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 air-tight 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.
[Illustration: FIG. 1.--Say's Stereometer.]
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 +
al¹)(h - k¹) = uh, whence u = al¹(h - k¹)/k¹. 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).
[Illustration: FIG. 2.]
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.
Another type of vessel, named the Sprengel tube or pycnometer (Gr.
[Greek: pyknos], 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.
[Illustration: FIG. 3.]
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.
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.
[Illustration: FIG. 4.]
The result is calculated by means of the formula:
W(1 + [alpha]t) × 7,980,000
D = -------------------------------------------------------------------------------,
(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; [alpha] = 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;
[beta] = coefficient of expansion of glass = .0000303; [gamma] =
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).
[Illustration: 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:
W(1 + [alpha]t) x 587,780
D = -------------------------,
(p - s)V
in which W = weight of substance taken, V = volume of air expelled,
[alpha] = 1/273 = .003665, t and p = temperature and pressure at
which expelled air is measured, and s = vapour pressure of water at
t°.
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°), phosphoruspentasulphide (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.
[Illustration: FIG. 6.]
(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:--
760w(1 + 0.003665t)
D = -------------------;
0.0012934 × V × B
h / h_1 h_2 \
B = -------------- - ( -------------- - ------------ + s),
1 + 0.00018t_1 \1 + 0.00018t_2 1 + 0.00018t /
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.)
[Illustration: 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
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 [Delta] = 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 [Delta](0°/4°) is given by
[Delta](0°/4°) = ([rho][alpha]W - [delta]W_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; [rho] is the density of the water in which the body is
weighed, [alpha] is (1 + [alpha]t°) in which a is the coefficient of
cubical expansion of the body, and [delta] is the density of the air at
t°, p mm. Less accurate formulae are [Delta] = [rho] W/(W - W_1), the
factor involving the density of the air, and the coefficient of the
expansion of the solid being disregarded, and [Delta] = 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.
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, {1/10}th and {1/100}th 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.
[Illustration: FIG. 8.]
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.
_Silver-thallium nitrate_, TIAg(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.
[Illustration: FIG. 9. Brewster's Staktometer]
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.*)
DENTATUS, MANIUS CURIUS, Roman general, conqueror of the Samnites and
Pyrrhus, king of Epirus, was born of humble parents, and was possibly of
Sabine origin. He is said to have been called Dentatus because he was
born with his teeth already grown (Pliny, _Nat. Hist._ vii. 15). Except
that he was tribune of the people, nothing certain is known of him until
his first consulship in 290 B.C. when, in conjunction with his colleague
P. Cornelius Rufinus, he gained a decisive victory over the Samnites,
which put an end to a war that had lasted fifty years. He also reduced
the revolted Sabines to submission; a large portion of their territory
was distributed among the Roman citizens, and the most important towns
received the citizenship without the right of voting for magistrates
(_civitas sine suffragio_). With the proceeds of the spoils of the war
Dentatus cut an artificial channel to carry off the waters of Lake
Velinus, so as to drain the valley of Reate. In 275, after Pyrrhus had
returned from Sicily to Italy, Dentatus (again consul) took the field
against him. The decisive engagement took place near Beneventum in the
Campi Arusini, and resulted in the total defeat of Pyrrhus. Dentatus
celebrated a magnificent triumph, in which for the first time a number
of captured elephants were exhibited. Dentatus was consul for the third
time in 274, when he finally crushed the Lucanians and Samnites, and
censor in 272. In the latter capacity he began to build an aqueduct to
carry the waters of the Anio into the city, but died (270) before its
completion. Dentatus was looked upon as a model of old Roman simplicity
and frugality. According to the well-known anecdote, when the Samnites
sent ambassadors with costly presents to induce him to exercise his
influence on their behalf in the senate, they found him sitting on the
hearth and preparing his simple meal of roasted turnips. He refused
their gifts, saying that earthen dishes were good enough for him, adding
that he preferred ruling those who possessed gold to possessing it
himself. It is also said that he died so poor that the state was obliged
to provide dowries for his daughters. But these and similar anecdotes
must be received with caution, and it should be remembered that what was
a competence in his day would have been considered poverty by the Romans
of later times.
Livy, epitome, 11-14; Polybius ii. 19; Eutropius ii. 9, 14; Florus i.
18; Val. Max. iv. 3, 5, vi. 3, 4; Cicero, _De senectute_, 16; Juvenal
xi. 78; Plutarch, _Pyrrhus_, 25.
DENTIL (from Lat. _dens_, a tooth), in architecture, a small
tooth-shaped block used as a repeating ornament in the bed-mould of a
cornice. Vitruvius (iv. 2) states that the dentil represents the end of
a rafter (_asser_); and since it occurs in its most pronounced form in
the Ionic temples of Asia Minor, the Lycian tombs and the porticoes and
tombs of Persia, where it represents distinctly the reproduction in
stone of timber construction, there is but little doubt as to its
origin. The earliest example is that found on the tomb of Darius, c. 500
B.C., cut in the rock in which the portico of his palace is reproduced.
Its first employment in Athens is in the cornice of the caryatid portico
or tribune of the Erechtheum (480 B.C.). When subsequently introduced
into the bed-mould of the cornice of the choragic monument of Lysicrates
it is much smaller in its dimensions. In the later temples of Ionia, as
in the temple of Priene, the larger scale of the dentil is still
retained. As a general rule the projection of the dentil is equal to its
width, and the intervals between to half the width. In some cases the
projecting band has never had the sinkings cut into it to divide up the
dentils, as in the Pantheon at Rome, and it is then called a
dentil-band. The dentil was the chief decorative feature employed in the
bed-mould by the Romans and the Italian Revivalists. In the porch of the
church of St John Studius at Constantinople, the dentil and the interval
between are equal in width, and the interval is splayed back from top to
bottom; this is the form it takes in what is known as the "Venetian
dentil," which was copied from the Byzantine dentil in Santa Sophia,
Constantinople. There, however, it no longer formed part of a bed-mould:
its use at Santa Sophia was to decorate the projecting moulding
enclosing the encrusted marbles, and the dentils were cut alternately on
both sides of the moulding. The Venetian dentil was also introduced as a
label round arches and as a string course.