Chapter II: Forensic Speeches (6)

DENOTATION (from Lat. _denotare_, to mark out, specify), in logic, a technical term used strictly as the correlative of Connotation, to describe one of the two functions of a concrete term. The concrete term "connotes" attributes and "denotes" all the individuals which, as possessing these attributes, constitute the genus or species described by the term. Thus "cricketer" denotes the individuals who play cricket, and connotes the qualities or characteristics by which these individuals are marked. In this sense, in which it was first used by J. S. Mill, Denotation is equivalent to Extension, and Connotation to Intension. It is clear that when the given term is qualified by a limiting adjective the Denotation or Extension diminishes, while the Connotation or Intension increases; e.g. a generic term like "flower" has a larger Extension, and a smaller Intension than "rose": "rose" than "moss-rose." In more general language Denotation is used loosely for that which is meant or indicated by a word, phrase, sentence or even an action. Thus a proper name or even an abstract term is said to have Denotation. (See CONNOTATION.)

DENS, PETER (1690-1775), Belgian Roman Catholic theologian, was born at Boom near Antwerp. Most of his life was spent in the archiepiscopal college of Malines, where he was for twelve years reader in theology and for forty president. His great work was the _Theologia moralis et dogmatica_, a compendium in catechetical form of Roman Catholic doctrine and ethics which has been much used as a students' text-book. Dens died on the 15th of February 1775.

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 [Delta] = 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 [Delta] = 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 lb. 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 lb.. 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

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.

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).

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.

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.

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).

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.

(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.)

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.

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.

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.

DENTISTRY

Historical sketch.

(from Lat. _dens_, a tooth), a special department of medical science, embracing the structure, function and therapeutics of the mouth and its contained organs, specifically the teeth, together with their surgical and prosthetic treatment. (For the anatomy of the teeth see TEETH.) As a distinct vocation it is first alluded to by Herodotus (500 B.C.). There are evidences that at an earlier date the Egyptians and Hindus attempted to replace lost teeth by attaching wood or ivory substitutes to adjacent sound teeth by means of threads or wires, but the gold fillings reputed to have been found in the teeth of Egyptian mummies have upon investigation been shown to be superficial applications of gold leaf for ornamental purposes. The impetus given to medical study in the Grecian schools by the followers of Aesculapius and especially Hippocrates (500 to 400 B.C.) developed among the practitioners of medicine and surgery considerable knowledge of dentistry. Galen (A.D. 131) taught that the teeth were true bones existing before birth, and to him is credited the belief that the upper canine teeth receive branches from the nerve which supplies the eye, and hence should be called "eye-teeth." Abulcasis (10th cent. A.D.) describes the operation by which artificial crowns are attached to adjacent sound teeth. Vesalius (1514), Ambroise Paré, J. J. Scaliger, T. Kerckring, M. Malpighi, and lesser anatomists of the same period contributed dissertations which threw some small amount of light upon the structure and functions of the teeth. The operation of transplanting teeth is usually attributed to John Hunter (1728-1793), who practised it extensively, and gave to it additional prominence by transplanting a human tooth to the comb of a cock, but the operation was alluded to by Ambroise Paré (1509-1590), and there is evidence to show that it was practised even earlier. A. von Leeuwenhoek in 1678 described with much accuracy the tubular structure of the dentine, thus making the most important contribution to the subject which had appeared up to that time. Until the latter part of the 18th century extraction was practically the only operation for the cure of toothache.

The early contributions of France exerted a controlling influence upon the development of dental practice. Urbain Hémard, surgeon to the cardinal Georges of Armagnac, whom Dr Blake (1801) calls an ingenious surgeon and a great man, published in 1582 his _Researches upon the Anatomy of the Teeth, their Nature and Properties_. Of Hémard, M. Fauchard says: "This surgeon had read Greek and Latin authors, whose writings he has judiciously incorporated in his own works." In 1728 Fauchard, who has been called the father of modern dentistry, published his celebrated work, entitled _Le Chirurgien Dentiste ou traité des dents_. The preface contains the following statement as to the existing status of dental art and science in France, which might have been applied with equal truth to any other European country:--" The most celebrated surgeons having abandoned this branch of surgery, or having but little cultivated it, their negligence gave rise to a class of persons who, without theoretic knowledge or experience, and without being qualified, practised it at hazard, having neither principles nor system. It was only since the year 1700 that the intelligent in Paris opened their eyes to these abuses, when it was provided that those who intended practising dental surgery should submit to an examination by men learned in all the branches of medical science, who should decide upon their merits." After the publication of Fauchard's work the practice of dentistry became more specialized and distinctly separated from medical practice, the best exponents of the art being trained as apprentices by practitioners of ability, who had acquired their training in the same way from their predecessors. Fauchard suggested porcelain as an improvement upon bone and ivory for the manufacture of artificial teeth, a suggestion which he obtained from R. A. F. de Réaumur, the French savant and physicist, who was a contributor to the royal porcelain manufactory at Sévres. Later, Duchateau, an apothecary of St Germain, made porcelain teeth, and communicated his discovery to the Academy of Surgery in 1776, but kept the process secret. Du Bois Chémant carried the art to England, and the process was finally made public by M. Du Bois Foucou. M. Fonzi improved the art to such an extent that the Athenaeum of Arts in Paris awarded him a medal and crown (March 14, 1808).

In Great Britain the 19th century brought the dawning of dental science. The work of Dr Blake in 1801 on the anatomy of the teeth was distinctly in advance of anything previously written on the subject. Joseph Fox was one of the first members of the medical profession to devote himself exclusively to dentistry, and his work is a repository of the best practice of his time. The processes described, though comparatively crude, involve principles in use at the present time. Thomas Bell, the successor of Fox as lecturer on the structure and disease of the teeth at Guy's Hospital, published his well-known work in 1829. About this period numerous publications on dentistry made their appearance, notably those of Koecker, Johnson and Waite, followed somewhat later by the admirable work of Alexander Nasmyth (1839). By this time Cuvier, Serres, Rousseau, Bertin, Herissant and others in France had added to the knowledge of human and comparative dental anatomy, while M. G. Retzius, of Sweden, and E. H. Weber, J. C. Rosenmüller, Schreger, J. E. von Purkinje, B. Fraenkel and J. Müller in Germany were carrying forward the same lines of research. The sympathetic nervous relationships of the teeth with other parts of the body, and the interaction of diseases of the teeth with general pathological conditions, were clearly established. Thus a scientific foundation was laid, and dentistry came to be practised as a specialty of medicine. Certain minor operations, however, such as the extraction of teeth and the stopping of caries in an imperfect way, were still practised by barbers, and the empirical practice of dentistry, especially of those operations which were almost wholly mechanical, had developed a considerable body of dental artisans who, though without medical education in many cases, possessed a high degree of manipulative skill. Thus there came to be two classes of practitioners, the first regarding dentistry as a specialty of medicine, the latter as a distinct and separate calling.

In America representatives of both classes of dentists began to arrive from England and France about the time of the Revolution. Among these were John Wooffendale (1766), a student of Robert Berdmore of Liverpool, surgeon-dentist to George III.; James Gardette (1778), a French physician and surgeon; and Joseph Lemaire (1781), a French dentist who went out with the army of Count Rochambeau. During the winter of 1781-1782, while the Continental army was in winter quarters at Providence, Rhode Island, Lemaire found time and opportunity to practise his calling, and also to instruct one or two persons, notably Josiah Flagg, probably the first American dentist. Dental practice was thus established upon American soil, where it has produced such fertile results.

Course of training.