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of element weighed is one gram, and its rise of
temperature one degree, the numerical value of this
product is about 6*4.

Now the specific heat of mercury has been
found to equal 0'032 ; that is to say, it requires



vi THE PROPERTIES OF ARGON 199

only a fraction of the value of 0*032 of a unit of
heat to raise the temperature of say 1 gram of
mercury through one degree, whereas the amount
of heat necessary to raise 1 gram of water through
one degree is represented by the number 1. Hence
this number, 0'032, multiplied by the atomic
weight of mercury, should yield the product 6'4 ;
and it is seen at once that that number must be
200, for 200x0-032 = 6-4. This is an additional
reason for believing that the atomic weight of
mercury must be represented by the number
200.

We come next to a confirmatory piece of
evidence which greatly strengthens the view that
the atomic weight of mercury must be 200 ; but
before entering into detail let us see what an
atomic weight of 200 involves. The density of
mercury gas is 100, and its molecular weight must
be 200. But if its atomic weight is also 200, it
follows of necessity that its molecule and its atom
must be identical ; that unlike oxygen and hydro-
gen, its molecule consists, not of two atoms, but of
one single atom. There is nothing strange in this
conclusion ; there is no evident reason why single
atoms should not act as molecules, or independent



200 THE GASES OF THE ATMOSPHERE CHAP.



particles, able to exist in a free state, uncombined
with each other or with any other molecules.

The specific heat of a gas is measured in much
the same manner as that of a solid. A known
volume of the gas is caused to pass through a
spiral tube, heated to a certain definite high tem-
perature ; it then enters a vessel containing a
known weight of water, traverses a spiral tube
immersed in the water, and parts with its heat to
the water. Knowing, therefore, the weight of
the gas and its initial temperature, and also the
rise of temperature of the water, the specific heat
of the gas can be compared with that required to
raise an equal weight of water through one degree.
But gases are found to possess two specific heats.
If the volume of the gas is kept constant, so that
the gas does not contract during its loss of heat,
one number for its specific heat is obtained ; while
if it is allowed to alter its volume a higher figure
represents its specific heat. It will be necessary to
consider the cause of this difference, in order to un-
derstand what conclusions can be drawn respecting
the molecular nature of argon from a determination
of the ratio between its two specific heats that at
constant pressure and that at constant volume.



vi THE PROPERTIES OF ARGON 201

If a gas is allowed to expand into a vertical
cylinder so as to drive up a piston loaded with a
weight, it is said to "do work/' The work is
measured by the weight on the piston, and also by
the height to which it is raised. Thus, if the
weight is one pound, and the height one foot, one
foot-pound of work is done ; if the mass is one
gram and the height one centimetre, one gram-
centimetre of work is done. During this process
the gas must expand ; and if it were enclosed in
some form of casing through which heat could not
pass we know of no such casing, but we can con-
trive casings through which heat passes very slowly
the temperature of the gas would fall during its
expansion, and it would lose heat. For each loss
of one heat-unit or calory i.e. the amount of heat
given off by 1 gram of water in cooling through 1
Centigrade the gas would perform 42,380 gram-
centimetres of work ; it would raise a weight of
nearly 4j kilograms, or about 9j Ibs., through 1
centimetre, or nearly half an inch.

When a gas expands into the atmosphere it
may be regarded as "raising the atmosphere"
through a certain height, for the atmosphere
possesses weight, equal on the average to 1033



202 THE GASES OF THE ATMOSPHERE CHAP.

grams on each square centimetre of the earth's
surface, or between 15 and 16 Ibs. on each square
inch. Suppose a quantity of air, weighing 1 gram,
to be enclosed in a long cylindrical tube of one
square centimetre in section. At the usual pressure
of the atmosphere on the earth's surface, and at
Centigrade, the volume of the air would be 773*3
cubic centimetres ; and, as the sectional area of the
tube is 1 square centimetre, the air would occupy
773*3 centimetres' length of the tube. If heat be
given to this air, so that its temperature is raised
from to 1, it will expand, as Gay-Lussac
showed, by ^^rd of its volume. Now the product
of 773*3 and ^fg- is 2*83 centimetres; the level of
the surface of the air will rise in the tube through
that amount. In doing so it will perform the work
of raising 1033 grams through 2*83 centimetres,
or 2927 gram-centimetres. Careful measurements
have shown that, in order to do this work, heat to the
amount of 0*0692 calory must be given to the gas.
But it has been found that to heat the air through
one degree, without allowing it to expand, requires
0*1683 calory; that is, the same amount of heat
which would raise a gram of air through one
degree, its volume being kept constant, will raise a



vi THE PROPERTIES OF ARGON 203

gram of water through 0*1683 ; or, in other words,
the specific heat of air is 0*1683. But if allowed
to expand, more heat is required an additional
0*0692 calory must be given it; consequently its
specific heat at constant pressure is greater ; it is
actually the sum of these two numbers, 0*1683 -f
0*0692 = 0-2375.
We have thus

Specific heat at constant pressure . 0'2375

volume ; 0-1683

0'2375



Ratio between these numbers :



/ns
U'lboo



This ratio is termed the ratio between the specific
heats of air, and such a ratio is represented usually
by the letter 7.

But it is not necessary to determine both kinds
of specific heat in order to arrive at a knowledge
of the value of this ratio. One plan, adopted by
Gay-Lussac and Desormes at the suggestion of
Laplace, 1 is to actually measure the fall of tem-
perature by allowing a known volume of gas, of
which the weight can of course be deduced, to
expand from a pressure somewhat higher than that
of the atmosphere to atmospheric pressure. It is

1 Mtchanique ctteste, vol. v. p. 123.



204 THE GASES OF THE ATMOSPHERE CHAP.

true that heat will rapidly flow in through the
walls of the vessel ; but by choosing a sufficiently
large vessel, and surrounding its walls with badly-
conducting material, the entry of heat will be
so slow that it may, for practical purposes, be
neglected. The number for this ratio, actually
found by Gay-Lussac and Welters for air, was
1*376; but subsequent and more accurate experi-
ments have given as a result 1*405, which is almost
identical with that calculated above.

This method, however, can be employed only
when an unlimited supply of gas is at disposal, for it
entails the use of large vessels, and the compressed
gas must be allowed to escape into the atmosphere,
and is lost. There is, fortunately, another method
by which the same results can be obtained, and
which requires only a small amount of gas.

Sir Isaac Newton calculated that the velocity
of sound in a gas was dependent on its pressure
and on its density, in such a manner that

5

where c stands for velocity (celerity), p for
pressure, and d for density. When waves of sound
are transmitted through air, the air is compressed



vi THE PROPERTIES OF ARGON 205

in parts and rarefied in parts, in such a manner that
compression follows rarefaction very rapidly, that
part which is compressed at one instant being rarefied
at the next, compressed again at a third, and rarefied
at a fourth, and so on. Laplace was the first to
point out that during such rapid changes of pressure
as occur while a sound-wave is passing, the pressure
will not rise proportionally to the density, as
would be the case if Boyle's law were followed ; for
on sudden rise of pressure the temperature of the
compressed portion of the gas will be increased;
and, correspondingly, on sudden fall of pressure, the
wave of compression having passed, the temperature
will fall. He showed that instead of two pressures
being inversely proportional to their two volumes,
under such circumstances, as they are according
to Boyle's law, or

Pi v *

they must be inversely proportional to the volumes
raised to a power, the numerical expression of
which is the ratio of the specific heats of the two
gases, 7, thus;



or as



2o6 THE GASES OF THE ATMOSPHERE CHAP.

v* : v :: d: d*, c = I y^ 7 , and y = .
\] I d p

The ratio of the two specific heats can therefore be
determined by finding the velocity of sound in the
gas, and by noting at the same time its density and
its pressure.

To determine the velocity of sound in a gas it
is not necessary to adopt the plan which has been
successfully carried out with air ; that is, to make
a sudden sound at one spot and to measure the
interval of time which the sound takes to travel
to another spot some miles distant. There is a
simpler method, depending on the fact that the
lengths of the waves of compression and rarefaction
are proportional to the velocity of the sound. So
that, knowing the velocity of sound in air, the
velocity in any other gas may be found by deter-
mining the relative length of the sound-waves in
air and in that gas.

The simple apparatus with which such deter-
minations are made is due to the physicist Kundt.
It consists of a glass tube, through one end of which
a glass rod passes, so that half the rod. is enclosed
in the tube, while the other half projects outside
it. In the experiments on argon, the rod was



vi THE PROPERTIES OF ARGON 207

sealed into the tube ; in other cases it is better to
attach it with indiarubber, or to cause the rod to
pass through a cork. The open end of the tube is
connected with a supply of the gas, so that, after







FIG. 4.

the tube has been pumped empty of air, the gas, in
a pure and dry condition, can be admitted. Some
light powder (and for this purpose lycopodium dust
the dried spores of a species of clubmoss is best)
is placed in the tube, and distributed uniformly
throughout it, so that when the latter is in a hori-
zontal position, a streak of the powder lies along it
from end to end. The portion of rod outside the
tube is rubbed with a rag wetted with alcohol, when
it emits a shrill tone or squeak, due to longitudinal
vibrations ; the pitch of the tone depends, naturally,
on the length of the rod, a long rod giving a deeper
tone than a short one. The vibrations of the rod
set the gas in the tube in motion, and the sound-
waves are conveyed from end to end of the tube
through the gas. As the tube is closed at the end
through which the gas was admitted, these waves



208 THE GASES OF THE ATMOSPHERE CHAP.



echo back through it ; and a great deal of care
must be taken to make the echo strengthen the
waves, so that the compressions produced by the
back waves are coincident in position with the com-
pressions produced by the forward waves travelling
onwards from the rod. The gas, could we see it,
would represent portions compressed and portions
rarefied at regular intervals along the tube. Where
the gas is compressed, it gathers the lycopodium
dust together in small heaps, the position of each
heap signifying a node of compression. Hence,
comparing the distances between the nodes of
compression for any gas and for air, we find
the relative wave-lengths of sound in the two
gases; and, as the velocity of sound in air
has been accurately measured, we thus determine
the velocity of sound-waves in the gas under
experiment.

Such experiments were made by Kundt and by
his co-worker Warburg on mercury gas, and they
found that in this case the value of 7 was 1*67;
that is, in the equation



the value of 1*67 had to be ascribed to 7, in order to



vi THE PROPERTIES OF ARGON 209

render it equal to the product of the square of the
velocity into the density, divided by the pressure.

Similar experiments with argon led to the same
result as Kundt and Warburg found for mercury
gas ; but the calculation becomes more simple if it
is allowable to take for granted that the elasticity,
or alteration of pressure produced by unit alteration
of volume, is identical in the case of argon and air.
The full equations are



and



nX = c =

axgon ar:on



where n is the number of vibrations per second,
A, the wave-length of sound, and a the coefficient
of the expansion of a gas for a rise of 1 in tem-
perature, t, viz. 0*00367. Now if the expression^?
(1 + at) can be shown to be identical for argon and
for air, the value of 7 for argon can be calculated
by the very simple proportion

A 2 4, : >?d m :: 1'408 : y argon .

This involved a measurement of the rate of
rise of pressure of argon, p t per degree of rise of
temperature, t ; or, in other words, the verification



210 THE GASES OF THE ATMOSPHERE CHAP.

of Boyle's and Gay-Lussac's laws for argon ; and
this research was successfully carried out by Dr.
Kandall of the Johns Hopkins University of
Baltimore, U.S.A., and Dr. Kuenen, of Ley den,
working in Professor Kamsay's laboratory. 1 They
made use of a constant volume thermometer, and
measured the rise of pressure corresponding to a
definite rise of temperature, comparing the gases
argon and helium in this respect with air. The
values found between and 100 for air, argon,
and helium were

One volume in air, heated from to 100, raises
pressure in the proportion of 1 to 1-3663

Argon 1-3668

Helium 1*3665

It may therefore be taken for certain that, within
the limits of experimental error, the value of the
expression p (l + at) is identical for all three
gases.

We see, then, that for argon, as for mercury gas,
the value of 7, the ratio between the specific heats
at constant volume and at constant pressure, is 1 to
1*66, whereas for air, hydrogen, oxygen, nitrogen,
carbon monoxide, and nitric oxide, it is 1 to 1*4.

* Proc. Roy, Soc. vol. lix. p. 63.



vi THE PROPERTIES OF ARGON 211

We have now to consider what conclusion can be
drawn from this difference.

On the usually accepted theory of the constitu-
tion of matter, it is held that for simplicity's sake
atoms may be regarded as spheres, hard, elastic,
smooth, and practically incompressible. True, we
really know little or nothing regarding the properties
of such particles, if particles there be ; but in con-
sidering their behaviour it is necessary to make
certain suppositions, and to see whether observed
facts can be pictured to our minds in accordance
with such postulates. If, from the known behaviour
of large masses, conclusions can be drawn regarding
small masses, and if these conclusions harmonise
with what is found to be the behaviour of large
numbers of small masses, acting at once, the justice
of the supposition is, although not proved, at least
rendered defensible as one mode of regarding
natural phenomena.

Molecules, on this supposition, may consist of
single atoms, or they may consist of pairs of such
atoms, joined in some fashion like the bulged ends of
a dumb-bell ; or lastly, they may consist of greater
numbers of atoms arranged in some different manner,
the arrangements depending on their relative size



212 THE GASES OF THE ATMOSPHERE CHAP



and attraction for each other. It must be clearly
understood, however, that such mental pictures are
not to be taken as actually representing the true
constitution of matter, but merely as attempts to
picture such forms as will allow of our drawing
conclusions regarding their behaviour from known
configurations of large masses.

The molecules of gases are imagined to be in a
state of continual motion, up and down, backwards
and forwards, and from side to side. It is true
that they must also move in directions which can-
not be described by any of these expressions, but
such other directions may be conceived as par-
taking more or less of motions in the three
directions specified ; i.e. in being resolvable into
these. To these motions have been applied
the term " degrees of freedom." Such motions
through space in which the molecule is trans-
ported from one position in space to another, form
three of the possible six degrees of freedom which a
molecule may possess, and the molecules are said to
possess " energy of translation " in virtue of this
motion. The other three consist in rotations in
three planes at right angles to each other.

Now, it can be shown that the product of pres-



vi THE PROPERTIES OF ARGON 213

sure and volume of a gas, pv, is equal to rds of
the energy of translation of all molecules of the
gas, or



where N stands for the number of molecules in
unit volume, and E for their energy of translation ;
inasmuch as a pressure diminishing a volume is of
the nature of work, or energy. For one gram of air
at C. and 76 cms. pressure (normal temperature
and pressure), the pressure (p), measured in grams
per square centimetre, is 1033, and the volume (v) is
773*3 cubic centimetres ; and the raising of the tem-
perature through 1, as was shown before, requires
2927 gram-centimetres of work. Further, since the
product of pressure into volume is equal to f rds of
the energy due to motion, or the translational
energy of the gas,



NR = fp> = fx2927 = 4391 gram-centimetres.

Dividing this number by 42,380, the mechanical
equivalent of heat, or thenumber of gram-centimetres
corresponding to one calory, the quotient is 0'1040
calory. If the energy of the air were due to the
translational motion of its molecules, we should
expect this number, 0'1040, to stand for the specific



214 THE GASES OF THE ATMOSPHERE CHAP

heat of air at constant volume ; but it has been
found equal to 0*1683, as already shown.

We have seen that to convert specific heat at
constant volume into specific heat at constant pres-
sure ' 6 9 2 must be added. Hence at constant pres-
sure the specific heat of such an ideal gas should
be 0*1732. And the relation between specific
heat at constant volume and that at constant
pressure should be 0*1040 to 0*1732, or 1 to If.
The conclusion to be drawn from these numbers for
air, 0*1683 and 0'2375, which bear to each other
the ratio of 1 : 1*41, is that air cannot be such an
ideal gas ; that in communicating heat to it some
of that heat must be employed in performing some
kind of work other than that of raising its tempera-
ture. What this work may possibly be we shall
consider later.

But Kundt and Warburg found, from their ex-
periments on the ratio between the specific heats of
mercury gas, this ideal ratio, 1 to If ; and Pro-
fessor Eamsay obtained the same ideal ratio, or one
very close to it indeed, 1 to 1*659, for argon. He
subsequently found this ideal ratio also to hold for
helium (1 to 1*652), and also for three other gases
of the same group, and it must therefore be con-



vi THE PROPERTIES OF ARGON 215

eluded that such gases possess only three degrees of
freedom ; or, in other words, their molecules, when
heated, expend all the energy imparted to them in
translational motion through space.

This is the consequence which we should infer
from the supposition that such molecules are hard,
smooth, elastic spheres. Were they each composed
of two atoms, we should have to picture them as
dumb-bell-like structures ; and here we enter on a
theoretical conception put forward by Professor
Boltzmann, but which has not been accepted
universally by physicists.

Boltzmann imagines that to the three " degrees
of freedom" of a single-atom molecule there may
be added, provided the molecule consists of two
atoms, two other degrees of freedom, namely, free-
dom to rotate about two planes at right angles
to each other. The knobs at the end of each
imaginary dumb-bell may revolve round a central
point in the handle joining them, and it is clear
that they may revolve in one horizontal and in
one vertical plane, as shown in Fig. 5. Such dia-
tomic molecules are said to possess five " degrees
of freedom." They will not, it is supposed, rotate
round the line joining the centres of the spheres,



216 THE GASES OF THE ATMOSPHERE CHAP.

because, as before said, the atoms are pictured as
perfectly smooth. But if the molecules are tria-
tomic as, for example, C0 2 or N 2 they will have
six degrees of freedom, for with the addition of an
additional atom they have an additional plane of
rotation (see Fig. 6). Boltzmann has attempted





FIG. 5. FIG.

to show that the ratio of the specific heats of
diatomic molecules should be as 1 to 1*4. In
actual fact it approximates to that number. For
the commoner gases it is

Oxygen . . ... 1-402

Nitrogen ! . , . . . 1-411

Hydrogen V ; . . . 1'412

Carbon monoxide . ..... ... . . 1'418

In all cases the numbers are too large, and this is
a serious difficulty, because any tendency to rotate
round the central line would cause the values to
be less, not greater than 1'4. For triatomic mole-
cules the calculated value of 7 is 1^, but in actual



vi THE PROPERTIES OF ARGON 217

fact the ratio in the case of triatomic molecules,
such as H 2 0, C0 2 , N 2 0, etc., is always less than 1^.
These speculations stand on a basis very different
from the first conception, namely, that all heat
must be employed in communicating translational
motion to molecules of mercury gas, argon, neon,
krypton, xenon, and helium, and it appears that
the atoms of these six elements must necessarily be
regarded as having the properties of smooth elastic
spheres. The atoms and the molecules must in
their several cases be identical. And, inasmuch as
the chemical evidence regarding mercury leads to
the same conclusion, it appears legitimate to infer
that argon and its congeners must also be mona-
tomic elements.



CHAPTER VII

THE POSITION OF ARGON AMONG THE ELEMENTS

FEOM what has been said in the preceding chapter
there can be no doubt that the molecular weight of
argon is 39*88. We have now to consider what
this conclusion involves. Taken in conjunction
with the fact that the ratio between its specific
heat at constant volume and that at constant
pressure is If, it follows that energy imparted to it
is employed solely in communicating translational
motion to its molecules. In the case of mercury
gas such behaviour is taken as evidence that the
conclusion following from the formulae of its com-
pounds, from the density of its compounds in the
gaseous state, and from its own vapour-density,
as well as from its specific heat in the liquid
state, namely, that its molecules are monatomic, is

correct. Is it legitimate to conclude that because

218



CHAP, vii ARGON AND OTHER ELEMENTS 219

argon in the gaseous state has the same ratio
of specific heats, therefore it also is a monatomic
gas?

The conclusion will depend on our conception
of an atom and a molecule, and in the present
state of our ignorance regarding these abstract
entities no positive answer can be given. It
appears certain that, on raising the temperature of
argon, very little, if any, energy is absorbed in
imparting vibrational motion to its molecules ; and
our choice lies between our ability or inability to
conceive of a molecule so constituted as to be
incapable of internal motion. If there be any
truth underlying Professor Boltzmann's conception,
a molecule of argon cannot consist of any complex
structure of atoms, otherwise it would possess more
than three degrees of freedom, and heat would be
utilised in causing rotational motions. As we
know for a fact that the ratio between the specific
heats of gases diminishes with the increasing
complexity of their molecules, perhaps the safest
conclusion is the one adopted by the discoverers
of argon, that the balance of evidence drawn from
this source is in favour of its monatomic nature.

But this hypothesis raises difficulties which are



220



THE GASES OF THE ATMOSPHERE



CHAP.



not lightly to be met. These difficulties arise from
a consideration of the position of argon when it is
classified with other elements.

After a preliminary attempt by de Chancourtois,
which met with no attention, Mr. John Newlands
pointed out in 1863, in a letter to the Chemical
News, that if the elements be arranged in the order
of their atomic weights in a tabular form, they fall
naturally into such groups that elements similar to
each other in chemical behaviour occur in the same
columns. This idea was elaborated further in 1869
by Professor Mendeleeff of St. Petersburg and by


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