But it is still more simple to introduce a drop of mercury into the tube, so as to form a little cylinder, and then to mark the two extremities of the cylinder. If it were possible to push the drop of mercury from one end of the tube to the other, in such a manner as to make it coincide, at every removal, with the last mark, it would be very easy to divide the tube accurately; but as it is very difficult, not to say impossible, to attain this precision of result in moving the column of mercury, you must endeavour to approach exactness as nigh as may be. You measure, every time you move the mercury, the length of the cylinder it produces, and carry this length to the last mark, presuming the small space which is found between the mark and the commencement of the column to be fairly represented by the same space after the column. You thus obtain a series of small and corresponding capacities.
Graduation of Gas Jars, Test Tubes, &c.—If the tube is regular in the bore, close one end, either by sealing it at the lamp, or by inserting a cork, and pour into the interior two or three small and equal portions of mercury, in order to have an opportunity of observing the irregularities produced by the sealed part. Take care to mark, with a writing diamond, the height of the mercury, after the addition of each portion. When equal portions of mercury are perceived to fill equal spaces, take with the compass the length of the last portion, and mark it successively along the side of the tube, where you must previously trace a line parallel to its axis.
For tubes which are irregular in the bore, and where equal lengths indicate unequal capacities, it is necessary to continue the graduation in the same manner that you commenced it—that is to say, to fill the tubes by adding successively many small and equal portions of mercury, and marking the height of the metallic column after every addition. These divisions will of course represent parts of an ounce or of a cubic inch according to the measure which you make use of. When you have thus traced on the tube a certain number of equal parts, you can, by means of the compasses, divide each of them into two other parts of equal length. The first divisions being very close to one another, the small portion of tube between every two may be considered without much risk of error as being sensibly of equal diameter in its whole extent.
When the tube which you desire to graduate is long and has thin sides, it would be difficult to fill it with mercury without running the risk of seeing it break under the weight of the metal. In this case, you must use water instead of mercury.
Bell-glasses of large dimensions are graduated by filling them with water, placing them in an inverted position on a smooth and horizontal surface, which is slightly covered with water, and passing under them a series of equal measures of air. But it is then necessary to operate constantly at the same temperature and under the same atmospheric pressure, because air is very elastic and capable of being greatly expanded.
In all cases, tubes, bell-glasses, &c. ought to be held in a position perfectly vertical. The most convenient measure is a dropping-tube, on the stalk of which a mark has been made, or a small piece of tube, sealed at one end, and ground flat at the other; the latter can be accurately closed by a plate of glass.
The marks which are traced on tubes being generally very close to one another, you facilitate the reading of the scale by giving a greater length to those marks which represent every fifth division, and by writing the figures merely to every tenth division. See [pl. 4], fig. 8. The number of divisions is somewhat arbitrary; nevertheless, 100, 120, 360, 1000, are divisions which, in practice, offer most advantages.
Graduation of Hydrometers.—Cut a band of paper on which the graduation of the instrument can be traced, and let fall upon it a little drop of sealing-wax; then roll the paper upon a little glass tube, and introduce it into the stalk of the hydrometer. The instrument is afterwards to be plunged into distilled water, which is carefully kept at the temperature of 40° F. above zero. Give the instrument sufficient ballast to make it sink till the point (a, [pl. 4], fig. 20,) which you desire to make to represent the density of water, touches the surface of the water. Mark this point with much precision; it is the zero of the instrument. The other degrees are taken by plunging the hydrometer into distilled water to which you have added 1, 2, 3, 4, 5, &c. tenths, or 1, 2, 3, 4, 5, &c. hundredths, of the substance for which you wish to construct the hydrometer, according as you desire the scale to indicate tenths or hundredths.