by Berzelius, frequently marked by divisional lines into tenths, and one of the small weights, as a tenth or hundredth of a grain, or a milligramme, is bent into the form of a hook, so that it may be moved along the beam to any one of these lines to bring the balance to exact equilibrium. By this arrangement the picking up and trying one weight after another is avoided, and the proportional part of the weight used is that indicated by the decimal number upon the beam at which it rests to produce equilibrium. The best materials for a balance are those which combine strength with lightness, and are least liable to be affected by the atmosphere and acid vapors.

Brass, platinum, or steel is used for the beam; but probably aluminum will prove to be better adapted for this purpose than either. The pans are commonly of platinum, made very thin, and suspended by fine platinum wires. The support is a brass pillar secured to the floor of the glass case in which the instrument is kept Doors are provided in front and at the sides, by which access is had to the instrument; but these are commonly kept closed, and are always shut in delicate weighing, that the beam shall not be disturbed by currents of air. So delicate are the best balances, that when lightly loaded and left to-vibrate, they may be affected by the approach of a person to one side of the glass case, the warmth radiated from the body causing the nearest arm of the beam to be slightly expanded and elongated, so as to sensibly preponderate. The degree of sensibility is estimated by the smallest weight in proportion to the load that will cause the beam to be deflected from a horizontal line. It is said that a balance is in possession of Bowdoin college, Maine, which, with a charge of 10 kilogrammes in each scale, is sensitive to 1/10 of a milligramme.

Becker and Sons of New York made the balance; and they make ordinary chemical balances which with one kilogramme in each scale are sensitive to one tenth of a milligramme; their small balances now in use in the assay office, New York, show a difference in load of less than 1/100 part of a milligramme. - The torsion balance, invented by Coulomb to measure minute electrical forces, is still more 'delicate than the best beam balance. It consists of a brass wire, hung by one end and stretched by a light weight, carrying at its lower end a horizontal needle. Any force applied to one end of this needle, tending to rotate it horizontally, will be measured by the angle through which it causes the needle to move; that is, by the torsion of the wire. (See Elec-trometer.) - The steelyard, the Roman statera, is one of the forms of the balance, the two arms being of unequal length, the body to be weighed being suspended in a pan or otherwise from the short arm, and the counterpoise, which is a constant weight, being slid along the longer arm until equilibrium is established.

As this occurs when the weight on one side multi-plied by its distance from the fulcrum is equal to the weight on the other multiplied by its distance from the fulcrum, and as on one side the weight is constant, and on the other the distance from the centre of motion, the unknown weight must be determined by the distance of the constant weight from the centre. - The Danish balance differs from the common steelyard in having the counterpoise fixed at one end, and the fulcrum being slid along the graduated beam. The graduation commences at a [joint near the counterpoise, at which the beam with the pan suspended at the other end is in equilibrium, and the numbers increase toward the pan. A balance called the bent lever is employed to some extent for purposes not requiring extreme accuracy. The pan is attached to one end of the beam and the other carries a constant weight. From the bent form of the lever this weight is raised to a height varying with the weight placed in the scale pan. A pointer attached to the constant weight and moving along a graduated arc indicates by the number at which it stops the weight of the body in the scale pan.

Its indications are the least to be depended upon when the constant weight approaches to the horizontal or vertical line passing through the centre of motion. The scales generally used in the United States for weighing loaded wagons and canal boats are modifications of the steelyard, wherein the weight of these ponderous bodies is divided by means of levers, and a known fraction of it sustained by one end of a beam, the other end of which is graduated for a moving weight. Modern modifications of the steelyard contain a pan hung at the end of the arm to receive larger weights, while the sliding weight is used only to balance the fractional parts. - Spring balances are popular instruments, and consist of a helix of wire enclosed in a cylinder. The body to be weighed is suspended to a wire passing up through the centre of the helix and fastened to the upper coil, which carries a pointer down a narrow slit in the cylinder, thus indicating the weight on the graduated sides of the cylinder.