SPECIFIC GRAVITY
It is one of our earliest experiences that different substances of
the same size have often markedly different weights; thus, there is
a great difference between wood and iron, and still greater between
wood and lead. It is usual to say that iron is heavier than wood,
but the statement is misleading, because it would be possible by
selecting a large enough piece of wood to find one at least as heavy
as a particular piece of iron. We have, in fact, to compare equal
volumes of the two substances, and all ambiguity is removed if we
speak of relative density or specific gravity—the former term being
usually applied to liquids and the latter to solids—instead of weight
or heaviness. The density of water at 4° C. is taken as unity, that
being the temperature at which it is highest; at other temperatures it
is somewhat lower, as will be seen from Table IX given at the end of
the book. The direct determination of the volume of an irregular solid
presents almost insuperable difficulty; but, fortunately, for finding
the specific gravity it is quite unnecessary to know the volume, as
will be shown when we proceed to consider the methods in use.
The specific gravity of a stone is a character which is within narrow
limits constant for each species, and is therefore very useful for
discriminative purposes. It can be determined whatever be the shape
of the stone, and it is immaterial whether it be transparent or not;
but, on the other hand, the stone must be unmounted and free from the
setting.
The methods for the determination of the specific gravity are of two
kinds: in the first a liquid is found of the same, or nearly the same,
density as the stone, and in the second weighings are made and the use
of an accurate balance is required.
(1) HEAVY LIQUIDS
Experiment tells us that a solid substance floats in a liquid denser
than itself, sinks in one less dense, and remains suspended at any
level in one of precisely the same density. If the stone be only
slightly less dense than the liquid, it will rise to the surface; if
it be just as slightly denser, it will as surely sink to the bottom,
a physical fact which has added so much to the difficulty and danger
of submarine manœuvring. If then we can find a liquid denser than the
stone to be tested, and place the latter in it, the stone will float on
the surface. If we take a liquid which is less dense than the stone and
capable of mixing with the heavier liquid, and add it to the latter,
drop by drop, gently stirring so as to assure that the density of
the combination is uniformly the same throughout, a stage is finally
reached when the stone begins to move downwards. It has now very nearly
the density of the liquid, and, if we find by some means this density,
we know simultaneously the specific gravity of the stone.
Various devices and methods are available for ascertaining the density
of liquids—for instance, Westphal’s balance; but, apart from the
inconvenience attending such a determination, the density of all
liquids is somewhat seriously affected by changes in the temperature,
and it is therefore better to make direct comparison with fragments
of substances of known specific gravity, which are termed indicators.
If of two fragments differing slightly in specific gravity one floats
on the surface of a uniform column of liquid and the other lies at
the bottom of the tube containing the liquid, we may be certain that
the density of the liquid is intermediate between the two specific
gravities. Such a precaution is necessary because, if the liquid be a
mixture of two distinct liquids, the density would tend to increase
owing to the greater volatility of the lighter of them, and in any case
the density is affected by change of temperature. The specific gravity
of stones is not much altered by variation in the temperature.
A more convenient variation of this method is to form a diffusion
column, so that the density increases progressively with the depth.
If the stone under test floats at a certain level in such a column
intermediate between two fragments of known specific gravity, its
specific gravity may be found by elementary interpolation. To form a
column of this kind the lighter liquid should be poured on to the top
of the heavier. Natural diffusion gives the most perfect column, but,
being a lengthy process, it may conveniently be quickened by gently
shaking the tube, and the column thus formed gives results sufficiently
accurate for discriminative purposes.
By far the most convenient liquid for ordinary use is methylene
iodide, which has already been recommended for its high refraction.
It has, when pure, a density at ordinary room-temperatures of 3·324,
and it is miscible in all proportions with benzol, whose density is
O·88, or toluol, another hydrocarbon which is somewhat less volatile
than benzol, and whose density is about the same, namely, 0·86. When
fresh, methylene iodide has only a slight tinge of yellow, but it
rapidly darkens on exposure to light owing to the liberation of iodine
which is in a colloidal form and cannot be removed by filtration.
The liquid may, however, be easily cleared by shaking it up with any
substance with which the iodine combines to form an iodide removable
by filtration. Copper filings answer the purpose well, though rather
slow in action; mercury may also be used, but is not very satisfactory,
because a small amount may be dissolved and afterwards be precipitated
on to the stone under test, carrying it down to the bottom of the tube.
Caustic potash (potassium hydroxide) is also recommended; in this case
the operation should preferably be carried out in a special apparatus
which permits the clear liquid to be drawn off underneath, because
water separates out and floats on the surface. In Fig. 32 three cut
stones, a quartz (_a_), a beryl (_b_), and a tourmaline (_c_) are shown
floating in a diffusion column of methylene iodide and benzol. Although
the beryl is only slightly denser than the quartz, it floats at a
perceptibly lower level. These three species are occasionally found as
yellow stones of very similar tint.
[Illustration: FIG. 32.—Stones of different Specific Gravities floating
in a Diffusion Column of heavy Liquid.]
Various other liquids have been used or proposed for the same
purpose, of which two may be mentioned. The first of them is a
saturated solution of potassium iodide and mercuric iodide in water,
which is known after the discoverer as Sonstadt’s solution. It is a
clear mobile liquid with an amber colour, having at 12° C. a density
of 3·085; it may be mixed with water to any extent, and is easily
concentrated by heating; moreover, it is durable and not subject to
alteration of any kind; on the other hand, it is highly poisonous and
cauterizes the skin, not being checked by albumen; it also destroys
brass-ware by amalgamating the metal. The second is Klein’s solution,
a clear yellow liquid which has at 15° C. a density of 3·28. It
consists of the boro-tungstate of cadmium, of which the formula is
9WO_{3}.B_{2}O_{3}.2CdO.2H_{2}O + 16Aq, dissolved in water, with which
it may be diluted. If the salt be heated, it fuses at 75° C. in its
own water of crystallization to a yellow liquid, very mobile, with a
density of 3·55. Klein’s solution is harmless, but it cannot compare
for convenience of manipulation with methylene iodide.
The most convenient procedure is to have at hand three glass tubes,
fitted with stoppers or corks, to contain liquids of different
densities—
(_a_) Methylene iodide reduced to 2·7; using as indicators orthoclase
2·55, quartz 2·66, and beryl 2·74.
(_b_) Methylene iodide reduced to 3·1; indicators, beryl 2·74 and
tourmaline 3·10.
(_c_) Methylene iodide, undiluted, 3·32.
The pure liquid in the last tube should on no account be diluted; but
the density of the other two liquids may be varied slightly, either
by adding benzol in order to lower it, or by allowing benzol, which
has far greater volatility than methylene iodide, to evaporate, or by
adding methylene iodide, in order to increase it. The density of the
liquids may be ascertained approximately from the indicators.
A glance at the table of specific gravities shows that as regards the
gem-stones methylene iodide is restricted in its application, since
it can be used to test only moonstone, quartz, beryl, tourmaline, and
spodumene; opal and turquoise, being amorphous and more or less porous,
should not be immersed in liquids, lest the appearance of the stone be
irretrievably injured. Methylene iodide readily serves to distinguish
the yellow quartz from the true topaz, with which jewellers often
confuse it, the latter stone sinking in the liquid; again aquamarine
floats, but the blue topaz, which is often very similar to it, sinks in
methylene iodide.
By saturating methylene iodide with iodine and iodoform, we have a
liquid (_d_) of density 3·6; a fragment of topaz, 3·55, may be used to
indicate whether the liquid has the requisite density. Unfortunately
this saturated solution is so dark as to be almost opaque, and is,
moreover, very viscous. Its principal use is to distinguish diamond,
3·535, from the brilliant colourless zircon, with which, apart from
a test for hardness, it may easily be confused. It is easy to see
whether the stone floats, as it would do if a diamond. To recover a
stone which has sunk, the only course is to pour off the liquid into
another tube, because it is far too dark for the position of the stone
to be seen.
It is possible to employ a similar method for still denser stones by
having recourse to Retgers’s salt, silver-thallium nitrate. This double
salt is solid at ordinary room-temperatures, but has the remarkable
property of melting at a temperature, 75° C., which is well below the
point of fusion of either of its constituents, to a clear, mobile
yellow liquid, which is miscible in any proportion with water, and
has, when pure, a density of 4·6. The salt may be purchased, or it may
be prepared by mixing 100 grams of thallium nitrate and 64 grams of
silver nitrate, or similar proportions, in a little water, and heating
the whole over a water-bath, keeping it constantly stirred with a
glass rod until it is liquefied. The two salts must be mixed in the
correct proportions, because otherwise the mixture might form other
double salts, which do not melt at so low a temperature. A glance at
the table of specific gravities shows that Retgers’s salt may be used
for all the gem-stones with the single exception of zircon (b). There
are, however, some objections to its use. It is expensive, and, unless
kept constantly melted, it is not immediately available. It darkens on
exposure to strong sunlight like all silver salts, stains the skin a
peculiar shade of purple which is with difficulty removed, and in fact
only by abrasion of the skin, and, like all thallium compounds, is
highly poisonous.
It is convenient to have three tubes, fitted as before with stoppers
or corks, to contain the following liquids, when heated:—
(_e_) Silver-thallium nitrate, reduced to 3·5; using as indicators,
peridot or idocrase 3·40 and topaz 3·53.
(_f_) Silver-thallium nitrate, reduced to 4·0; indicators, topaz 3·53
and sapphire 4·03.
(_g_) Silver-thallium nitrate, undiluted, 4·6.
The tubes must be heated in some form of water-bath; an ordinary glass
beaker serves the purpose satisfactorily. The pure salt should never be
diluted; but the density of the contents of tubes (_e_) and (_f_) may
be varied at will, water being added in order to lower the density, and
concentration by means of evaporation or addition of the nitrate being
employed in order to increase it. To avoid the discoloration of the
skin, rubber finger-stalls may be used, and the stones should not be
handled until after they have been washed in warm water. The staining
may be minimized if the hands be well washed in hot water before being
exposed to sunlight. It is advisable to warm the stone to be tested
in a tube containing water beforehand lest the sudden heating develop
cracks. A piece of platinum, or, failing that, copper wire is of
service for removing stones from the tubes; a glass rod, spoon-shaped
at one end, does equally well. It must be noted that although Retgers’s
salt is absolutely harmless to the ordinary gem-stones—with the
exception of opal and turquoise, which, as has already been stated,
being to some extent porous, should not be immersed in liquids—it
attacks certain substances, for instance, sulphides and cannot be
applied indiscriminately to minerals.
The procedure described above is intended only as a suggestion;
the method may be varied to any extent at will, depending upon the
particular requirements. If such tests are made only occasionally, a
smaller number of tubes may be used. Thus one tube may be substituted
for the two marked _a_ and _b_, the liquid contained in it being
diluted as required, and a series of indicators may be kept apart in
small glass tubes. On the other hand, any one having constantly to test
stones might increase the number of tubes with advantage, and might
find it useful to have at hand fragments of all the principal species
in order to make direct comparison.
(2) DIRECT WEIGHING
The balance which is necessary in both the methods described under this
head should be capable of giving results accurate to milligrams, _i.e._
the thousandth part of a gram, and consistent with that restriction
the beam may be as short as possible so as to give rapid swings and
thus shorten the time taken in the observations. A good assay balance
answers the purpose admirably. Of course, it is never necessary to wait
till the balance has come to rest. The mean of the extreme readings of
the pointer attached to the beam will give the position in which it
would ultimately come to rest. Thus, if the pointer just touches the
eighth division on the right-hand side and the second on the other,
the mean position is the third division on the right-hand side (½(8 −
2) = 3). Instead of the ordinary form of chemical balance, Westphal’s
form or Joly’s spring-balance may be employed. Weighings are made more
quickly, but are not so accurate.
In refined physical work the practice known as double-weighing is
employed to obviate any slight error there may be in the suspension
of the balance. A counterpoise which is heavier than anything to be
weighed is placed in one pan, and weighed. The counterpoise is retained
in its pan throughout the whole course of the weighings. Any substance
whose weight is to be found is placed in the other pan, and weights
added till the balance swings truly again. The difference between
the two sets of weights evidently gives the weight of the substance.
Balances, however, are so accurately constructed that for testing
purposes such refined precautions are not really necessary.
It is immaterial in what notation the weighings are made, so long as
the same is used throughout, but the metric system of weights, which
is in universal use in scientific work, should preferably be employed.
Jewellers, however, use carat weights, and a subdivision to the base
2 instead of decimals, the fractions being ½, ¼, ⅛, 1/16, 1/32, 1/64.
If these weights be employed, it will be necessary to convert these
fractions into decimals, and write ½ = ·500, ¼ ·250, ⅛ = ·125, 1/16 =
·062, 1/32 = ·031, 1/64 = ·016.
(a) _Hydrostatic Weighing_
The principle of this method is very simple. The stone, the specific
gravity of which is required, is first weighed in air and then when
immersed in water. If _W_ and _W´_ be these weights respectively, then
_W_ − _W´_ is evidently the weight of the water displaced by the stone
and having therefore the same volume as it, and the specific gravity is
_W_
therefore equal to ———————————.
_W_ − _W^r_
If the method of double-weighing had been adopted, the formula would
be slightly altered. Thus, suppose that _c_ corresponds to the
counterpoise, _w_ and _w´_ to the stone weighed in air and water
respectively; then we have _W_ = _c_ − _w_ and _W´_ = _c_ − _w´_, and
_c_ − _w_
therefore the specific gravity is equal to ——————————.
_w´_ − _w_
[Illustration: FIG. 33.—Hydrostatic Balance.]
Some precautions are necessary in practice to assure an accurate
result. A balance intended for specific gravity work is provided with
an auxiliary pan (Fig. 33), which hangs high enough up to permit of
the stone being suspended underneath. The weight of anything used for
the suspension must, of course, be determined and subtracted from the
weight found for the stone, both when in air and when in water. A piece
of fine silk is generally used for suspending the stone in water,
but it should be avoided, because the water tends to creep up it and
the error thus introduced affects the first place of decimals in the
case of a one-carat stone, the value being too high. A piece of brass
wire shaped into a cage is much to be preferred. If the same cage be
habitually used, its weight in air and when immersed in water to the
customary extent in such determinations should be found once for all.
Care must also be taken to remove all air-bubbles which cling to the
stone or the cage; their presence would tend to make the value too low.
The surface tension of water which makes it cling to the wire prevents
the balance swinging freely, and renders it difficult to obtain a
weighing correct to a milligram when the wire dips into water. This
difficulty may be overcome by substituting a liquid such as toluol,
which has a much smaller surface tension.
As has been stated above, the density of water at 4° C. is taken as
unity, and it is therefore necessary to multiply the values obtained
by the density of the liquid, whatever it be, at the temperature of
the observation. In Table IX, at the end of the book, are given the
densities of water and toluol at ordinary room-temperatures. It will be
noticed that a correct reading of the temperature is far more important
in the case of toluol.
_Example of a Hydrostatic Determination of Specific Gravity—_
Weight of stone in air = 1·471 gram
Weight of stone in water = 1·067 „
1·471 1·471
Specific gravity = ————————————— = —————
1·471 − 1·067 0·404.
Allowing for the density of water at the temperature of the room, which
was 16° C., the specific gravity is 3·637. Had no such allowance been
made, the result would have been four units too high in the third place
of decimals. For discriminative purposes, however, such refinement is
unnecessary.
(b) _Pycnometer, or Specific Gravity Bottle_
The specific gravity bottle is merely one with a fairly long neck on
which a horizontal mark has been scratched, and which is closed by
a ground glass stopper. The pycnometer is a refined variety of the
specific gravity bottle. It has two openings: the larger is intended
for the insertion of the stone and the water, and is closed by a
stopper through which a thermometer passes, while the other, which is
exceedingly narrow, is closed by a stopper fitting on the outside, and
is graduated to facilitate the determination of the height of the water
in it.
The stone is weighed as in the previous method. The bottle is then
weighed, and filled with water up to the mark and weighed again. The
stone is now introduced into the bottle, and the surplus water removed
with blotting-paper or otherwise until it is at the same level as
before, and the bottle with its contents is weighed. Let _W_ be the
weight of the stone, _w_ the weight of the bottle, _W_´ the weight of
the bottle and the water contained in it, and _W_″ the weight of the
bottle when containing the stone and the water. Then _W_´ − _w_ is the
weight of the water filling the bottle up to the mark, and
_W_″ − _w_ − _W_ is the reduced weight of water after the stone has
been inserted; the difference, _W_ + _W_´ − _W_″, is the weight of the
_W_
water displaced. The specific gravity is therefore ——————————————————.
_W_ + _W_´ − _W_″
As in the previous method, this value must be multiplied by the density
of the liquid at the temperature of the experiment. If the method of
double-weighing be adopted, the formula will be slightly modified.
• • • • •
Of the above methods, that of heavy liquids, as it is usually termed,
is by far the quickest and the most convenient for stones of ordinary
size, the specific gravity of which is less than the density of pure
methylene iodide, namely, 3·324, and by its aid a value may be obtained
which is accurate to the second place of decimals, a result quite
sufficient for a discriminative test. The method is applicable no
matter how small the stone may be, and, indeed, for very small stones
it is the only trustworthy method; for large stones it is inconvenient,
not only because of the large quantity of liquid required, but also
on account of the difficulty in estimating with sufficient certainty
the position of the centre of gravity of the stone. A negative
determination may be of value, especially if attention be paid to the
rate at which the stone falls through the liquid; the denser the stone
the faster it will sink, but the rate depends also upon the shape of
the stone. Retgers’s salt is less convenient because of the delay
involved in warming it and of the almost inevitable staining of the
hands, but its use presents no difficulty whatever.
Hydrostatic weighing is always available, unless the stone be very
small, but the necessary weighings occupy considerable time, and care
must be taken that no error creeps into the computation, simple though
it be. Even if everything is at hand, a determination is scarcely
possible under a quarter of an hour.
The third method, which takes even longer, is intended primarily for
powdered substances, and is not recommended for cut stones, unless
there happen to be a number of tiny ones which are known to be exactly
of the same kind.
The specific gravities of the gem-stones are given in Table VII at the
end of the book.