HYDROMETER 537 the extreme divisions of the scale. Now, by increasing v, leaving W and V unchanged, we may increase the range of the instrument in definitely. But it is clear that if we increase A, the sectional area of the stem, we shall diminish I, the length of a scale-division corre sponding to a given variation of density, and thereby proportionately diminish the sensibility of the instrument, while diminishing the section A will increase I and proportionately increase the sensibility, but will diminish the range over which the instrument can be em ployed, 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 porta bility ; for, in the first place, an instrument with a very long stem re quires a very deep vessel of liquid for its complete immersion, and, in the second place, when most of the stem is above tlie plane of flotation, this diminishes or may destroy the stability of the instru ment when floating. The various devices which have been adopted to overcome this difficulty will be described in the account given of the several hydrometers which have been hitherto generally em ployed. The plan commonly adopted to obviate the necessity of incon veniently long stems is to construct a number of hydrometers as nearly alike as may be, but to load them differently, so that the scale- divisions at the bottom of the stem of one hydrometer just overlap those at the top of the stem of the preceding. By this means a set of six hydrometers, each having a stem rather more than five inches long, will lie equivalent to a single hydrometer with a stem of thirty inches. But, instead of employing a number of instruments differ ing only in the weights with which they are loaded, we may employ the same instrument, and alter its weight either by adding mercury or shot to the interior (if it can be opened) or by attaching weights to the exterior. These two operations are not quite equivalent, since a weight added to the interior does not affect the volume of liquid displaced when the instrument is immersed up to a given division of the scale, while the addition of weights to the exterior increases the displacement. This difficulty may be met, as in Keene s hydro meter, by having all the weights of precisely the same volume but of different masses, and never using the instrument except with one of these weights attached. The first hydrometer intended for the determination of the densities of liquids, and furnished with a set of weights to be attached when necessary, was that constructed by Mr Clarke, and described by Dresaguliers in the Philo sophical Transactions for March and April 1730, No. 413, p. 278. The following is Desaguliers s account of the instrument (fig. 2) : "After having made several fruitless trials with ivory, because it imbibes spirituous liquors, and thereby alters its gravity, he (Mi- Clarke) at last made a copper hydrometer, re presented in fig. 2, having a brass wire of about 1 inch thick going through, and soldered into the copper ball B6. The upper part of this wire is filed flat on one side, for the stem of the hy drometer, with a mark at in, to which it sinks exactly in proof spirits. There are two other marks, A and B, at top and bottom of the stem, to show whether the liquor be ^th above proof (as when it sinks to A), or ^th under proof (as when it emerges to B), when a brass weight such as C has been screwed on to the bottom at c. There are a great many such weights, of different sizes, and marked to be screwed on instead of C, for liquors that differ more than T th from proof, so as to serve for the specific gravities in all such proportions as relate to the mixture of spirituous liquors, in all the variety made use of in trade. There are also other balls for showing the specific gravities quite to common water, which make the instru ment perfect in its kind. " Clarke s hydrometer, as afterwards con structed for the purposes of the excise, was provided with thirty-two weights to adapt it to spirits of different specific gravities, and eleven smaller weights, or " weather weights" as they were called, which were attached to the instrument in order to correct for variations of temperature. The weights were adjusted for successive intervals of 5 Fahr,, but for degrees intermediate between these no additional correction was applied. The correction for temperature thus afforded was not sufficiently accurate for excise purposes, and Mr Speer in his essay on the hydrometer (Tilloch s Phil. May., vol. xiv.) mentions cases in which this imperfect coinpeusa- Fifi. 2. Clarke s Hydrometer. tion led to the extra duty payable upon spirits which were more than 10 per cent, over proof being demanded on, spirits which were purposely diluted to below 10 per cent, over proof in order to avoid the charge. Desaguliers himself constructed a hydrometer of the ordinary type for comparing the specific gravities of different kinds of water (Desaguliers s Experimental Philo sophy, vol. ii. p. 234). In order to give great sensibility to the instrument, the large glass ball was made nearly 3 inches in diameter, while the stand consisted of a wire 10 inches in length and only -^ inch in diameter. The instru ment weighed 4000 grains, and the addition of a grain caused it to sink through an inch. By altering the quantity of shot in the small balls the instrument could be adapted for liquids other than water. To an instrument constructed for the same purpose, but on a still larger scale than that of Desaguliers, M. De parcieux added a small dish on the top of the stem for the reception of the weights necessary to sink the instru ment to a convenient depth. The effect of weights placed in such a dish or pan is of course the same as if they were placed within the bulb of the instrument, since they do not alter the volume of that part which is immersed. The first important improvement in the hydrometer after its reinvention by Boyle was introduced by Fahrenheit, who adopted the second mode of construction above referred to, arranging his instrument so as always to displace the same volume of liquid, its weight being varied accordingly. Instead of a scale, only a single mark is placed upon the stem, which is very slender, and bears at the top a small scale pan into which weights are placed until the instrument sinks to the mark upon its stem. The volume of the dis placed liquid being then always the same, its density will be proportional to the whole weight supported, that is, to the weight of the instrument together with the weights re quired to be placed in the scale pan. Nicholson s hydrometer (fig. 3) combines the character istics of Fahrenheit s hydrometer and of Boyle s essay in strument. 1 The following is the description given of it by Nicholson in the Manchester Memoirs, vol. ii. p. 374. "AA represents a small scale. It may be taken off at D. Diameter 1^ inch, weight 44 grains. " B a stem of hardened steel wire. Diameter T | inch. " E a hollow copper globe. Diameter 2^ inches. Weight with stem 369 grains. " FF a stirrup of wire screwed to the globe at C. " G a small scale, serving likewise as a counter poise. Diameter 1^ inch. Weight with stirrup 1634 grains. "The other dimensions maybe had from the drawing which is one-sixth of the linear mag nitude of the instrument itself. "In the construction, it is assumed that the upper scale shall constantly carry 1000 grains when the lower scale is empty, and the instrument sunk in distilled water at the temperature of 60 Fahrenheit to the middle of the wire or stem. The length of the stem is arbitrary, as is like- -,. . . wise the distance of the lower scale from the "? ;T surface of the globe. But, the length of the stem son s H > dr being settled, the lower scale may be made lighter, and, conse quently, the globe less, the greater its distance is taken from tin: surface of the globe ; and the contrary." In comparing the densities of different liquids, it is clear that this instrument is precisely equivalent to that of Fahrenheit, and must be employed in the same manner, weights being placed in the top scale only until the hydro meter sinks to the mark on the wire, when the specific gravity of the liquid will be proportional to the weight of the instrument together with the weights in the scale. In the subsequent portion of the paper above referred to 2 1 Nicholson s Journal, vol. i. p. Ill, footnote.
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