When you have thus marked the degrees on the stalk of the instrument, transfer them to the paper with the help of the compasses. The scale being completed, replace it in the tube of the hydrometer, where it must be fixed; in so doing, take care to make the degrees on the scale coincide precisely with those marked on the stalk.
You can thus procure hydrometers for alcohol, acids, salts, &c. which are instruments that indicate the proportion of alcohol, acid, salt, &c. contained in a given mass of water.
But if it were necessary to plunge the hydrometer in a hundred different solutions in order to produce the scale, it is easy to conceive that that would be extremely troublesome, especially for hydrometers which are employed in commerce, and which do not need to be so extremely accurate. When the density of the mixtures or solutions is a mean between those of the substances which enter into them, you may content yourself with marking the zero and one other fixed point, (a and b, [pl. 4], fig. 20.) Then, as the stalk of the hydrometer is evidently of equal diameter in all its extent, you can divide the space which separates the two fixed points into a certain number of equal parts. One of these, being taken for unity, represents a particular quantity of the substance which you have added to a determined weight of distilled water. By means of this unity you can carry the scale up and down the stalk of the instrument. It is thus, that, to obtain a Baumé’s hydrometer, after having obtained the zero by immersion in distilled water, you plunge the instrument into a solution containing a hundred parts of water and fifteen of common salt, to have the 15th degree, or containing a hundred water and thirty salt, to have the 30th degree. Upon dividing the interval into fifteen or thirty equal parts, according as you have employed one or the other solution, you obtain the value of the degree, which you can carry upwards or downwards as far as you wish.
Among the substances for which hydrometers are required in commerce, are some which it is impossible to obtain free from water—such are alcohol, the acids, &c. In this case it is necessary to employ the substances in their purest state, and deprived of as much water as possible.
The employment of hydrometers is very extensive: they are used to estimate the strength of lyes, of soap solutions, of wines, milk, &c. There is, in short, no branch of commerce in which these instruments are not required for the purpose of ascertaining the goodness of the articles which are bought and sold. The employment of hydrometers would be still more general, if they could be made to give immediately the absolute specific gravity of the liquids into which they might be plunged, the specific gravity of water being considered as unity. It is possible to graduate a thermometer of this description by proceeding as follows:—
Make choice of a hydrometer of which the exterior part of the stalk is very regular. Introduce the band of paper on which the scale is to be written, and then ballast the instrument. Make a mark where the surface of the distilled water touches the stalk. Remove the hydrometer from the water, wipe it perfectly dry, and weigh it very accurately with a sensible balance. Then pour into it a quantity of mercury equal to its own weight; plunge it again into the water, and again mark the point where the stalk touches the surface of the water. Pour the mercury out of the instrument, transfer the two marks to the scale, and divide this fixed distance into fifty equal parts. Having by this operation obtained the value of the degree, you carry it upwards and downwards, to augment the scale. If you take the first point near the reservoir, the hydrometer will be proper to indicate the density of liquids which are heavier than water; if you take it towards the middle of the tube, the contrary will be the case.
If you destine the hydrometer for liquids much heavier than water—such as acids, for example—you might, after having determined the first point, add to the original ballast as much mercury as is equal to the weight of the whole instrument; then the point where the stalk would touch the surface of the water, and which would be represented by 100, would be very high, and the second point, which would be found below, would be represented by 200. On dividing the space into a hundred equal parts, you would have the value of the degree, which could be carried up and down for the extension of the scale.
The specific gravities being in the inverse ratio of the volumes plunged into the liquid, the numbers of the scale which mark the specific gravities diminish from below; so that, on marking the lowest point 100, you have, on proceeding upwards, the successive degrees 0·99, 0·98, 0·97, 0·96, &c.
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.