The annexed figure represents a balance beam, invented by Mr. J. H. Patten, Rhode Island, United States, for the purpose of taking the specific gravities of different bodies, and for the accurate weighing of minute quantities. The manner of using the instrument, it will be seen, is similar to that of Lukin's balance, just described. The beam a b c is made of steel sufficiently strong, but light. The dish is suspended at a; the beam itself upon an axis at b; at c is the milled head of a long screw, which is fitted with a shoulder and axis, and goes through the slide e that traverses upon b c, and carries the weight d. Now, suppose it required to obtain ten grains, place that weight in the dish f, and screw back the weight d until it exactly counterbalances it. If the weight be now removed, and a quantity of the substance to be weighed be substituted, until the index points to where it did at first, there will then be very nearly the exact weight, differing only by the amount of the friction of the instrument. This beam may be used as a steelyard, by screwing the weight d to any number marked upon the scale ; and should a greater quantity be required than that marked in the first line, another weight, double that of d, may be substituted. The ancient balance was the staters, or steelyard, in which the arms are of unequal length, and one movable weight is used, placed at different distances from the centre of motion, or fulcrum. The annexed figure reoresents the common steelyard, in which c is the fulcrum, or centre; c 6 the longer arm, and c a the shorter. e is the article to be weighed, suspended to the shorter arm, and d the constant weight. Now, if the shorter arm, by its additional thickness, be a counterpoise to the longer, so that the beam, when un loaded, may hang in a horizontal position, it is manifest, that equal weight', hung at equal distances from the centre, will balance each other; but if one of the weiights be removed further from the centre, that side will preponderate. From this, it appears that a large weight e suspended at 6, may be counterpoised by a small one suspended at d. If the distance between c and d be nine times greater than that between c and e, a weight of 10 lbs. at d will counterbalance one of 90 lbs. at e. To prevent the necessity for calculation, the longer arm is graduated, so that the exact weight may be known by inspection.
The Danish Balance is also a steelyard, but in this the weight is fixed at one end, the article to be weighed at the other, and the fulcrum, or support, movable between them. In the annexed cut, b represents the standard weight, and a the hook, to which the article whose weight is required, may be sus pended, and d is the movable.fulcrum.
If a b were supposed a perfectly straight rod without weight, the gra dations on it should be at equal dis tances; but as this cannot be the case in practice, a different arrange ment is required. If c be the centre of gravity of the beam, and the fulcrum be placed at this point, it is clear that the beam will be supported in an hori zontal position ; but if a weight be appended to the hook a, the centre of gravity, which in all cases must be supported, will be removed to d, for example, and, consequently, the fulcrum must be moved to the same point. In this case, there is not only a difference in the leverage, or length of the arms, but there is the weight of the portion c d taken from one side and added to the other. The best method of graduating this instrument is by experiment,—by applying known quantities at the point a, and marking the place of the fulcrum d when an equilibrium takes place.
The Chinese Balance is a steelyard, somewhat different from the Roman staters. It is much used by the Eastern merchants in weighing gems and precious metals. The beam is a small rod of wood or ivory, about a foot in length. Upon this there are three lines of measure, made of delicate silver studded work. The scales commence at the end of the beam, whence the first extends to 8 inches; the second to 64 ; and the third to 84. The first indicates
European weight, and the other two Chinese. At the other end of the beam a scale is suspended; and at three several distances from this end are fastened so many fine strings, forming so many different points of suspension. The distance of the first point from the end is c of an inch; the second ; and the third . When the instrument is used, it is hung up by one of the strings, and a sealed weight of about 14 oz. is hung upon some one of the divisions of the rule, as to counterbalance the weight of the article, which is indicated by the graduations of the scale.
The Bent Lever Balance is represented in the annexed figure, in which a c b is a bent lever, moving on the centre c as its fulcrum, or axis, of motion. To the shorter arm of the lever at b, a scale-pan e is appended, while the other arm has a heavy weight affixed to its other extremity a, which passes over the quadrantal arch f g. The substance to be weighed being placed in the scale e, the end a will indicate the weight by the height to which it rises on the graduated arch. A little attention to the diagram will show that, as the end b descends, the other extremity a ascends, and, at the same time, removes to a greater distance, from a vertical line passing through the centre of motion. In the present posi tion of the balance, the effective length of the arm c b, is k i, and of the arm c a, is k d. Now, as these are of equal lengths, the weight a (omitting the weight of the lever itself) will be equal to that of the substance placed in the scale. But as the weight approaches the point g, the effective length of a c will be represented by k h, and the weight a will therefore act with as much more power, as the length of k h exceeds that of k d. If the point continued at the same distance from the vertical line, passing through c, the efficacy of the weight would, at any point in the arch, be proportional to the length of a per pendicular drawn from that point to the vertical line ; but as the distance of b is constantly varying, we can only state, generally, that the divisions will be nearer together as we approach the upper part of the scale.
Payne's Weighing Machine is of the steelyard kind ; the longer arm is divided by lines denoting the various weights, as usual ; but, instead of the weights being suspended by hooks immediately on the beam, they are attached to a long case, or box, which slides with some friction along the beam. Beneath one end of this sliding box is a large hook, to which is suspended the heavy weight, which is used to measure the larger quantities, as hundred weights, and quar ters, which are denoted by the divided lines on the beam, as the sliding box is drawn over it. To measure the smaller quantities, as pounds and ounces, there is a light scale of parts fixed to the top of the sliding box, to which a hook and weight are hung, which are applied in the same manner as the common steel yard. In the preceding engraving we have given a view of the whole arrange ment, the longer arm of the beam being somewhat shortened to save room. In this representation, a a is the beam ; o is the fulcrum ; d a long rectangular loop through which the arm a a passes, and which serves to support it when not in use, or to limit its vibrations when employed in weighing ; e is the sliding box, with its graduated scale, for the minuter quantities, which are to be ascer tained by the smaller weight g ; f the larger weight, which may be secured at pleasure, at any point, by means of a thumb-screw above, half a turn of which fixes the slide against the beam, while the more minute quantities are being taken. The goods are placed in the scale h, which may then be raised from the ground by turning the handles k k, which causes the screw i to enter the nut above. Machines on this principle are made of all sixes, to weigh either tons or ounces.