The hydrometers with two, three, and four branches, are graduated by having their tubes divided into a hundred or a thousand equal parts. The divisions on each branch must correspond with those on the other branches. * * * * * GRADUATION OF BAROMETERS.--The graduation of this instrument consists in dividing a piece of metal, wood, or ivory, into inches and parts of inches. The divided rod is then employed to measure the height of the mercury in the tube. As the rule is moveable, the operation presents no sort of difficulty: all that is necessary is to make the zero of the scale coincide with the inferior level of the mercury; the point which corresponds with the superior level of the mercury, seen in the tube, indicates the height of the barometric column. It is in this manner that the cistern barometer is graduated. But if the barometer is one of those in which the surface of the mercury is variable, such as the barometer of Gay-Lussac, it is necessary to have recourse to a different process of graduation. If the two branches of the instrument are very regular, and of equal diameter, you first measure with precision the height of the column of mercury, then divide it in the middle, and fix the scale, which must be graduated in such a manner that the mark of fifteen inches corresponds exactly with the middle point. This mode of graduation serves to indicate merely the apparent height of the barometric column. If you desire that the scale should immediately indicate the real height, you must fix the zero at the middle of the column, and then double the figure which marks each degree. When you do not wish to write the real height, you make two divisions, of which one proceeds upwards, the other downwards. You do not, in this case, double the value of each division, but in observations made with such a barometer scale you add the degree marked by the two surfaces, in order to find the real height. It is in an analogous manner that you graduate the gauges or short barometers which are employed to measure the density of air under the recipient of the air-pump. You take the height of the mercury in the gauge, and fix at the middle of the column the zero of a double scale, of which one division proceeds upwards, the other downwards; or, instead of this, if you choose to have only one scale, and that an ascending scale, you double the value of every degree. The zero of the barometric scale can be fixed below the inferior surface of the mercury; but then, to have the real height, it is necessary to measure precisely the height of the mercury in the two branches of the instrument, and to deduct the smaller from the larger.