# 1911 Encyclopædia Britannica/Hydrometer

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​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, 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 Essay Instrument.
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 w$_0$, W$_1$, 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 = Vw$_0$; or w$_0$ = W/V. Also
* W = (V + lA) w$_1$; or w$_1$ = W/(V + lA),
* w$_p$ = W/(V + plA), and
* w$_n$ = 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 w$_p$ = 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 ​the plane of flotation, the stability of the instrument when floating will be diminished or destroyed. 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 employed.
The plan commonly adopted to obviate the necessity of inconveniently 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 5 in. long, will be equivalent to a single hydrometer with a stem of 30 in. But, instead of employing a number of instruments differing 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 hydrometer, 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.
* Fig. 2.—Clarke’s Hydrometer.
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 (instrument-maker) and described by J. T. Desaguliers in the Philosophical 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 (Mr Clarke) at last made a copper hydrometer, represented in fig. 2, having a brass wire of about 1 in. thick going through, and soldered into the copper ball Bb. The upper part of this wire is filed flat on one side, for the stem of the hydrometer, with a mark at m, 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 1/10th above proof (as when it sinks to A), or 1/10th 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 1/10th 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 instrument perfect in its kind.”
Clarke’s hydrometer, as afterwards constructed 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° F., 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 William Speer in his essay on the hydrometer (Tilloch’s Phil. Mag., 1802, vol. xiv.) mentions cases in which this imperfect compensation led to the extra duty payable upon spirits which were more than 10% over proof being demanded on spirits which were purposely diluted to below 10% over proof in order to avoid the charge. Clarke’s hydrometer, however, remained the standard instrument for excise purposes from 1787 until it was displaced by that of Sikes.
Desaguliers himself constructed a hydrometer of the ordinary type for comparing the specific gravities of different kinds of water (Desaguliers’s Experimental Philosophy, ii. 234). In order to give great sensibility to the instrument, the large glass ball was made nearly 3 in. in diameter, while the stem consisted of a wire 10 in. in length and only 1/40in. in diameter. The instrument 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, A. Deparcieux added a small dish on the top of the stem for the reception of the weights necessary to sink the instrument 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.
* Fig. 3.—Nicholson’s Hydrometer.
The first important improvement in the hydrometer after its reinvention by Boyle was introduced by G. D. 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 displaced 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 required to be placed in the scale pan.
Nicholson’s hydrometer (fig. 3) combines the characteristics of Fahrenheit’s hydrometer and of Boyle’s essay instrument. The following is the description given of it by W. Nicholson in the Manchester Memoirs, ii. 374:—
“AA represents a small scale. It may be taken off at D. Diameter 11/2 in., weight 44 grains.
“B a stem of hardened steel wire. Diameter 1/100 in.
“E a hollow copper globe. Diameter 28/10 in. Weight with stem 369 grains.
“FF a stirrup of wire screwed to the globe at C.
“G a small scale, serving likewise as a counterpoise. Diameter 11/2 in. Weight with stirrup 1634 grains.
“The other dimensions may be had from the drawing, which is one-sixth of the linear magnitude 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° Fahr. to the middle of the wire or stem. The length of the stem is arbitrary, as is likewise the distance of the lower scale from the surface of the globe. But, the length of the stem being settled, the lower scale may be made lighter, and, consequently, the globe less, the greater its distance is taken from the 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 hydrometer 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, Nicholson explains how the instrument may be employed as a thermometer, since, fluids generally expanding more than the solids of which the instrument is constructed, the instrument will sink as the temperature rises.
To determine the density of solids heavier than water with this instrument, let the solid be placed in the upper scale pan, and let the weight now required to cause the instrument to sink in distilled water at standard temperature to the mark B be denoted by w, while W denotes the weight required when the solid is not present. Then W−w is the weight of the solid. Now let the solid be placed in the lower pan, care being taken that no bubbles of air remain attached to it, and let w$_1$ be the weight now required in the scale pan. This weight will exceed w in consequence of the water displaced by the solid, and the weight of the water thus displaced will be W$_1$−w, which is therefore the weight of a volume of water equal to that of the solid. Hence, since the weight of the solid itself is W−w, its density must be (W−w)/(w$_1$−w).
The above example illustrates how Nicholson’s or Fahrenheit’s hydrometer may be employed as a weighing machine for small weights.
In all hydrometers in which a part only of the instrument ​ is immersed, there is a liability to error in consequence of the surface tension, or capillary action, as it is frequently called, along the line of contact of the instrument and the surface of the liquid (see Capillary Action). This error diminishes as the diameter of the stem is reduced, but is sensible in the case of the thinnest stem which can be employed, and is the chief source of error in the employment of Nicholson’s hydrometer, which otherwise would be an instrument of extreme delicacy and precision. The following is Nicholson’s statement on this point:—
“One of the greatest difficulties which attends hydrostatical experiments arises from the attraction or repulsion that obtains at the surface of the water. After trying many experiments to obviate the irregularities arising from this cause, I find reason to prefer the simple one of carefully wiping the whole instrument, and especially the stem, with a clean cloth. The weights in the dish must not be esteemed accurate while there is either a cumulus or a cavity in the water round the stem.”
It is possible by applying a little oil to the upper part of the bulb of a common or of a Sikes’s hydrometer, and carefully placing it in pure water, to cause it to float with the upper part of the bulb and the whole of the stem emerging as indicated in fig. 4, when it ought properly to sink almost to the top of the stem, the surface tension of the water around the circumference of the circle of contact, AA′, providing the additional support required.
* Fig. 4.
The universal hydrometer of G. Atkins, described in the Phil. Mag. for 1808, xxxi. 254, is merely Nicholson’s hydrometer with the screw at C projecting through the collar into which it is screwed, and terminating in a sharp point above the cup G. To this point soft bodies lighter than water (which would float if placed in the cup) could be attached, and thus completely immersed. Atkins’s instrument was constructed so as to weigh 700 grains, and when immersed to the mark on the stem in distilled water at 60° F. it carried 300 grains in the upper dish. The hydrometer therefore displaced 1000 grains of distilled water at 60° F. and hence the specific gravity of any other liquid was at once indicated by adding 700 to the number of grains in the pan required to make the instrument sink to the mark on the stem. The small divisions on the scale corresponded to differences of 1/10th of a grain in the weight of the instrument.
The “Gravimeter,” constructed by Citizen Guyton and described in Nicholson’s Journal, 4to, i. 110, differs from Nicholson’s instrument in being constructed of glass, and having a cylindrical bulb about 21 centimetres in length and 22 millimetres in diameter. Its weight is so adjusted that an additional weight of 5 grammes must be placed in the upper pan to cause the instrument to sink to the mark on the stem in distilled water at the standard temperature. The instrument is provided with an additional piece, or “plongeur,” the weight of which exceeds 5 grammes by the weight of water which it displaces; that is to say, it is so constructed as to weigh 5 grammes in water, and consists of a glass envelope filled with mercury. It is clear that the effect of this “plongeur,” when placed in the lower pan, is exactly the same as that of the 5 gramme weight in the upper pan. Without the extra 5 grammes the instrument weighs about 20 grammes, and therefore floats in a liquid of specific gravity .8. Thus deprived of its additional weight it may be used for spirits. To use the instrument for liquids of much greater density than water additional weights must be placed in the upper pan, and the “plongeur” is then placed in the lower pan for the purpose of giving to the instrument the requisite stability.
Charles’s balance areometer is similar to Nicholson’s hydrometer, except that the lower basin admits of inversion, thus enabling the instrument to be employed for solids lighter than water, the inverted basin serving the same purpose as the pointed screw in Atkins’s modification of the instrument.
Adie’s sliding hydrometer is of the ordinary form, but can be adjusted for liquids of widely differing specific gravities by drawing out a sliding tube, thus changing the volume of the hydrometer while its weight remains constant.
The hydrometer of A. Baumé, which has been extensively used in France, consists of a common hydrometer graduated in the following manner. Certain fixed points were first determined upon the stem of the instrument. The first of these was found by immersing the hydrometer in pure water, and marking the stem at the level of the surface. This formed the zero of the scale. Fifteen standard solutions of pure common salt in water were then prepared, containing respectively 1, 2, 3, ... 15% (by weight) of dry salt. The hydrometer was plunged in these solutions in order, and the stem having been marked at the several surfaces, the degrees so obtained were numbered 1, 2, 3, ... 15. These degrees were, when necessary, repeated along the stem by the employment of a pair of compasses till 80 degrees were marked off. The instrument thus adapted to the determination of densities exceeding that of water was called the hydrometer for salts.
The hydrometer intended for densities less than that of water, or the hydrometer for spirits, is constructed on a similar principle. The instrument is so arranged that it floats in pure water with most of the stem above the surface. A solution containing 10% of pure salt is used to indicate the zero of the scale, and the point at which the instrument floats when immersed in distilled water at 10° R. (541/2° F.) is numbered 10. Equal divisions are then marked off upwards along the stem as far as the 50th degree.
The densities corresponding to the several degrees of Baumé’s hydrometer are given by Nicholson (Journal of Philosophy, i. 89) as follows:—
| Degrees. | Density. | Degrees. | Density. | Degrees. | Density. |
| 10 | 1.000 | 21 | .922 | 31 | .861 |
| 11 | .990 | 22 | .915 | 32 | .856 |
| 12 | .985 | 23 | .909 | 33 | .852 |
| 13 | .977 | 24 | .903 | 34 | .847 |
| 14 | .970 | 25 | .897 | 35 | .842 |
| 15 | .963 | 26 | .892 | 36 | .837 |
| 16 | .955 | 27 | .886 | 37 | .832 |
| 17 | .949 | 28 | .880 | 38 | .827 |
| 18 | .943 | 29 | .874 | 39 | .822 |
| 19 | .935 | 30 | .867 | 40 | .817 |
| 20 | .928 | | | | |
| Degrees. | Density. | Degrees. | Density. | Degrees. | Density. |
| 0 | 1.000 | 27 | 1.230 | 51 | 1.547 |
| 3 | 1.020 | 30 | 1.261 | 54 | 1.594 |
| 6 | 1.040 | 33 | 1.295 | 57 | 1.659 |
| 9 | 1.064 | 36 | 1.333 | 60 | 1.717 |
| 12 | 1.089 | 39 | 1.373 | 63 | 1.779 |
| 15 | 1.114 | 42 | 1.414 | 66 | 1.848 |
| 18 | 1.140 | 45 | 1.455 | 69 | 1.920 |
| 21 | 1.170 | 48 | 1.500 | 72 | 2.000 |
| 24 | 1.200 | | | | |
* Fig. 5.—Jones’s
* Hydrometer.
Carrier’s hydrometer was very similar to that of Baumé, Cartier having been employed by the latter to construct his instruments for the French revenue. The point at which the instrument floated in distilled water was marked 10° by Cartier, and 30° on Carrier’s scale corresponded to 32° on Baumé’s.
Perhaps the main object for which hydrometers have been constructed is the determination of the value of spirituous liquors, chiefly for revenue purposes. To this end an immense variety of hydrometers have been devised, differing mainly in the character of their scales.
In Speer’s hydrometer the stem has the form of an octagonal prism, and upon each of the eight faces a scale is engraved, indicating the percentage strength of the spirit corresponding to the several divisions of the scale, the eight scales being adapted respectively to the temperature 35°, 40°, 45°, 50°, 55°, 60°, 65° and 70° F. Four small pins, which can be inserted into the counterpoise of the instrument, serve to adapt the instrument to the temperatures intermediate between those for which the scales are constructed. William Speer was supervisor and chief assayer of spirits in the port of Dublin. For a more complete account of this instrument see Tilloch’s Phil. Mag., xiv. 151.
* Fig. 6.
The hydrometer constructed by Jones, of Holborn, consists of a spheroidal bulb with a rectangular stem (fig. 5). Between the bulb and counterpoise is placed a thermometer, which serves to indicate the temperature of the liquid, and the instrument is provided with three weights which can be attached to the top of the stem. On the four sides of the stem AD are engraved four scales corresponding respectively to the unloaded instrument, and to the instrument loaded with the respective weights. The instrument when unloaded serves for the range from 74 to 47 over proof; when loaded with the first weight it indicates from 46 to 13 over proof, with the second weight from 13 over proof to 29 under proof, and with the third ​ from 29 under proof to pure water, the graduation corresponding to which is marked W at the bottom of the fourth scale. One side of the stem AD is shown in fig. 5, the other three in fig. 6. The thermometer is also provided with four scales corresponding to the scales above mentioned. Each scale has its zero in the middle corresponding to 60° F. If the mercury in the thermometer stand above this zero the spirit must be reckoned weaker than the hydrometer indicates by the number on the thermometer scale level with the top of the mercury, while if the thermometer indicate a temperature lower than the zero of the scale (60° F.) the spirit must be reckoned stronger by the scale reading. At the side of each of the four scales on the stem of the hydrometer is engraved a set of small numbers indicating the contraction in volume which would be experienced if the requisite amount of water (or spirit) were added to bring the sample tested to the proof strength.
The hydrometer constructed by Dicas of Liverpool is provided with a sliding scale which can be adjusted for different temperatures, and which also indicates the contraction in volume incident on bringing the spirit to proof strength. It is provided with thirty-six different weights which, with the ten divisions on the stem, form a scale from 0 to 370. The employment of so many weights renders the instrument ill-adapted for practical work where speed is an object.
* Fig. 7.—Atkins’s Hydrometer.
This instrument was adopted by the United States in 1790, but was subsequently discarded by the Internal Revenue Service for another type. In this latter form the observations have to be made at the standard temperature of 60° F., at which the graduation 100 corresponds to proof spirit and 200 to absolute alcohol. The need of adjustable weights is avoided by employing a set of five instruments, graduated respectively 0°-100°, 80°-120°, 100°-140°, 130°-170°, 160°-200°. The reading gives the volume of proof spirit equivalent to the volume of liquor; thus the readings 80° and 120° mean that 100 volumes of the test liquors contain the same amount of absolute alcohol as 80 and 120 volumes of proof spirit respectively. Proof spirit is defined in the United States as a mixture of alcohol and water which contains equal volumes of alcohol and water at 60° F., the alcohol having a specific gravity of 0.7939 at 60° as compared with water at its maximum density. The specific gravity of proof spirit is 0.93353 at 60°; and 100 volumes of the mixture is made from 50 volumes of absolute alcohol and 53.71 volumes of water.
Quin’s universal hydrometer is described in the Transactions of the Society of Arts, viii. 98. It is provided with a sliding rule to adapt it to different temperatures, and has four scales, one of which is graduated for spirits and the other three serve to show the strengths of worts. The peculiarity of the instrument consists in the pyramidal form given to the stem, which renders the scale-divisions more nearly equal in length than they would be on a prismatic stem.
Atkins’s hydrometer, as originally constructed, is described in Nicholson’s Journal, 8vo, ii. 276. It is made of brass, and is provided with a spheroidal bulb the axis of which is 2 in. in length, the conjugate diameter being 11/2 in. The whole length of the instrument is 8 in., the stem square of about 1/8-in. side, and the weight about 400 grains. It is provided with four weights, marked 1, 2, 3, 4, and weighing respectively 20, 40, 61 and 84 grains, which can be attached to the shank of the instrument at C (fig. 7) and retained there by the fixed weight B. The scale engraved upon one face of the stem contains fifty-five divisions, the top and bottom being marked 0 or zero and the alternate intermediate divisions (of which there are twenty-six) being marked with the letters of the alphabet in order. The four weights are so adjusted that, if the instrument floats with the stem emerging as far as the lower division 0 with one of the weights attached, then replacing the weight by the next heavier causes the instrument to sink through the whole length of the scale to the upper division 0, and the first weight produces the same effect when applied to the naked instrument. The stem is thus virtually extended to five times its length, and the number of divisions increased practically to 272. When no weight is attached the instrument indicates densities from .806 to .843; with No. 1 it registers from .843 to .880, with No. 2 from .880 to .918, with No. 3 from .918 to .958, and with No. 4 from .958 to 1.000, the temperature being 55° F. It will thus be seen that the whole length of the stem corresponds to a difference of density of about .04, and one division to about .00074, indicating a difference of little more than 1/3% in the strength of any sample of spirits.
The instrument is provided with a sliding rule, with scales corresponding to the several weights, which indicate the specific gravity corresponding to the several divisions of the hydrometer scale compared with water at 55° F. The slider upon the rule serves to adjust the scale for different temperatures, and then indicates the strength of the spirit in percentages over or under proof. The slider is also provided with scales, marked respectively Dicas and Clarke, which serve to show the readings which would have been obtained had the instruments of those makers been employed. The line on the scale marked “concentration” indicates the diminution in volume consequent upon reducing the sample to proof strength (if it is over proof, O.P.) or upon reducing proof spirit to the strength of the sample (if it is under proof, U.P.). By applying the several weights in succession in addition to No. 4 the instrument can be employed for liquids heavier than water; and graduations on the other three sides of the stem, together with an additional slide rule, adapt the instrument for the determination of the strength of worts.
Atkins subsequently modified the instrument (Nicholson’s Journal, 8vo, iii. 50) by constructing the different weights of different shapes, viz. circular, square, triangular and pentagonal, instead of numbering them 1, 2, 3 and 4 respectively, a figure of the weight being stamped on the sliding rule opposite to every letter in the series to which it belongs, thus diminishing the probability of mistakes. He also replaced the letters on the stem by the corresponding specific gravities referred to water as unity. Further information concerning these instruments and the state of hydrometry in 1803 will be found in Atkins’s pamphlet On the Relation between the Specific Gravities and the Strength of Spirituous Liquors (1803); or Phil. Mag. xvi. 26-33, 205–212, 305–312; xvii. 204–210 and 329–341.
In Gay-Lussac’s alcoholometer the scale is divided into 100 parts corresponding to the presence of 1, 2, ... % by volume of alcohol at 15° C., the highest division of the scale corresponding to the purest alcohol he could obtain (density .7947) and the lowest division corresponding to pure water. A table provides the necessary corrections for other temperatures.
Tralles’s hydrometer differs from Gay-Lussac’s only in being graduated at 4° C. instead of 15° C., and taking alcohol of density .7939 at 15.5° C. for pure alcohol instead of .7947 as taken by Gay-Lussac (Keene’s Handbook of Hydrometry).
In Beck’s hydrometer the zero of the scale corresponds to density 1.000 and the division 30 to density .850, and equal divisions on the scale are continued as far as is required in both directions.
* Fig. 8.—Sike’s Hydrometer.
In the centesimal hydrometer of Francœur the volume of the stem between successive divisions of the scale is always 1/100th of the whole volume immersed when the instrument floats in water at 4° C. In order to graduate the stem the instrument is first weighed, then immersed in distilled water at 4° C., and the line of flotation marked zero. The first degree is then found by placing on the top of the stem a weight equal to 1/100th of the weight of the instrument, which increases the volume immersed by 1/100th of the original volume. The addition to the top of the stem of successive weights, each 1/100th of the weight of the instrument itself, serves to determine the successive degrees. The length of 100 divisions of the scale, or the length of the uniform stem the volume of which would be equal to that of the hydrometer up to the zero graduation, Francœur called the “modulus” of the hydrometer. He constructed his instruments of glass, using different instruments for different portions of the scale (Francœur, Traité d’aréométrie, Paris, 1842).
Dr Boriés of Montpellier constructed a hydrometer which was based upon the results of his experiments on mixtures of alcohol and water. The interval between the points corresponding to pure alcohol and to pure water Boriés divided into 100 equal parts, though the stem was prolonged so as to contain only 10 of these divisions, the other 90 being provided for by the addition of 9 weights to the bottom of the instrument as in Clarke’s hydrometer.
The instrument which has now been exclusively used for revenue purposes for nearly a century is that associated with the name of Bartholomew Sikes, who was correspondent to the Board of Excise from 1774 to 1783, and for some time collector of excise for Hertfordshire.
Sikes’s hydrometer, on account of its similarity to that of Boriés, appears to have been borrowed from that instrument. It is made of gilded brass or silver, and consists of a spherical ball A (fig. 8), 1.5 in. in diameter, below which is a weight B connected with the ball by a short conical stem C. The stem D is rectangular in section and about 31/2 in. in length. This is divided into ten equal parts, each of which is subdivided into five. As in Boriés’s instrument, a series of 9 weights, each of the form shown at E, serves to extend the scale ​to 100 principal divisions. In the centre of each weight is a hole capable of admitting the lowest and thickest end of the conical stem C, and a slot is cut into it just wide enough to allow the upper part of the cone to pass. Each weight can thus be dropped on to the lower stem so as to rest on the counterpoise B. The weights are marked 10, 20, . . . 90; and in using the instrument that weight must be selected which will allow it to float in the liquid with a portion only of the stem submerged. Then the reading of the scale at the line of flotation, added to the number on the weight, gives the reading required. A small supernumerary weight F is added, which can be placed upon the top of the stem. F is so adjusted that when the 60 weight is placed on the lower stem the instrument sinks to the same point in distilled water when F is attached as in proof spirit when F is removed. The best instruments are now constructed for revenue purposes of silver, heavily gilded, because it was found that saccharic acid contained in some spirits attacked brass behind the gilding.
The following table gives the specific gravities corresponding to the principal graduations on Sikes’s hydrometer at 60° F. and 62° F., together with the corresponding strengths of spirits. The latter are based upon the tables of Charles Gilpin, clerk to the Royal Society, for which the reader is referred to the Phil. Trans. for 1794. Gilpin’s work is a model for its accuracy and thoroughness of detail, and his results have scarcely been improved upon by more recent workers. The merit of Sikes’s system lies not so much in the hydrometer as in the complete system of tables by which the readings of the instrument are at once converted into percentage of proof-spirit.
| Sike’s  Indications. | 60° F. | 60° F. | 62° F. | 62° F. |
| Sike’s  Indications. | Density. | Proof Spirit per cent. | Density. | Proof Spirit per cent. |
| 0 | .815297 | 167.0 | .815400 | 166.5 |
| 1 | .816956 | 166.1 | .817059 | 165.6 |
| 2 | .818621 | 165.3 | .818725 | 164.8 |
| 3 | .820294 | 164.5 | .820397 | 163.9 |
| 4 | .821973 | 163.6 | .822077 | 163.1 |
| 5 | .823659 | 162.7 | .823763 | 162.3 |
| 6 | .825352 | 161.8 | .825457 | 161.4 |
| 7 | .827052 | 160.9 | .827157 | 160.5 |
| 8 | .828759 | 160.0 | .828864 | 159.6 |
| 9 | .830473 | 159.1 | .830578 | 158.7 |
| 10 | .832195 | 158.2 | .832300 | 157.8 |
| 11 | .833888 | 157.3 | .833993 | 156.8 |
| 12 | .835587 | 156.4 | .835692 | 155.9 |
| 13 | .837294 | 155.5 | .837400 | 155.0 |
| 14 | .839008 | 154.6 | .839114 | 154.0 |
| 15 | .840729 | 153.7 | .840835 | 153.1 |
| 16 | .842458 | 152.7 | .842564 | 152.1 |
| 17 | .844193 | 151.7 | .844299 | 151.1 |
| 18 | .845936 | 150.7 | .846042 | 150.1 |
| 19 | .847685 | 149.7 | .847792 | 149.1 |
| 20 | .849442 | 148.7 | .849549 | 148.1 |
| 20b | .849393 | 148.7 | .849500 | 148.1 |
| 21 | .851122 | 147.6 | .851229 | 147.1 |
| 22 | .852857 | 146.6 | .852964 | 146.1 |
| 23 | .854599 | 145.6 | .854707 | 145.1 |
| 24 | .856348 | 144.6 | .856456 | 144.0 |
| 25 | .858105 | 143.5 | .858213 | 142.9 |
| 26 | .859869 | 142.4 | .859978 | 141.8 |
| 27 | .861640 | 141.3 | .861749 | 140.8 |
| 28 | .863419 | 140.2 | .863528 | 139.7 |
| 29 | .865204 | 139.1 | .865313 | 138.5 |
| 30 | .866998 | 138.0 | .867107 | 137.4 |
| 30b | .866991 | 138.0 | .867100 | 137.4 |
| 31 | .868755 | 136.9 | .868865 | 136.2 |
| 32 | .870526 | 135.7 | .870636 | 135.1 |
| 33 | .872305 | 134.5 | .872415 | 133.9 |
| 34 | .874090 | 133.4 | .874200 | 132.8 |
| 35 | .875883 | 132.2 | .873994 | 131.6 |
| 36 | .877684 | 131.0 | .877995 | 130.4 |
| 37 | .879492 | 129.8 | .879603 | 129.1 |
| 38 | .881307 | 128.5 | .881419 | 127.9 |
| 39 | .883129 | 127.3 | .883241 | 126.7 |
| 40 | .884960 | 126.0 | .885072 | 125.4 |
| 40b | .884888 | 126.0 | .885000 | 125.4 |
| 41 | .886689 | 124.8 | .886801 | 124.2 |
| 42 | .888497 | 123.5 | .888609 | 122.9 |
| 43 | .890312 | 122.2 | .890425 | 121.6 |
| 44 | .892135 | 120.9 | .892248 | 120.3 |
| 45 | .893965 | 119.6 | .894078 | 119.0 |
| 46 | .895803 | 118.3 | .895916 | 117.6 |
| 47 | .897647 | 116.9 | .897761 | 116.3 |
| 48 | .899509 | 115.6 | .899614 | 114.9 |
| 49 | .901360 | 114.2 | .901417 | 113.5 |
| 50 | .903229 | 112.8 | .903343 | 112.1 |
| 50b | .903186 | 112.8 | .903300 | 112.1 |
| 51 | .905024 | 111.4 | .905138 | 110.7 |
| 52 | .906869 | 110.0 | .906983 | 109.3 |
| 53 | .908722 | 108.6 | .908837 | 107.9 |
| 54 | .910582 | 107.1 | .910697 | 106.5 |
| 55 | .912450 | 105.6 | .912565 | 105.0 |
| 56 | .914326 | 104.2 | .914441 | 103.5 |
| 57 | .916209 | 102.7 | .916323 | 102.0 |
| 58 | .918100 | 101.3 | .918216 | 100.5 |
| 59 | .919999 | 99.7 | .820115 | 98.9 |
| 60 | .921906 | 98.1 | .922022 | 97.4 |
| 60b | .921884 | 98.1 | .922000 | 97.4 |
| 61 | .923760 | 96.6 | .923877 | 95.9 |
| 62 | .925643 | 95.0 | .925760 | 94.2 |
| 63 | .927534 | 93.3 | .927652 | 92.6 |
| 64 | .929433 | 91.7 | .929550 | 90.9 |
| 65 | .931339 | 90.0 | .931457 | 89.2 |
| 66 | .933254 | 88.3 | .933372 | 87.5 |
| 67 | .935176 | 86.5 | .935294 | 85.8 |
| 68 | .937107 | 84.7 | .937225 | 84.0 |
| 69 | .939045 | 82.9 | .939163 | 82.2 |
| 70 | .940991 | 81.1 | .941110 | 80.3 |
| 70b | .940981 | 81.1 | .941100 | 80.3 |
| 71 | .942897 | 79.2 | .943016 | 78.4 |
| 72 | .944819 | 77.3 | .944938 | 76.5 |
| 73 | .946749 | 75.3 | .946869 | 74.5 |
| 74 | .948687 | 73.3 | .948807 | 72.5 |
| 75 | .950634 | 71.2 | .950753 | 70.4 |
| 76 | .952588 | 69.0 | .952708 | 68.2 |
| 77 | .954550 | 66.8 | .954670 | 66.0 |
| 78 | .956520 | 64.4 | .956641 | 63.5 |
| 79 | .958498 | 61.9 | .958619 | 61.1 |
| 80 | .960485 | 59.4 | .960606 | 58.5 |
| 80b | .960479 | 59.4 | .960600 | 58.5 |
| 81 | .962433 | 56.7 | .962555 | 55.8 |
| 82 | .964395 | 53.9 | .964517 | 53.0 |
| 83 | .966366 | 50.9 | .966488 | 50.0 |
| 84 | .968344 | 47.8 | .968466 | 47.0 |
| 85 | .970331 | 44.5 | .970453 | 43.8 |
| 86 | .972325 | 41.0 | .972448 | 40.4 |
| 87 | .974328 | 37.5 | .974451 | 36.9 |
| 88 | .976340 | 34.0 | .976463 | 33.5 |
| 89 | .978359 | 30.6 | .978482 | 30.1 |
| 90 | .980386 | 27.2 | .980510 | 26.7 |
| 90b | .980376 | 27.2 | .980500 | 26.7 |
| 91 | .982371 | 23.9 | .982496 | 23.6 |
| 92 | .984374 | 20.8 | .984498 | 20.5 |
| 93 | .986385 | 17.7 | .986510 | 17.4 |
| 94 | .988404 | 14.8 | .988529 | 14.5 |
| 95 | .990431 | 12.0 | .990557 | 11.7 |
| 96 | .992468 | 9.3 | .992593 | 9.0 |
| 97 | .994512 | 6.7 | .994637 | 6.5 |
| 98 | .996565 | 4.1 | .996691 | 4.0 |
| 99 | .998626 | 1.8 | .998752 | 1.6 |
| 100 | 1.000696 | 0.0 | 1.000822 | 0.0 |
In the above table for Sikes’s hydrometer two densities are given corresponding to each of the degrees 20, 30, 40, 50, 60, 70, 80 and 90, indicating that the successive weights belonging to the particular instrument for which the table has been calculated do not quite agree. The discrepancy, however, does not produce any sensible error in the strength of the corresponding spirit.
A table which indicates the weight per gallon of spirituous liquors for every degree of Sikes’s hydrometer is printed in 23 and 24 Vict. c. 114, schedule B. This table differs slightly from that given above, which has been abridged from the table given in Keene’s Handbook of Hydrometry, apparently on account of the equal divisions on Sikes’s scale having been taken as corresponding to equal increments of density.
Sikes’s hydrometer was established for the purpose of collecting the revenue of the United Kingdom by Act of Parliament, 56 Geo. III. c. 140, by which it was enacted that “all spirits shall be deemed and taken to be of the degree of strength which the said hydrometers called Sikes’s hydrometers shall, upon trial by any officer or officers of the customs or excise, denote such spirits to be.” This act came into force on January 5, 1817, and was to have remained in force until August 1, 1818, but was repealed by 58 Geo. III. c. 28, which established Sikes’s hydrometer on a permanent footing. By 3 and 4 Will. IV. c. 52, § 123, it was further enacted that the same instruments and methods should be employed in determining the duty upon imported spirits as should in virtue of any Act of Parliament be employed in the determination of the duty upon spirits distilled at home. It is the practice of the officers of the inland revenue to adjust Sikes’s hydrometer at 62° F., that being the temperature at which the imperial gallon is defined as containing 10 ℔ avoirdupois of distilled water. The specific gravity of any sample of spirits thus determined, when multiplied by ten, gives the weight in pounds per imperial gallon, and the weight of any bulk of spirits divided by this number gives its volume at once in imperial gallons.
Mr (afterwards Colonel) J. B. Keene, of the Hydrometer Office, London, has constructed an instrument after the model of Sikes’s, but provided with twelve weights of different masses but equal volumes, and the instrument is never used without having one of these attached. When loaded with either of the lightest two weights the instrument is specifically lighter than Sikes’s hydrometer when unloaded, and it may thus be used for specific gravities as low as that of absolute alcohol. The volume of each weight being the same, the whole volume immersed is always the same when it floats at the same mark whatever weight may be attached.
Besides the above, many hydrometers have been employed for special purposes. Twaddell’s hydrometer is adapted for densities greater than that of water. The scale is so arranged that the reading multiplied by 5 and added to 1000 gives the specific gravity with reference to water as 1000. To avoid an inconveniently long stem, different instruments are employed for different parts of the scale as mentioned above.
The lactometer constructed by Dicas of Liverpool is adapted for the determination of the quality of milk. It resembles Sikes’s hydrometer in other respects, but is provided with eight weights. It is also provided with a thermometer and slide rule, to reduce the readings to the standard temperature of 55° F. Any determination of density can be taken only as affording prima facie evidence of the quality of milk, as the removal of cream and the addition of water are operations which tend to compensate each other in their influence on the density of the liquid, so that the lactometer cannot be regarded as a reliable instrument.
The marine hydrometers, as supplied by the British government to the royal navy and the merchant marine, are glass instruments with slender stems, and generally serve to indicate specific gravities from 1.000 to 1.040. Before being issued they are compared with a standard instrument, and their errors determined. They are employed for taking observations of the density of sea-water.
The salinometer is a hydrometer originally intended to indicate the strength of the brine in marine boilers in which sea-water is employed. Saunders’s salinometer consists of a hydrometer which floats in a chamber through which the water from the boiler is allowed to flow in a gentle stream, at a temperature of 200° F. The peculiarity of the instrument consists in the stream of water, as it enters the hydrometer chamber, being made to impinge against a disk of metal, by which it is broken into drops, thus liberating the steam, which would otherwise disturb the instrument.
The use of Sikes’s hydrometer necessitates the employment of a considerable quantity of spirit. For the testing of spirits in bulk no more convenient instrument has been devised, but where very small quantities are available more suitable laboratory methods must be adopted.
In England, the Finance Act 1907 (7 Ed. VII. c. 13), section 4, provides as follows: (1) The Commissioners of Customs and the Commissioners of Inland Revenue may jointly make regulations authorizing the use of any means described in the regulations for ascertaining for any purpose the strength or weight of spirits. (2) Where under any enactment Sykes’s (sic) Hydrometer is directed to be used or may be used for the purpose of ascertaining the strength or weight of spirits, any means so authorized by regulations may be used instead of Sykes’s Hydrometer and references to Sykes’s Hydrometer in any enactment shall be construed accordingly. (3) Any regulations made under this section shall be published in the London, Edinburgh and Dublin Gazette, and shall take effect from the date of publication, or such later date as may be mentioned in the regulations for the purpose. (4) The expression “spirits” in this section has the same meaning as in the Spirits Act 1880. (W. G.)
* ↑ 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.
* ↑ Nicholson’s Journal, vol. i. p. 111, footnote.