We think the description above given will be sufficiently intelligible without a representation of this instrument. An account of its application to the determination of specific gravities will be found in vol. iii. of the Philosophical Magazine. _The Chinese Steelyard._ This instrument is used in China and the East Indies for weighing gems, precious metals, &c. The beam is a small rod of ivory, about a foot in length. Upon this are three lines of divisions, marked by fine silver studs, all beginning from the end of the beam, whence the first is extended 8 inches, the second 6-1/2, and the third 8-1/2. The first is European weight, and the other two Chinese. At the other end of the beam hangs a round scale, and at three several distances from this end are holes, through which pass so many fine strings, serving as different points of suspension. The first distance makes 1-3/5 inches, the second 3-1/5, or double the former, and the third 4-4/5, or triple the same. The instrument, when used, is held by one of the strings, and a sealed weight of about 1-1/4 oz. troy, is slid upon the beam until an equilibrium is produced; the weight of the body is then indicated by the graduated scale above mentioned. _The Danish Balance._ The Danish balance is a straight bar or lever, having a heavy weight fixed to one end, and a hook or scale-pan to receive the substance, the weight of which is to be determined, suspended from the other end. The fulcrum is moveable, and is made to slide upon the bar, till the beam rests in a horizontal position, when the place of the fulcrum indicates the weight required. In order to construct a balance of this kind, let the distance of the centre of gravity from that point to which the substance to be weighed is suspended be found by experiment, when the beam is unloaded. Multiply this distance by the weight of the whole apparatus, and divide the product by the weight of the apparatus increased by the weight of the body. This will give the distance from the point of suspension, at which the fulcrum being placed, the whole will be in equilibrio: for example, supposing the distance of the centre of gravity from the point of suspension to be 10 inches, and the weight of the whole apparatus to be ten pounds; suppose, also, it were required to mark the divisions which should indicate weights of one, two, or three pounds, &c. First, for the place of the division indicating one pound we have (10 × 10)/(10 + 1) = 100/(10 + 1) = 9-1/11 inches, the place of the division marking one pound. For two pounds we have 100/(10 + 2) = 8-1/3 inches, the place of the division indicating two pounds; and for three pounds 100/(10 + 3) = 7-9/13 inches for the place of the division indicating three pounds, and so on.