Page:Encyclopædia Britannica, Ninth Edition, v. 12.djvu/552

536 536 HYDKOMETER HYDROMETER. The object of the hydrometer is the determination of the density of bodies, generally of fluids, but some forms of the instrument are adapted to the determination of the density of solids. It is shown in the article HYDROMECHANICS that, 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. 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 displac ing the same volume of different fluids, or we may com pare the volumes of the different fluids which are displaced by the same weight. In the latter case, the densities of the fluids will bo inversely- proportional to the volumes thus displaced. Perhaps the simplest method of experimentally deter mining the densities of different liquids is afforded by the series of areometrical glass beads, or hollow balls, first proposed by Dr Wilson, professor of astronomy in the university of Glasgow. As subsequently improved by Mrs Lovi, these beads were constructed in sets, each bead in the set differing in density from its predecessor by 002 (of the density of water). Each bead is numbered according to its density, and in order to determine the specific gravity of a liquid it is only necessary to throw into it the set of beads, or so many of them as are known to include between their extremes the density of the liquid, when all the beads whose densities exceed that of the liquid will sink, while those whose densities are less than that of the liquid will float. If thers is a bead of exactly the same density as the liquid, it will rest in any position, provided it is com pletely immersed. Failing this, all that is immediately apparent is that the density is intermediate between that of the lightest bead that sinks and that of the heaviest that floats. For example, if all the beads numbered 1/466 and upwards sink, while those below 1 466 float, it is obvious tli.it the density of the liquid is intermediate between 1 464 and 1 4G6. In the case of most fluids the intervals may be divided approximately by slightly warm ing the liquid. Thus, if on heating the liquid 6 C. it is found that the bead 1 466 begins to sink, and on heating it still farther through 12C. (i.e., through 18C. altogether) the bead 1 468 begins to sink, then the density of the liquid is approximately 1-465. 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 &quot; New Essay Instrument,&quot; 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 counter feit 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 &quot; 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.&quot; 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 &quot; a sm?ll glass instrument for estimating the specific gravities of liquors,&quot; an account of which was 1 In Nicholson s Journal, vol. iii. p. 89, Citizen Eusebe Salverte calls attention to the poem &quot; De Ponderibus et Mensuris &quot; generally ascribed to Rhemnius Fannius Palsemon, and consequently 300 years older than Hypatia, in which the hydrometer is described, and attri buted to Archimedes. promised by Boyle in the following number of the Phil. Trans., but did not appear. 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 com mon hydrometer. It is usually made of glass, the lower bulb being loaded with mercury or small shot which serves as bal last, causing the instrument to float with the stem vertical. The quantity of mercury or shot inserted depends upon the den sity 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 hy drometer will float in the lightest liquid for which it is required. The stem is usually divided into a number of equal parts, the FIG. 1. Boyle s New Essay divisions of the scale being varied Instrument. 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 hydro meter floats coincides with the lowest division of the scale, A the area of the transverse section of the stem, I 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 iv , VJ&amp;gt; 1} w. 2. . . w n 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 or Also or So and or the densities of the several liquids vary inversely as the respec tive 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 = N7A then N expresses the ratio of the volume of the in strument 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- i divisions below the zero of the scale. In this case we have W W p -- I or the density of the liquid varies inversely as N +p, that is, as the i 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 de scribed above can be employed is, while the least density is W W &amp;gt;.= , or = -, where v represents the volume of the stem between,