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(E. A. M.)
HYDROMETER (Gr. ὕδωρ, water, and μέτρον, a measure), an
instrument for determining the density of bodies, generally of
fluids, but in some cases of solids. When a body floats in a
fluid under the action of gravity, the weight of the body is equal
to that of the fluid which it displaces (see Hydromechanics). It
is upon this principle that the hydrometer is constructed, and it
obviously admits of two modes of application in the case of fluids:
either we may compare the weights of floating bodies which are
capable of displacing the same volume of different fluids, or we
may compare the volumes of the different fluids which are displaced
by the same weight. In the latter case, the densities of
the fluids will be inversely proportional to the volumes thus
displaced.
The hydrometer is said by Synesius Cyreneus in his fifth letter to have been invented by Hypatia at Alexandria,[1] but appears to have been neglected until it was reinvented by Robert Boyle, whose “New Essay Instrument,” as described in the Phil. Trans. for June 1675, differs in no essential particular from Nicholson’s hydrometer. This instrument was devised for the purpose of detecting counterfeit coin, especially guineas and half-guineas. In the first section of the paper (Phil. Trans. No. 115, p. 329) the author refers to a glass instrument exhibited by himself many years before, and “consisting of a bubble furnished with a long and slender stem, which was to be put into several liquors, to compare and estimate their specific gravities.” This seems to be the first reference to the hydrometer in modern times.
In fig. 1 C represents the instrument used for guineas, the circular plates A representing plates of lead, which are used as ballast when lighter coins than guineas are examined. B represents “a small glass instrument for estimating the specific gravities of liquors,” an account of which was promised by Boyle in the following number of the Phil. Trans., but did not appear.
|
Fig. 1.—Boyle’s New |
The instrument represented at B (fig. 1), which is copied from Robert Boyle’s sketch in the Phil. Trans. for 1675, is generally known as the common hydrometer. It is usually made of glass, the lower bulb being loaded with mercury or small shot which serves as ballast, causing the instrument to float with the stem vertical. The quantity of mercury or shot inserted depends upon the density of the liquids for which the hydrometer is to be employed, it being essential that the whole of the bulb should be immersed in the heaviest liquid for which the instrument is used, while the length and diameter of the stem must be such that the hydrometer will float in the lightest liquid for which it is required. The stem is usually divided into a number of equal parts, the divisions of the scale being varied in different instruments, according to the purposes for which they are employed.
Let V denote the volume of the instrument immersed (i.e. of liquid displaced) when the surface of the liquid in which the hydrometer floats coincides with the lowest division of the scale, A the area of the transverse section of the stem, l the length of a scale division, n the number of divisions on the stem, and W the weight of the instrument. Suppose the successive divisions of the scale to be numbered 0, 1, 2 . . . n starting with the lowest, and let w0, W1, w2 . . . wn be the weights of unit volume of the liquids in which the hydrometer sinks to the divisions 0, 1, 2 . . . n respectively. Then, by the principle of Archimedes,
| W = Vw0; or w0 = W/V. Also |
| W = (V + lA) w1; or w1 = W/(V + lA), |
| wp = W/(V + plA), and |
| wn = W/(V + nlA), |
or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.
If V = NlA then N expresses the ratio of the volume of the instrument up to the zero of the scale to that of one of the scale-divisions. If we suppose the lower part of the instrument replaced by a uniform bar of the same sectional area as the stem and of volume V, the indications of the instrument will be in no respect altered, and the bottom of the bar will be at a distance of N scale-divisions below the zero of the scale.
In this case we have wp = W/(N + p)lA; or the density of the liquid varies inversely as N + p, that is, as the whole number of scale-divisions between the bottom of the tube and the plane of flotation.
If we wish the successive divisions of the scale to correspond to equal increments in the density of the corresponding liquids, then the volumes of the instrument, measured up to the successive divisions of the scale, must form a series in harmonical progression, the lengths of the divisions increasing as we go up the stem.
The greatest density of the liquid for which the instrument described above can be employed is W/V, while the least density is W/(V + nlA), or W/(V + v), where v represents the volume of the stem between the extreme divisions of the scale. Now, by increasing v, leaving W and V unchanged, we may increase the range of the instrument indefinitely. But it is clear that if we increase A, the sectional area of the stem, we shall diminish l, the length of a scale-division corresponding to a given variation of density, and thereby proportionately diminish the sensibility of the instrument, while diminishing the section A will increase l and proportionately increase the sensibility, but will diminish the range over which the instrument can be employed, unless we increase the length of the stem in the inverse ratio of the sectional area. Hence, to obtain great sensibility along with a considerable range, we require very long slender stems, and to these two objections apply in addition to the question of portability; for, in the first place, an instrument with a very long stem requires a very deep vessel of liquid for its complete immersion, and, in the second place, when most of the stem is above
- ↑ In Nicholson’s Journal, iii. 89, Citizen Eusebe Salverte calls attention to the poem “De Ponderibus et Mensuris” generally ascribed to Rhemnius Fannius Palaemon, and consequently 300 years older than Hypatia, in which the hydrometer is described and attributed to Archimedes.
