# 1911 Encyclopædia Britannica/Density

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​DENSITY (Lat. densus, thick), in physics, the mass or quantity of matter contained in unit volume of any substance: this is the absolute density; the term relative density or specific gravity denotes the ratio of the mass of a certain volume of a substance to the mass of the same volume of some standard substance. Since the weights used in conjunction with a balance are really standard masses, the word “weight” may be substituted for the word “mass” in the preceding definitions; and we may symbolically express the relations thus:—If M be the weight of substance occupying a volume V, then the absolute density Δ = M/V; and if m, m$_1$ be the weights of the substance and of the standard substance which occupy the same volume, the relative density or specific gravity S = m/m$_1$; or more generally if m$_1$ be the weight of a volume v of the substance, and m$_1$ the weight of a volume v$_1$ of the standard, then S = mv$_1$/m$_1$v. In the numerical expression of absolute densities it is necessary to specify the units of mass and volume employed; while in the case of relative densities, it is only necessary to specify the standard substance, since the result is a mere number. Absolute densities are generally stated in the C.G.S. system, i.e. as grammes per cubic centimetre. In commerce, however, other expressions are met with, as, for example, “pounds per cubic foot” (used for woods, metals, &c.), “pounds per gallon,” &c. The standard substances employed to determine relative densities are: water for liquids and solids, and hydrogen or atmospheric air for gases; oxygen (as 16) is sometimes used in this last case. Other standards of reference may be used in special connexions; for example, the Earth is the usual unit for expressing the relative density of the other members of the solar system. Reference should be made to the article Gravitation for an account of the methods employed to determine the “mean density of the earth.”
In expressing the absolute or relative density of any substance, it is necessary to specify the conditions for which the relation holds: in the case of gases, the temperature and pressure of the experimental gas (and of the standard, in the case of relative density); and in the case of solids and liquids, the temperature. The reason for this is readily seen; if a mass M of any gas occupies a volume V at a temperature T (on the absolute scale) and a pressure P, then its absolute density under these conditions is Δ = M/V; if now the temperature and pressure be changed to T$_1$ and P$_1$, the volume V$_1$ under these conditions is VPT/P$_1$T$_1$, and the absolute density is MP$_1$T/VPT$_1$. It is customary to reduce gases to the so-called “normal temperature and pressure,” abbreviated to N.T.P., which is 0°C. and 760 mm.
The relative densities of gases are usually expressed in terms of the standard gas under the same conditions. The density gives very important information as to the molecular weight, since by the law of Avogadro it is seen that the relative density is the ratio of the molecular weights of the experimental and standard gases. In the case of liquids and solids, comparison with water at 4°C, the temperature of the maximum density of water; at 0°C, the zero of the Centigrade scale and the freezing-point of water; at 15° and 18°, ordinary room-temperatures; and at 25°, the temperature at which a thermostat may be conveniently maintained, are common in laboratory practice. The temperature of the experimental substance may or may not be the temperature of the standard. In such cases a bracketed fraction is appended to the specific gravity, of which the numerator and denominator are respectively the temperatures of the substance and of the standard; thus 1.093 (0°/4°) means that the ratio of the weight of a definite volume of a substance at 0° to the weight of the same volume of water 4° is 1.093. It may be noted that if comparison be made with water at 4°, the relative density is the same as the absolute density, since the unit of mass in the C.G.S. system is the weight of a cubic centimetre of water at this temperature. In British units, especially in connexion with the statement of relative densities of alcoholic liquors for Inland Revenue purposes, comparison is made with water at 62° F. (16.6° C); a reason for this is that the gallon of water is defined by statute as weighing 10 ℔ at 62° F., and hence the densities so expressed admit of the ready conversion of volumes to weights. Thus if d be the relative density, then 10d represents the weight of a gallon in ℔. The brewer has gone a step further in simplifying his expressions by multiplying the density by 1000, and speaking of the difference between the density so expressed and 1000 as “degrees of gravity” (see Beer).
Practical Determination of Densities
* Fig. 1.—Say’s Stereometer.
* Fig. 2.
The methods for determining densities may be divided into two groups according as hydrostatic principles are employed or not. In the group where the principles of hydrostatics are not employed the method consists in determining the weight and volume of a certain quantity of the substance, or the weights of equal volumes of the substance and of the standard. In the case of solids we may determine the volume in some cases by direct measurement—this gives at the best a very rough and ready value; a better method is to immerse the body in a fluid (in which it must sink and be insoluble) contained in a graduated glass, and to deduce its volume from the height to which the liquid rises. The weight may be directly determined by the balance. The ratio “weight to volume” is the absolute density. The separate determination of the volume and mass of such substances as gunpowder, cotton-wool, soluble substances, &c., supplies the only means of determining their densities. The stereometer of Say, which was greatly improved by Regnault and further modified by Kopp, permits an accurate determination of the volume of a given mass of any such substance. In its simplest form the instrument consists of a glass tube PC (fig. 1), of uniform bore, terminating in a cup PE, the mouth of which can be rendered airtight by the plate of glass E. The substance whose volume is to be determined is placed in the cup PE, and the tube PC is immersed in the vessel of mercury D, until the mercury reaches the mark P. The plate E is then placed on the cup, and the tube PC raised until the surface of the mercury in the tube stands at M, that in the vessel D being at C, and the height MC is measured. Let k denote this height, and let PM be denoted by l. Let u represent the volume of air in the cup before the body was inserted, v the volume of the body, a the area of the horizontal section of the tube PC, and h the height of the mercurial barometer. Then, by Boyle’s law (u − v + al)(h − k) = (u − v)h, and therefore v = u − al(h − k)/k.
The volume u may be determined by repeating the experiment when only air is in the cup. In this case v = 0, and the equation becomes (u + al$^1$)(h − k$^1$) = uh, whence u = al$^1$(h − k$^1$)/k$^1$. Substituting this value in the expression for v, the volume of the body inserted in the cup becomes known. The chief errors to which the stereometer is liable are (1) variation of temperature and atmospheric pressure during the experiment, and (2) the presence of moisture which disturbs Boyle’s law.
The method of weighing equal volumes is particularly applicable to the determination of the relative densities of liquids. It consists in weighing a glass vessel (1) empty, (2) filled with the liquid, (3) filled with the standard substance. Calling the weight of the empty vessel w, when filled with the liquid W, and when filled with the standard substance W$_1$, it is obvious that W − w, and W$_1$ − w, are the weights of equal volumes of the liquid and standard, and hence the relative density is (W − w)/(W$_1$ − w).
Many forms of vessels have been devised. The commoner type of “specific gravity bottle” consists of a thin glass bottle (fig. 2) of a capacity varying from 10 to 100 cc., fitted with an accurately ground stopper, which is vertically perforated by a fine hole. The bottle is carefully cleansed by washing with soda, hydrochloric acid and distilled water, and then dried by heating in an air bath or by blowing in warm air. It is allowed to cool and then weighed. The bottle is then filled with distilled water, and brought to a definite temperature by immersion in a thermostat, and the stopper inserted. It is removed from the thermostat, and carefully ​wiped. After cooling it is weighed. The bottle is again cleaned and dried, and the operations repeated with the liquid under examination instead of water. Numerous modifications of this bottle are in use. For volatile liquids, a flask provided with a long neck which carries a graduation and is fitted with a well-ground stopper is recommended. The bringing of the liquid to the mark is effected by removing the excess by means of a capillary. In many forms a thermometer forms part of the apparatus.
* Fig. 3.
Another type of vessel, named the Sprengel tube or pycnometer (Gr. πυκυός, dense), is shown in fig. 3. It consists of a cylindrical tube of a capacity ranging from 10 to 50 cc., provided at the upper end with a thick-walled capillary bent as shown on the left of the figure. From the bottom there leads another fine tube, bent upwards, and then at right angles so as to be at the same level as the capillary branch. This tube bears a graduation. A loop of platinum wire passed under these tubes serves to suspend the vessel from the balance arm. The manner of cleansing, &c., is the same as in the ordinary form. The vessel is filled by placing the capillary in a vessel containing the liquid and gently aspirating. Care must be taken that no air bubbles are enclosed. The liquid is adjusted to the mark by withdrawing any excess from the capillary end by a strip of bibulous paper or by a capillary tube. Many variations of this apparatus are in use; in one of the commonest there are two cylindrical chambers, joined at the bottom, and each provided at the top with fine tubes bent at right angles; sometimes the inlet and outlet tubes are provided with caps.
The specific gravity bottle may be used to determine the relative density of a solid which is available in small fragments, and is insoluble in the standard liquid. The method involves three operations:—(1) weighing the solid in air (W), (2) weighing the specific gravity bottle full of liquid (W$_1$), (3) weighing the bottle containing the solid and filled up with liquid (W$_2$). It is readily seen that W + W$_1$ - W$_2$ is the weight of the liquid displaced by the solid, and therefore is the weight of an equal volume of liquid; hence the relative density is W/(W + W$_1$ - W$_2$).
The determination of the absolute densities of gases can only be effected with any high degree of accuracy by a development of this method. As originated by Regnault, it consisted in filling a large glass globe with the gas by alternately exhausting with an air-pump and admitting the pure and dry gas. The flask was then brought to 0° by immersion in melting ice, the pressure of the gas taken, and the stop-cock closed. The flask is removed from the ice, allowed to attain the temperature of the room, and then weighed. The flask is now partially exhausted, transferred to the cooling bath, and after standing the pressure of the residual gas is taken by a manometer. The flask is again brought to room-temperature, and re-weighed. The difference in the weights corresponds to the volume of gas at a pressure equal to the difference of the recorded pressures. The volume of the flask is determined by weighing empty and filled with water. This method has been refined by many experimenters, among whom we may notice Morley and Lord Rayleigh. Morley determined the densities of hydrogen and oxygen in the course of his classical investigation of the composition of water. The method differed from Regnault’s inasmuch as the flask was exhausted to an almost complete vacuum, a performance rendered possible by the high efficiency of the modern air-pump. The actual experiment necessitates the most elaborate precautions, for which reference must be made to Morley’s original papers in the Smithsonian Contributions to Knowledge (1895), or to M. Travers, The Study of Gases. Lord Rayleigh has made many investigations of the absolute densities of gases, one of which, namely on atmospheric and artificial nitrogen, undertaken in conjunction with Sir William Ramsay, culminated in the discovery of argon (q.v.). He pointed out in 1888 (Proc. Roy. Soc. 43, p. 361) an important correction which had been overlooked by previous experimenters with Regnault’s method, viz. the change in volume of the experimental globe due to shrinkage under diminished pressure; this may be experimentally determined and amounts to between 0.04 and 0.16% of the volume of the globe.
Related to the determination of the density of a gas is the determination of the density of a vapour, i.e. matter which at ordinary temperatures exists as a solid or liquid. This subject owes its importance in modern chemistry to the fact that the vapour density, when hydrogen is taken as the standard, gives perfectly definite information as to the molecular condition of the compound, since twice the vapour density equals the molecular weight of the compound. Many methods have been devised. In historical order we may briefly enumerate the following:—in 1811, Gay-Lussac volatilized a weighed quantity of liquid, which must be readily volatile, by letting it rise up a short tube containing mercury and standing inverted in a vessel holding the same metal. This method was developed by Hofmann in 1868, who replaced the short tube of Gay-Lussac by an ordinary barometer tube, thus effecting the volatilization in a Torricellian vacuum. In 1826 Dumas devised a method suitable for substances of high boiling-point; this consisted in its essential point in vaporizing the substance in a flask made of suitable material, sealing it when full of vapour, and weighing. This method is very tedious in detail. H. Sainte-Claire Deville and L. Troost made it available for specially high temperatures by employing porcelain vessels, sealing them with the oxyhydrogen blow-pipe, and maintaining a constant temperature by a vapour bath of mercury (350°), sulphur (440°), cadmium (860°) and zinc (1040°). In 1878 Victor Meyer devised his air-expulsion method.
Before discussing the methods now used in detail, a summary of the conclusions reached by Victor Meyer in his classical investigations in this field as to the applicability of the different methods will be given:
(1) For substances which do not boil higher than 260° and have vapours stable for 30° above the boiling-point and which do not react on mercury, use Victor Meyer’s “mercury expulsion method.”
(2) For substances boiling between 260° and 420°, and which do not react on metals, use Meyer’s “Wood’s alloy expulsion method.”
(3) For substances boiling at higher temperatures, or for any substance which reacts on mercury, Meyer’s “air expulsion method” must be used. It is to be noted, however, that this method is applicable to substances of any boiling-point (see below).
(4) For substances which can be vaporized only under diminished pressure, several methods may be used. (a) Hofmann’s is the best if the substance volatilizes at below 310°, and does not react on mercury; otherwise (b) Demuth and Meyer’s, Eykman’s, Schall’s, or other methods may be used.
* Fig. 4.
1. Meyer’s “Mercury Expulsion” Method.—A small quantity of the substance is weighed into a tube, of the form shown in fig. 4, which has a capacity of about 35 cc., provided with a capillary tube at the top, and a bent tube about 6 mm. in diameter at the bottom. The vessel is completely filled with mercury, the capillary sealed, and the vessel weighed. The vessel is then lowered into a jacket containing vapour at a known temperature which is sufficient to volatilize the substance. Mercury is expelled, and when this expulsion ceases, the vessel is removed, allowed to cool, and weighed. It is necessary to determine the pressure exerted on the vapour by the mercury in the narrow limb; this is effected by opening the capillary and inclining the tube until the mercury just reaches the top of the narrow tube; the difference between the height of the mercury in the wide tube and the top of the narrow tube represents the pressure due to the mercury column, and this must be added to the barometric pressure in order to deduce the total pressure on the vapour.
The result is calculated by means of the formula:
$\textstyle D={\frac {W(1+\alpha t)\times 7,980,000}{(p+p_{1}-s)[m\{1+\beta (t-t_{0})\}-m_{1}\{1+\gamma (t-t_{0})\}](1+\gamma t)}},$
in which W = weight of substance taken; t = temperature of vapour bath; α = 0.00366 = temperature coefficient of gases; p = barometric pressure; p$_1$ = height of mercury column in vessel; s = vapour tension of mercury at t°; m = weight of mercury contained in the vessel; m$_1$ = weight of mercury left in vessel after heating; β = coefficient of expansion of glass = .0000303; γ = coefficient of expansion of mercury = 0.00018 (0.00019 above 240°) (see Ber. 1877, 10, p. 2068; 1886, 19, p. 1862).
2. Meyer’s Wood’s Alloy Expulsion Method.—This method is a modification of the one just described. The alloy used is composed of 15 parts of bismuth, 8 of lead, 4 of tin and 3 of cadmium; it melts at 70°, and can be experimented with as readily as mercury. The cylindrical vessel is replaced by a globular one, and the pressure on the vapour due to the column of alloy in the side tube is readily reduced to millimetres of mercury since the specific gravity of the alloy at the temperature of boiling sulphur, 444° (at which the apparatus is most frequently used), is two-thirds of that of mercury (see Ber. 1876, 9, p. 1220).
* Fig. 5.
3. Meyer’s Air Expulsion Method.—The simplicity, moderate accuracy, and adaptability of this method to every class of substance which can be vaporized entitles it to rank as one of the most potent methods in analytical chemistry; its invention is indissolubly connected with the name of Victor Meyer, being termed “Meyer’s method” to the exclusion of his other original methods. It consists in determining the air expelled from a vessel by the vapour of a given quantity of the substance. The apparatus is shown in fig. 5. A long tube (a) terminates at the bottom in a cylindrical chamber of about 100-150 cc. capacity. The top is fitted with a rubber stopper, or in some forms with a stop-cock, while a little way down there is a bent delivery tube (b). To use the apparatus, the long tube is placed in a vapour bath (c) of the requisite temperature, and after the air within the tube is in equilibrium, the delivery tube is placed beneath the surface of the water in a pneumatic trough, the rubber stopper pushed home, and observation made as to whether any more air is being expelled. If this be not so, a graduated tube (d) is filled with water, and inverted over the delivery tube. The rubber stopper is removed and the experimental substance introduced, and the stopper quickly replaced to the same extent as before. Bubbles are quickly disengaged and collect in the ​graduated tube. Solids may be directly admitted to the tube from a weighing bottle, while liquids are conveniently introduced by means of small stoppered bottles, or, in the case of exceptionally volatile liquids, by means of a bulb blown on a piece of thin capillary tube, the tube being sealed during the weighing operation, and the capillary broken just before transference to the apparatus. To prevent the bottom of the apparatus being knocked out by the impact of the substance, a layer of sand, asbestos or sometimes mercury is placed in the tube. To complete the experiment, the graduated tube containing the expelled air is brought to a constant and determinate temperature and pressure, and this volume is the volume which the given weight of the substance would occupy if it were a gas under the same temperature and pressure. The vapour density is calculated by the following formula:
${\mbox{D}}={\frac {{\mbox{W}}(1+\alpha t)\times 587,780}{(p-s){\mbox{V}}}}$
in which W = weight of substance taken, V = volume of air expelled, α = 1/273 = .003665, t and p = temperature and pressure at which expelled air is measured, and s = vapour pressure of water at t°.
* Fig. 6.
By varying the material of the bulb, this apparatus is rendered available for exceptionally high temperatures. Vapour baths of iron are used in connexion with boiling anthracene (335°), anthraquinone (368°), sulphur (444°), phosphorus pentasulphide (518°); molten lead may also be used. For higher temperatures the bulb of the vapour density tube is made of porcelain or platinum, and is heated in a gas furnace.
(4a) Hofmann’s Method.—Both the modus operandi and apparatus employed in this method particularly recommend its use for substances which do not react on mercury and which boil in a vacuum at below 310°. The apparatus (fig. 6) consists of a barometer tube, containing mercury and standing in a bath of the same metal, surrounded by a vapour jacket. The vapour is circulated through the jacket, and the height of the mercury read by a cathetometer or otherwise. The substance is weighed into a small stoppered bottle, which is then placed beneath the mouth of the barometer tube. It ascends the tube, the substance is rapidly volatilized, and the mercury column is depressed; this depression is read off. It is necessary to know the volume of the tube above the second level; this may most efficiently be determined by calibrating the tube prior to its use. Sir T. E. Thorpe employed a barometer tube 96 cm. long, and determined the volume from the closed end for a distance of about 35 mm. by weighing in mercury; below this mark it was calibrated in the ordinary way so that a scale reading gave the volume at once. The calculation is effected by the following formulae:—
${\mbox{D}}={\frac {760w(1+0.003665t)}{0.0012934\times {\mbox{V}}\times {\mbox{B}}}}$
${\mbox{B}}={\frac {h}{1+0.00018t_{1}}}-\left({\frac {h_{1}}{1+0.00018t_{2}}}-{\frac {h_{2}}{1+0.00018t}}+s\right),$
in which w = weight of substance taken; t = temperature of vapour jacket; V = volume of vapour at t; h = height of barometer reduced to 0°; t$_1$ = temperature of air; h$_1$ = height of mercury column below vapour jacket; t$_2$ = temperature of mercury column not heated by vapour; h$_2$ = height of mercury column within vapour jacket; s = vapour tension of mercury at t°. The vapour tension of mercury need not be taken into account when water is used in the jacket.
(4b) Demuth and Meyer’s Method.—The principle of this method is as follows:—In the ordinary air expulsion method, the vapour always mixes to some extent with the air in the tube, and this involves a reduction of the pressure of the vapour. It is obvious that this reduction may be increased by accelerating the diffusion of the vapour. This may be accomplished by using a vessel with a somewhat wide bottom, and inserting the substance so that it may be volatilized very rapidly, as, for example, in tubes of Wood’s alloy, and by filling the tube with hydrogen. (For further details see Ber. 23, p. 311.)
* Fig. 7.
We may here notice a modification of Meyer’s process in which the increase of pressure due to the volatilization of the substance, and not the volume of the expelled air, is measured. This method has been developed by J. S. Lumsden (Journ. Chem. Soc. 1903, 83, p. 342), whose apparatus is shown diagrammatically in fig. 7. The vaporizing bulb A has fused about it a jacket B, provided with a condenser c. Two side tubes are fused on to the neck of A: the lower one leads to a mercury manometer M, and to the air by means of a cock C; the upper tube is provided with a rubber stopper through which a glass rod passes—this rod serves to support the tube containing the substance to be experimented upon, and so avoids the objection to the practice of withdrawing the stopper of the tube, dropping the substance in, and reinserting the stopper. To use the apparatus, a liquid of suitable boiling-point is placed in the jacket and brought to the boiling-point. All parts of the apparatus are open to the air, and the mercury in the manometer is adjusted so as to come to a fixed mark a. The substance is now placed on the support already mentioned, and the apparatus closed to the air by inserting the cork at D and turning the cock C. By turning or withdrawing the support the substance enters the bulb; and during its vaporization the free limb of the manometer is raised so as to maintain the mercury at a. When the volatilization is quite complete, the level is accurately adjusted, and the difference of the levels of the mercury gives the pressure exerted by the vapour. To calculate the result it is necessary to know the capacity of the apparatus to the mark a, and the temperature of the jacket.
Methods depending on the Principles of Hydrostatics.—Hydrostatical principles can be applied to density determinations in four typical ways: (1) depending upon the fact that the heights of liquid columns supported by the same pressure vary inversely as the densities of the liquids; (2) depending upon the fact that a body which sinks in a liquid loses a weight equal to the weight of liquid which it displaces; (3) depending on the fact that a body remains suspended, neither floating nor sinking, in a liquid of exactly the same density; (4) depending on the fact that a floating body is immersed to such an extent that the weight of the fluid displaced equals the weight of the body.
1. The method of balancing columns is of limited use. Two forms are recognized. In one, applicable only to liquids which do not mix, the two liquids are poured into the limbs of a U tube. The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids. In the second form, named after Robert Hare (1781–1858), professor of chemistry at the university of Pennsylvania, the liquids are drawn or aspirated up vertical tubes which have their lower ends placed in reservoirs containing the different liquids, and their upper ends connected to a common tube which is in communication with an aspirator for decreasing the pressure within the vertical tubes. The heights to which the liquids rise, measured in each case by the distance between the surfaces in the reservoirs and in the tubes, are inversely proportional to the densities.
2. The method of “hydrostatic weighing” is one of the most important. The principle may be thus stated: the solid is weighed in air, and then in water. If W be the weight in air, and W$_1$ the weight in water, then W$_1$ is always less than W, the difference W − W$_1$$_1$ representing the weight of the water displaced, i.e. the weight of a volume of water equal to that of the solid. Hence W/(W − W$_1$) is the relative density or specific gravity of the body. The principle is readily adapted to the determination of the relative densities of two liquids, for it is obvious that if W be the weight of a solid body in air, W$_1$ and W$_2$ its weights when immersed in the liquids, then W − W$_1$ and W − W$_2$ are the weights of equal volumes of the liquids, and therefore the relative density is the quotient (W − W$_1$)/(W − W$_2$). The determination in the case of solids lighter than water is effected by the introduction of a sinker, i.e. a body which when affixed to the light solid causes it to sink. If W be the weight of the experimental solid in air, w the weight of the sinker in water, and W$_1$ the weight of the solid plus sinker in water, then the relative density is given by W/(W + w − W$_1$). In practice the solid or plummet is suspended from the balance arm by a fibre—silk, platinum, &c.—and carefully weighed. A small stool is then placed over the balance pan, and on this is placed a beaker of distilled water so that the solid is totally immersed. Some balances are provided with a “specific gravity pan,” i.e. a pan with short suspending arms, provided with a hook at the bottom to which the fibre may be attached; when this is so, the stool is unnecessary. Any air bubbles are removed from the surface of the body by brushing with a camel-hair brush; if the solid be of a porous nature it is desirable to boil it for some time in water, thus expelling the air from its interstices. The weighing is conducted in the usual way by vibrations, except when the weight be small; it is then advisable to bring the pointer to zero, an operation rendered necessary by the damping due to the adhesion of water to the fibre. The temperature and pressure of the air and water must also be taken.
There are several corrections of the formula Δ = W/(W − W$_1$) necessary to the accurate expression of the density. Here we can only summarize the points of the investigation. It may be assumed that the weighing is made with brass weights in air at t° and p mm. pressure. To determine the true weight in vacuo at 0°, account must be taken of the different buoyancies, or losses of true weight, due to the different volumes of the solids and weights. Similarly in the case of the weighing in water, account must be taken of the buoyancy of the weights, and also, if absolute densities be required, of the density of water at the temperature of the experiment. In a form of great accuracy the absolute density Δ(0°/4°) is given by
Δ(0°/4°) = (ραW − δW$_1$)/(W − W$_1$),
in which W is the weight of the body in air at t° and p mm. pressure, W$_1$ the weight in water, atmospheric conditions remaining very nearly the same; ρ is the density of the water in which the body is weighed, α is (1 + αt°) in which α is the coefficient of cubical expansion of the body, and δ is the density of the air at t°, p mm. Less accurate formulae are Δ = ρ W/(W − W$_1$), the factor involving the density of the air, and the coefficient of the expansion of the solid being disregarded, and Δ = W/(W − W$_1$), in which the density of water is taken as unity. Reference may be made to J. Wade and R. W. Merriman, Journ. Chem. Soc. 1909, 95, p. 2174.
* Fig. 8.
The determination of the density of a liquid by weighing a plummet in air, and in the standard and experimental liquids, has been put into a very convenient laboratory form by means of the apparatus known as a Westphal balance (fig. 8). It consists of a steelyard mounted on a fulcrum; one arm carries at its extremity a heavy bob and pointer, the latter moving along a scale affixed to the stand and serving to indicate when the beam is in its standard position. The other arm is graduated in ten divisions and carries riders—bent pieces of wire of determined weights—and at its extremity a hook from which the glass plummet is suspended. To complete the apparatus there is a glass jar which serves to hold the liquid experimented with. The apparatus is so designed that when the plummet is suspended in air, the index of the beam is at the zero of the scale; if this be not so, then it is adjusted by a levelling screw. The plummet is now placed in distilled water at 15°, and the beam brought to equilibrium by means of a rider, which we shall call 1, hung on a hook; other riders are provided, 1/10th and 1/100th respectively of 1. To determine the density of any liquid it is only necessary to suspend the plummet in the liquid, and to bring the beam to its normal position by means of the riders; the relative density is read off directly from the riders.
3. Methods depending on the free suspension of the solid in a liquid of the same density have been especially studied by Retgers and Gossner in view of their applicability to density determinations of crystals. Two typical forms are in use; in one a liquid is prepared in which the crystal freely swims, the density of the liquid being ascertained by the pycnometer or other methods; in the other a liquid of variable density, the so-called “diffusion column,” is prepared, and observation is made of the level at which the particle comes to rest. The first type is in commonest use; since both necessitate the use of dense liquids, a summary of the media of most value, with their essential properties, will be given.
Acetylene tetrabromide, C$_2$H$_2$Br$_4$, which is very conveniently prepared by passing acetylene into cooled bromine, has a density of 3.001 at 6° C. It is highly convenient, since it is colourless, odourless, very stable and easily mobile. It may be diluted with benzene or toluene.
Methylene iodide, CH$_2$I$_2$, has a density of 3.33, and may be diluted with benzene. Introduced by Brauns in 1886, it was recommended by Retgers. Its advantages rest on its high density and mobility; its main disadvantages are its liability to decomposition, the originally colourless liquid becoming dark owing to the separation of iodine, and its high coefficient of expansion. Its density may be raised to 3.65 by dissolving iodoform and iodine in it.
Thoulet’s solution, an aqueous solution of potassium and mercuric iodides (potassium iodo-mercurate), introduced by Thoulet and subsequently investigated by V. Goldschmidt, has a density of 3.196 at 22.9°. It is almost colourless and has a small coefficient of expansion; its hygroscopic properties, its viscous character, and its action on the skin, however, militate against its use. A. Duboin (Compt. rend., 1905, p. 141) has investigated the solutions of mercuric iodide in other alkaline iodides; sodium iodo-mercurate solution has a density of 3.46 at 26°, and gives with an excess of water a dense precipitate of mercuric iodide, which dissolves without decomposition in alcohol; lithium iodo-mercurate solution has a density of 3.28 at 25.6°; and ammonium iodo-mercurate solution a density of 2.98 at 26°.
Rohrbach’s solution, an aqueous solution of barium and mercuric iodides, introduced by Carl Rohrbach, has a density of 3.588.
Klein’s solution, an aqueous solution of cadmium borotungstate, 2Cd(OH)$_2$·B$_2$O$_3$·9WO$_3$·16H$_2$O, introduced by D. Klein, has a density up to 3.28. The salt melts in its water of crystallization at 75°, and the liquid thus obtained goes up to a density of 3.6.
* Fig. 9. Brewster’s Staktometer
Silver-thallium nitrate, TlAg(NO$_3$)$_2$, introduced by Retgers, melts at 75° to form a clear liquid of density 4.8; it may be diluted with water.
The method of using these liquids is in all cases the same; a particle is dropped in; if it floats a diluent is added and the mixture well stirred. This is continued until the particle freely swims, and then the density of the mixture is determined by the ordinary methods (see Mineralogy).
In the “diffusion column” method, a liquid column uniformly varying in density from about 3.3 to 1 is prepared by pouring a little methylene iodide into a long test tube and adding five times as much benzene. The tube is tightly corked to prevent evaporation, and allowed to stand for some hours. The density of the column at any level is determined by means of the areometrical beads proposed by Alexander Wilson (1714–1786), professor of astronomy at Glasgow University. These are hollow glass beads of variable density; they may be prepared by melting off pieces of very thin capillary tubing, and determining the density in each case by the method just previously described. To use the column, the experimental fragment is introduced, when it takes up a definite position. By successive trials two beads, of known density, say d$_1$, d$_2$, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube. If the bead of density d$_1$ be at the distance l$_1$ above the crystal, and that of d$_2$ at l$_2$ below, it is obvious that if the density of the column varies uniformly, then the density of the test crystal is (d$_1$l$_2$ + d$_2$l$_1$)/(l$_1$ + l$_2$).
Acting on a principle quite different from any previously discussed is the capillary hydrometer or staktometer of Brewster, which is based upon the difference in the surface tension and density of pure water, and of mixtures of alcohol and water in varying proportions.
If a drop of water be allowed to form at the extremity of a fine tube, it will go on increasing until its weight overcomes the surface tension by which it clings to the tube, and then it will fall. Hence any impurity which diminishes the surface tension of the water will diminish the size of the drop (unless the density is proportionately diminished). According to Quincke, the surface tension of pure water in contact with air at 20° C. is 81 dynes per linear centimetre, while that of alcohol is only 25.5 dynes; and a small percentage of alcohol produces much more than a proportional decrease in the surface tension when added to pure water. The capillary hydrometer consists simply of a small pipette with a bulb in the middle of the stem, the pipette terminating in a very fine capillary point. The instrument being filled with distilled water, the number of drops required to empty the bulb and portions of the stem between two marks m and n (fig. 9) on the latter is carefully counted, and the experiments repeated at different temperatures. The pipette having been carefully dried, the process is repeated with pure alcohol or with proof spirits, and the strength of any admixture of water and spirits is determined from the corresponding number of drops, but the formula generally given is not based upon sound data. Sir David Brewster found with one of these instruments that the number of drops of pure water was 734, while of proof spirit, sp. gr. 920, the number was 2117.
References.—Density and density determinations are discussed in all works on practical physics; reference may be made to B. Stewart and W. W. Haldane Gee, Practical Physics, vol. i. (1901); Kohlrausch, Practical Physics; Ostwald, Physico-Chemical Measurements. The density of gases is treated in M. W. Travers, The Experimental Study of Gases (1901); and vapour density determinations in Lassar-Cohn’s Arbeitsmethoden für organisch-chemische Laboratorien (1901), and Manual of Organic Chemistry (1896), and in H. Biltz, Practical Methods for determining Molecular Weights (1899). (C. E.*)