is based on the fact that a space _b_ is heated to a constant
      temperature _t_ (by the surrounding vapours of a liquid of
      constant boiling point), and the air (or other gas enclosed in
      this space) is allowed to attain this temperature, and when it
      has done so a glass bulb containing a weighed quantity of the
      substance to be experimented with is dropped into the space. The
      substance is immediately converted into vapour, and displaces
      the air into the graduated cylinder _e_. The amount of this air
      is calculated from its volume, and hence the volume at _t_, and
      therefore also the volume occupied by the vapour, is found. The
      general arrangement of the apparatus is given in fig. 55.

Such an investigation (either direct, or by calculation from the
densities and composition) of every chemical reaction, resulting in the
formation of definite chemical compounds, shows that the volumes of
the reacting substances in a gaseous or vaporous state are either equal
or are in simple multiple proportion.[3] This forms the _first law_
of those discovered by _Gay-Lussac_. It may be formulated as follows:
_The amounts of substances entering into chemical reaction occupy under
similar physical conditions, in a gaseous or vaporous state, equal or
simple multiple volumes._ This law refers not only to elements, but
also to compounds entering into mutual chemical combination; thus, for
example, one volume of ammonia gas combines with one volume of hydrogen
chloride. For in the formation of sal-ammoniac, NH_{4}Cl, there enter
into reaction 17 parts by weight of ammonia, NH_{3}, which is 8·5 times
denser than hydrogen, and 36·5 parts by weight of hydrogen chloride,
whose vapour density is 18·25 times that of hydrogen, as has been
proved by direct experiment. By dividing the weights by the respective
densities we find that the volume of ammonia, NH_{3}, is equal to two,
and so also the volume of hydrogen chloride. Hence the volumes of the
compounds which here combine together are equal to each other. Taking
into consideration that the law of Gay-Lussac holds good, not only for
elements, but also for compounds, it should be expressed as follows:
_Substances interact with one another in commensurable volumes of their
vapours._[4]

  [3] Vapours and gases, as already explained in the second chapter, are
      subject to the same laws, which are, however, only approximate. It
      is evident that for the deduction of the laws which will presently
      be enunciated it is only possible to take into consideration
      a perfect gaseous state (far removed from the liquid state)
      and chemical invariability in which the _vapour density is
      constant_--that is, the volume of a given gas or vapour varies
      like a volume of hydrogen, air, or other gas, with the pressure
      and temperature.

      It is necessary to make this statement in order that it may be
      clearly seen that the laws of gaseous volumes, which we shall
      describe presently, are in the most intimate connection with the
      laws of the variations of volumes with pressure and temperature.
      And as these latter laws (Chapter II.) are not infallible, but
      only approximately exact, the same, therefore, applies to the laws
      about to be described. And as it is possible to find more exact
      laws (a second approximation) for the variation of _v_ with _p_
      and _t_ (for example, van der Waals' formula, Chapter II., Note
      33), so also a more exact expression of the relation between the
      composition and the density of vapours and gases is also possible.
      But to prevent any doubt arising at the very beginning as to the
      breadth and general application of the laws of volumes, it will be
      sufficient to mention that the density of such gases as oxygen,
      nitrogen, and carbonic anhydride is already known to _remain
      constant_ (within the limits of experimental error) between the
      ordinary temperature and a white heat; whilst, judging from what
      is said in my work on the 'Tension of Gases' (vol. i. p. 9),
      it may be said that, as regards pressure, the relative density
      remains very constant, even when the deviations from Mariotte's
      law are very considerable. However, in this respect the number of
      data is as yet too small to arrive at an exact conclusion.

  [4] We must recollect that this law is only approximate, like Boyle
      and Mariotte's law, and that, therefore, like the latter, a more
      exact expression may be found for the exceptions.

The law of combining volumes and the law of multiple proportion were
discovered independently of each other--the one in France by Gay-Lussac,
the other in England by Dalton--almost simultaneously. In the language
of the atomic hypothesis it may be said that atomic quantities of
elements occupy equal or multiple volumes.

The first law of Gay-Lussac expresses the relation between the volumes
of the component parts of a compound. Let us now consider the relation
existing between the volumes of the component parts and of the compounds
which proceed from them. This may sometimes be determined by direct
observation. Thus the volume occupied by water, formed by two volumes
of hydrogen and one volume of oxygen, may be determined by the aid of
the apparatus shown in fig. 56. The long glass tube is closed at the
top and open at the bottom, which is immersed in a cylinder containing
mercury. The closed end is furnished with wires like a eudiometer. The
tube is filled with mercury, and then a certain volume of detonating gas
is introduced. This gas is obtained from the decomposition of water,
and therefore in every three volumes contains two volumes of hydrogen
and one volume of oxygen. The tube is surrounded by a second and wider
glass tube, and the vapour of a substance boiling above 100°--that is,
whose boiling point is higher than that of water--is passed through
the annular space between them. Amyl alcohol, whose boiling point is
132°, may be taken for this purpose. The amyl alcohol is boiled in the
vessel to the right hand and its vapour passed between the walls of the
two tubes. In the case of amyl alcohol the outer glass tube should be
connected with a condenser to prevent the escape into the air of the
unpleasant-smelling vapour. The detonating gas is thus heated up to a
temperature of 132°. When its volume becomes constant it is measured,
the height of the column of mercury in the tube above the level of the
mercury in the cylinder being noted. Let this volume equal _v_; it will
therefore contain 1/3 _v_ of oxygen and 2/3 _v_ of hydrogen. The current
of vapour is then stopped, and the gas exploded; water is formed, which
condenses into a liquid. The volume occupied by the vapour of the water
formed has now to be determined. For this purpose the vapour of the amyl
alcohol is again passed between the tubes, and thus the whole of the
water formed is converted into vapour at the same temperature as that at
which the detonating gas was measured; and the cylinder of mercury being
raised until the column of mercury in the tube stands at the same height
above the surface of the mercury in the cylinder as it did before the
explosion, it is found that the volume of the water formed is equal to
2/3 _v_--that is, it is equal to the volume of the hydrogen contained
in it. Consequently the volumetric composition of water is expressed in
the following terms: Two volumes of hydrogen combine with one volume of
oxygen to form two volumes of aqueous vapour. For substances which are
gaseous at the ordinary temperature, this direct method of observation
is sometimes very easily conducted; for instance, with ammonia, nitric
and nitrous oxides. Thus to determine the composition by volume of
nitrous oxide, the above-described apparatus may be employed. Nitrous
oxide is introduced into the tube, and after measuring its volume
electric sparks are passed through the gas; it is then found that two
volumes of nitrous oxide have given three volumes of gases--namely,
two volumes of nitrogen and one volume of oxygen. Consequently the
composition of nitrous oxide is similar to that of water; two volumes of
nitrogen and one volume of oxygen give two volumes of nitrous oxide. By
decomposing ammonia it is found to be composed in such a manner that two
volumes give one volume of nitrogen and three volumes of hydrogen; also
two volumes of nitric oxide are formed by the union of one volume of
oxygen with one volume of nitrogen. The same relations may be proved by
calculation from the vapour densities, as was described above.

[Illustration: FIG. 56.--Apparatus for demonstrating the volume occupied
by the steam formed from the explosion of detonating gas.]

Comparisons of various results made by the aid of direct observations or
calculation, an example of which has just been cited, led Gay-Lussac to
the conclusion that _the volume of a compound in a gaseous or vaporous
state is always in simple multiple proportion to the volume of each of
the component parts of which it is formed_ (and consequently to the
sum of the volumes of the elements of which it is formed). This is the
_second law of Gay-Lussac_; it extends the simplicity of the volumetric
relations to compounds, and is of the same nature as that presented
by the elements entering into mutual combination. Hence not only the
substances forming a given compound, but also the substances formed,
exhibit a simple relation of volume when measured as vapour or gas.[5]

  [5] This second law of volumes may be considered as a consequence of the
      first law. The first law requires simple ratios between the
      volumes of the combining substances _A_ and _B_. A substance _AB_
      is produced by their combination. It may, according to the law
      of multiple proportion, combine, not only with substances _C_,
      _D_, &c., but also with _A_ and with _B_. In this new combination
      the volume of _AB_, combining with the volume of _A_, should be
      in simple multiple proportion with the volume of _A_; hence the
      volume of the compound _AB_ is in simple proportion to the volume
      of its component parts. Therefore only one law of volumes need be
      accepted. We shall afterwards see that there is a third law of
      volumes embracing also the two first laws.

When a compound is formed from two or more components, there may
or may not be a contraction; the volume of the reacting substances
is in this case either equal to or greater than the volume of the
resultant compound. The reverse is naturally observed in the case of
decompositions, when from one substance there are produced several of
simpler nature. Therefore in the future we shall term _combination_ a
reaction in which a contraction is observed--that is, a diminution in
the volume of the component bodies in a state of vapour or gas; and we
shall term _decomposition_ a reaction in which an expansion is produced;
while those reactions in which the volumes in a gaseous or vaporous
state remain constant (the volumes being naturally compared at the same
temperature and pressure) we shall term reactions of _substitution_ or
of double decomposition. Thus the transition of oxygen into ozone is a
reaction of combination, the formation of nitrous oxide from oxygen and
nitrogen will also be a combination, the formation of nitric oxide from
the same will be a reaction of substitution, the action of oxygen on
nitric oxide a combination, and so on.

The degree of contraction produced in the formation of chemical
compounds not unfrequently leads to the possibility of distinguishing
the degree of change which takes place in the chemical character of the
components when combined. In those cases in which a contraction occurs,
the properties of the resultant compound are very different from the
properties of the substances of which it is composed. Thus ammonia bears
no resemblance in its physical or chemical properties to the elements
from which it is derived; a contraction takes place in a state of
vapour, indicating a proximation of the elements--the distance between
the atoms is diminished, and from gaseous substances there is formed a
liquid substance, or at any rate one which is easily liquefied. For this
reason nitrous oxide formed by the condensation of two permanent gases
is a substance which is somewhat easily converted into a liquid; again,
nitric acid, which is formed from elements which are permanent gases,
is a liquid, whilst, on the contrary, nitric oxide, which is formed
without contraction and is decomposed without expansion, remains a gas
which is as difficult to liquefy as nitrogen and oxygen. In order to
obtain a still more complete idea of the dependence of the properties
of a compound on the properties of the component substances, it is
further necessary to know the quantity of heat which is developed in the
formation of the compound. If this quantity be large--as, for example,
in the formation of water--then the amount of energy in the resultant
compound will be considerably less than the energy of the elements
entering into its composition; whilst, on the contrary, if the amount of
heat evolved in the formation of a compound be small, or if there even
be an absorption of heat, as in the formation of nitrous oxide, then the
energy of the elements is not destroyed, or is only altered to a slight
extent; hence, notwithstanding the contraction (compression) involved in
its formation, nitrous oxide supports combustion.

The preceding laws were deduced from purely experimental and empirical
data and as such evoke further consequences, as the law of multiple
proportions gave rise to the atomic theory and the law of equivalents
(Chapter IV.) In view of the atomic conception of the constitution of
substances, the question naturally arises as to what, then, are the
relative volumes proper to those physically indivisible molecules which
chemically react on each other and consist of the atoms of elements.
The simplest possible hypothesis in this respect would be that the
volumes of the molecules of substances are equal; or, what is the same
thing, to suppose that equal volumes of vapours and gases contain an
equal number of molecules. This proposition was first enunciated by the
Italian savant _Avogadro_ in 1810. It was also admitted by the French
physico-mathematician _Ampère_ (1815) for the sake of simplifying all
kinds of physico-mathematical conceptions respecting gases. But Avogadro
and Ampère's propositions were not generally received in science
until Gerhardt in the forties had applied them to the generalisation
of chemical reactions, and had demonstrated, by aid of a series of
phenomena, that the reactions of substances actually take place with
the greatest simplicity, and more especially that such reactions take
place between those quantities of substances which occupy equal volumes,
and until he had stated the hypothesis in an exact manner and deduced
the consequences that necessarily follow from it. Following Gerhardt,
Clausius, in the fifties, placed this hypothesis of the equality of
the number of molecules in equal volumes of gases and vapours on the
basis of the kinetic theory of gases. At the present day the hypothesis
of Avogadro and Gerhardt lies at the basis of contemporary physical,
mechanical, and chemical conceptions; the consequences arising from it
have often been subject to doubt, but in the end have been verified by
the most diverse methods; and now, when all efforts to refute those
consequences have proved fruitless, the hypothesis must be considered
as verified,[6] and the _law of Avogadro-Gerhardt_ must be spoken of as
fundamental, and as of great importance for the comprehension of the
phenomena of nature. The law may now be formulated from two points of
view. In the first place, from a physical aspect: _equal volumes of
gases_ (or vapours) at equal temperatures and pressures _contain the
same number of molecules_--or of particles of matter which are neither
mechanically nor physically divisible--previous to chemical change. In
the second place, from a chemical aspect, the same law may be expressed
thus: _the quantities of substances entering into chemical reactions
occupy, in a state of vapour, equal volumes_. For our purpose the
chemical aspect is the most important, and therefore, before developing
the law and its consequences, we will consider the chemical phenomena
from which the law is deduced or which it serves to explain.

  [6] It must not be forgotten that Newton's law of gravity was first a
      hypothesis, but it became a trustworthy, perfect theory, and
      acquired the qualities of a fundamental law owing to the concord
      between its deductions and actual facts. All laws, all theories,
      of natural phenomena, are at first hypotheses. Some are rapidly
      established by their consequences exactly agreeing with facts;
      others only take root by slow degrees; and there are many which
      are destined to be refuted owing to their consequences being found
      to be at variance with facts.

When two isolated substances interact with each other directly and
easily--as, for instance, an alkali and an acid--then it is found that
the reaction is accomplished between quantities which in a gaseous
state occupy equal volumes. Thus ammonia, NH_{3}, reacts directly with
hydrochloric acid, HCl, forming sal-ammoniac, NH_{4}Cl, and in this
case the 17 parts by weight of ammonia occupy the same volume as the
36·5 parts by weight of hydrochloric acid.[7] Ethylene, C_{2}H_{4},
combines with chlorine, Cl_{2}, in only one proportion, forming
ethylene dichloride, C_{2}H_{4}Cl_{2}, and this combination proceeds
directly and with great facility, the reacting quantities occupying
equal volumes. Chlorine reacts with hydrogen in only one proportion,
forming hydrochloric acid, HCl, and in this case equal volumes interact
with each other. If an equality of volumes is observed in cases of
combination, it should be even more frequently encountered in cases
of decomposition, taking place in substances which split up into two
others. Indeed, acetic acid breaks up into marsh gas, CH_{4}, and
carbonic anhydride, CO_{2}, and in the proportions in which they
are formed from acetic acid they occupy equal volumes. Also from
phthalic acid, C_{8}H_{6}O_{4}, there may be obtained benzoic acid,
C_{7}H_{6}O_{2}, and carbonic anhydride, CO_{2}, and as all the elements
of phthalic acid enter into the composition of these substances, it
follows that, although they cannot re-form it by their direct action
on each other (the reaction is not reversible), still they form the
direct products of its decomposition, and they occupy equal volumes.
But benzoic acid, C_{7}H_{6}O_{2}, is itself composed of benzene,
C_{6}H_{6}, and carbonic anhydride, CO_{2}, which also occupy equal
volumes.[8] There is an immense number of similar examples among those
organic substances to whose study Gerhardt consecrated his whole life
and work, and he did not allow such facts as these to escape his
attention. Still more frequently in the phenomena of substitution,
when two substances react on one another, and two are produced without
a change of volume, it is found that the two substances acting on
each other occupy equal volumes as well as each of the two resultant
substances. Thus, in general, reactions of substitution take place
between volatile acids, HX, and volatile alcohols, R(OH), with the
formation of ethereal salts, RX, and water, H(OH), and the volume of the
vapour of the reacting quantities, HX, R(OH), and RX, is the same as
that of water H(OH), whose weight, corresponding with the formula, 18,
occupies 2 volumes, if 1 part by weight of hydrogen occupy 1 volume and
the density of aqueous vapour referred to hydrogen is 9. Such general
examples, of which there are many,[9] show that the reaction of equal
volumes forms a chemical phenomenon of frequent occurrence, indicating
the necessity for acknowledging the law of Avogadro-Gerhardt.

  [7] This is not only seen from the above calculations, but may be proved
      by experiment. A glass tube, divided in the middle by a stopcock,
      is taken and one portion filled with _dry_ hydrogen chloride
      (the dryness of the gases is very necessary, because ammonia
      and hydrogen chloride are both very soluble in water, so that a
      small trace of water may contain a large amount of these gases in
      solution) and the other with dry ammonia, under the atmospheric
      pressure. One orifice (for instance, of that portion which
      contains the ammonia) is firmly closed, and the other is immersed
      under mercury, and the cock is then opened. Solid sal-ammoniac is
      formed, but if the volume of one gas be greater than that of the
      other, some of the first gas will remain. By immersing the tube in
      the mercury in order that the internal pressure shall equal the
      atmospheric pressure, it may easily be shown that the volume of
      the remaining gas is equal to the difference between the volumes
      of the two portions of the tube, and that this remaining gas is
      part of that whose volume was the greater.

  [8] Let us demonstrate this by figures. From 122 grams of benzoic acid
      there are obtained (_a_) 78 grams of benzene, whose density
      referred to hydrogen = 39, hence the relative volume = 2; and
      (_b_) 44 grams of carbonic anhydride, whose density = 22, and
      hence the volume = 2. It is the same in other cases.

  [9] A large number of such generalised reactions, showing reaction
      by equal volumes, occur in the case of the hydrocarbon
      derivatives, because many of these compounds are volatile. The
      reactions of alkalis on acids, or anhydrides on water, &c.,
      which are so frequent between mineral substances, present but
      few such examples, because many of these substances are not
      volatile and their vapour densities are unknown. But essentially
      the same is seen in these cases also; for instance, sulphuric
      acid, H_{2}SO_{4}, breaks up into the anhydride, SO_{3}, and
      water, H_{2}O, which exhibit an equality of volumes. Let us take
      another example where three substances combine in equal volumes:
      carbonic anhydride, CO_{2}, ammonia, NH_{3}, and water, H_{2}O
      (the volumes of all are equal to 2), form acid ammonium carbonate,
      (NH_{4})HCO_{3}.

But the question arises, What is the relation of volumes if the reaction
of two substances takes place in more than one proportion, according to
the law of multiple proportions? A definite answer can only be given in
cases which have been very thoroughly studied. Thus chlorine, in acting
on marsh gas, CH_{4}, forms four compounds, CH_{3}Cl, CH_{2}Cl_{2},
CHCl_{3}, and CCl_{4}, and it may be established by direct experiment
that the substance CH_{3}Cl (methylic chloride) precedes the remainder,
and that the latter proceed from it by the further action of chlorine.
And this substance, CH_{3}Cl, is formed by the reaction of equal volumes
of marsh gas, CH_{4}, and chlorine, Cl_{2}, according to the equation
CH_{4} + Cl_{2} = CH_{3}Cl + HCl. A great number of similar cases are
met with amongst organic--that is, carbon--compounds. Gerhardt was led
to the discovery of his law by investigating many such reactions, and by
observing that in them the reaction of equal volumes precedes all others.

But if nitrogen or hydrogen give several compounds with oxygen, the
question proposed above cannot be answered with complete clearness,
because the successive formations of the different combinations cannot
be so strictly defined. It may be supposed, but neither definitely
affirmed nor experimentally confirmed, that nitrogen and oxygen
first give nitric oxide, NO, and only subsequently the brown vapours
N_{2}O_{3} and NO_{2}. Such a sequence in the combination of nitrogen
with oxygen can only be supposed on the basis of the fact that NO forms
N_{2}O_{3} and NO_{2} directly with oxygen. If it be admitted that NO
(and not N_{2}O or NO_{2}) be first formed, then this instance would
also confirm the law of Avogadro-Gerhardt, because nitric oxide contains
equal volumes of nitrogen and oxygen. So, also, it may be admitted that,
in the combination of hydrogen with oxygen, hydrogen peroxide is first
formed (equal volumes of hydrogen and oxygen), which is decomposed by
the heat evolved into water and oxygen. This explains the presence of
traces of hydrogen peroxide (Chapter IV.) in almost all cases of the
combustion or oxidation of hydrogenous substances; for it cannot be
supposed that water is first formed and then the peroxide of hydrogen,
because up to now such a reaction has not been observed, whilst the
formation of H_{2}O from H_{2}O_{2} is very easily reproduced.[10]

  [10] This opinion which I have always held (since the first editions
       of this work), as to the primary origin of hydrogen peroxide
       and of the formation of water by means of its decomposition,
       has in latter days become more generally accepted, thanks more
       especially to the work of Traube. Probably it explains most
       simply the necessity for the presence of traces of water in
       many reactions, as, for instance, in the explosion of carbonic
       oxide with oxygen, and perhaps the theory of the explosion of
       detonating gas itself and of the combustion of hydrogen will
       gain in clearness and truth if we take into consideration the
       preliminary formation of hydrogen peroxide and its decomposition.
       We may here point out the fact that Ettingen (at Dorpat, 1888)
       observed the existence of currents and waves in the explosion of
       detonating gas by taking photographs, which showed the periods of
       combustion and the waves of explosion, which should be taken into
       consideration in the theory of this subject. As the formation of
       H_{2}O_{2} from O_{2} and H_{2} corresponds with a less amount of
       heat than the formation of water from H_{2} and O, it may be that
       the temperature of the flame of detonating gas depends on the
       pre-formation of hydrogen peroxide.

Thus a whole series of phenomena show that the chemical reaction of
substances actually takes place, as a rule, between equal volumes,
but this does not preclude the possibility of the frequent reaction
of unequal volumes, although, in this case, it is often possible to
discover a preceding reaction between equal volumes.[11]

  [11] The possibility of reactions between unequal volumes,
       notwithstanding the general application of the law of
       Avogadro-Gerhardt, may, in addition to what has been said
       above, depend on the fact that the participating substances,
       at the moment of reaction, undergo a preliminary modification,
       decomposition, isomeric (polymeric) transformation, &c. Thus,
       if NO_{2}, seems to proceed from N_{2}O_{4}, if O_{2} is formed
       from O_{3}, and the converse, then it cannot be denied that
       the production of molecules containing only one atom is also
       possible--for instance, of oxygen--as also of higher polymeric
       forms--as the molecule N from N_{2}, or H_{3} from H_{2}. In
       this manner it is obviously possible, by means of a series of
       hypotheses, to explain the cases of the formation of ammonia,
       NH_{3}, from 3 vols. of hydrogen and 1 vol. of nitrogen. But
       it must be observed that perhaps our information in similar
       instances is, as yet, far from being complete. If hydrazine or
       diamide N_{2}H_{4} (Chapter VI. Note 20 bis) is formed and the
       imide N_{2}H_{2} in which 2 vols. of hydrogen are combined with
       2 vols. of nitrogen, then the reaction here perhaps first takes
       place between equal volumes. If it be shown that diamide gives
       nitrogen and ammonia (3N_{2}H_{4} = N_{2} + 4NH_{3}) under the
       action of sparks, heat, or the silent discharge, &c., then it
       will be possible to admit that it is formed before ammonia. And
       perhaps the still less stable imide N_{2}H_{2}, which may also
       decompose with the formation of ammonia, is produced before the
       amide N_{2}H_{4}.

       I mention this to show that the fact of apparent exceptions
       existing to the law of reactions between equal volumes does not
       prove the impossibility of their being included under the law
       on further study of the subject. Having put forward a certain
       law or hypothesis, consequences must be deduced from it, and
       if by their means clearness and consistency are attained--and
       especially, if by their means that which could not otherwise
       be known can be predicted--then the consequences verify the
       hypothesis. This was the case with the law now under discussion.
       The mere simplicity of the deduction of the weights proper to
       the atoms of the elements, or the mere fact that having admitted
       the law it follows (as will afterwards be shown) that the _vis
       viva_ of the molecules of all gases is a constant quantity, is
       quite sufficient reason for retaining the hypothesis, if not
       for believing in it as a fact beyond doubt. And such is the
       whole doctrine of atoms. And since by the acceptance of the law
       it became possible to foretell even the properties and atomic
       weights of elements which had not yet been discovered, and these
       predictions afterwards proved to be in agreement with the actual
       facts, it is evident that the law of Avogadro-Gerhardt penetrates
       deeply into the nature of the chemical relation of substances.
       This being granted, it is possible at the present time to exhibit
       and deduce the truth under consideration in many ways, and in
       every case, like all that is highest in science (for example,
       the laws of the indestructibility of matter, of the conservation
       of energy, of gravity, &c.), it proves to be not an empirical
       conclusion from direct observation and experiment, not a direct
       result of analysis, but a creation, or instinctive penetration,
       of the inquiring mind, guided and directed by experiment and
       observation--a synthesis of which the exact sciences are
       capable equally with the highest forms of art. Without such a
       synthetical process of reasoning, science would only be a mass
       of disconnected results of arduous labour, and would not be
       distinguished by that vitality with which it is really endowed
       when once it succeeds in attaining a synthesis, or concordance
       of outward form with the inner nature of things, without losing
       sight of the diversities of individual parts; in short, when
       it discovers by means of outward phenomena, which are apparent
       to the sense of touch, to observation, and to the common mind,
       the internal signification of things--discovering simplicity in
       complexity and uniformity in diversity. And this is the highest
       problem of science.

The law of Avogadro-Gerhardt may also be easily expressed in an
algebraical form. If the weight of a molecule, or of that quantity
of a substance which enters into chemical reaction and occupies in a
state of vapour, according to the law, a volume equal to that occupied
by the molecules of other bodies, be indicated by the letters M_{1},
M_{2} ... or, in general, M, and if the letters D_{1}, D_{2}, ... or,
in general, D, stand for the density or weight of a given volume of the
gases or vapours of the corresponding substances under certain definite
conditions of temperature and pressure, then the law requires that

                 M_{1}/D_{1} = M_{2}/D_{2} ... = M/D = C

where C is a certain constant. This expression shows directly that the
volumes corresponding with the weights M_{1}, M_{2} ... M, are equal to
a certain constant, because the volume is proportional to the weight and
inversely proportional to the density. The magnitude of C is naturally
conditioned by and dependent on the units taken for the expression of
the weights of the molecules and the densities. The weight of a molecule
(equal to the sum of the atomic weights of the elements forming it) is
usually expressed by taking the weight of an atom of hydrogen as unity,
and hydrogen is now also chosen as the unit for the expression of the
densities of gases and vapours; it is therefore only necessary to find
the magnitude of the constant for any one compound, as it will be the
same for all others. Let us take water. Its reacting mass is expressed
(conditionally and relatively) by the formula or molecule H_{2}O,
for which M = 18, if H = 1, as we already know from the composition
of water. Its vapour density, or D, compared to hydrogen = 9, and
consequently for water C = 2, and therefore and in general for the
molecules of all substances M/D = 2.

Consequently the weight of a molecule is equal to twice its vapour
density expressed in relation to hydrogen, and conversely _the density
of a gas is equal to half the molecular weight referred to hydrogen_.

The truth of this may be seen from a very large number of observed
vapour densities by comparing them with the results obtained by
calculation. As an illustration, we may point out that for ammonia,
NH_{3}, the weight of the molecule or quantity of the reacting
substance, as well as the composition and weight corresponding with
the formula, is expressed by the figures 14 + 3 = 17. Consequently M
= 17. Hence, according to the law, D = 8·5. And this result is also
obtained by experiment. The density, according to both formula and
experiment, of nitrous oxide, N_{2}O, is 22, of nitric acid 15, and of
nitric peroxide 23. In the case of nitrous anhydride, N_{2}O_{3}, as a
substance which dissociates into NO + NO_{2}, the density should vary
between 38 (so long as the N_{2}O_{3} remains unchanged) and 19 (when
NO + NO_{2} is obtained). There are no figures of constant density for
H_{2}O_{2}, NHO_{3}, N_{2}O_{4}, and many similar compounds which are
either wholly or partially decomposed in passing into vapour. Salts and
similar substances either have no vapour density because they do not
pass into vapour (for instance, potassium nitrate, KNO_{3}) without
decomposition, or, if they pass into vapour without decomposing,
their vapour density is observed with difficulty only at very high
temperatures. The practical determination of the vapour density at these
high temperatures (for example, for sodium chloride, ferrous chloride,
stannous chloride, &c.) requires special methods which have been worked
out by Sainte-Claire Deville, Crafts, Nilson and Pettersson, Meyer,
Scott, and others. Having overcome the difficulties of experiment, it
is found that the law of Avogadro-Gerhardt holds good for such salts
as potassium iodide, beryllium chloride, aluminium chloride, ferrous
chloride, &c.--that is, the density obtained by experiment proves to
be equal to half the molecular weight--naturally within the limits of
experimental error or of possible deviation from the law.

Gerhardt deduced his law from a great number of examples of volatile
carbon compounds. We shall become acquainted with certain of them in
the following chapters; their entire study, from the complexity of
the subject, and from long-established custom, forms the subject of a
special branch of chemistry termed 'organic' chemistry. With all these
substances the observed and calculated densities are very similar.

When the consequences of a law are verified by a great number of
observations, it should be considered as confirmed by experiment. But
this does not exclude the possibility of _apparent_ deviations. They may
evidently be of two kinds: the fraction M/D may be found to be either
greater or less than 2--that is, the calculated density may be either
greater or less than the observed density. When the difference between
the results of experiment and calculation falls within the possible
errors of experiment (for example, equal to hundredths of the density),
or within a possible error owing to the laws of gases having an only
approximate application (as is seen from the deviations, for instance,
from the law of Boyle and Mariotte), then the fraction M/D proves but
slightly different from 2 (between 1·9 and 2·2), and such cases as these
may be classed among those which ought to be expected from the nature
of the subject. It is a different matter if the quotient of M/D be
several times, and in general a multiple, _greater_ or less than 2. The
application of the law must then be explained or it must be laid aside,
because the laws of nature admit of no exceptions. We will therefore
take two such cases, and first one in which the _quotient_ M/D _is
greater than 2, or the density obtained by experiment is less than is in
accordance with the law_.

It must be admitted, as a consequence of the law of Avogadro-Gerhardt,
that there is a decomposition in those cases where the volume of the
vapour corresponding with the weight of the amount of a substance
entering into reaction is greater than the volume of two parts by
weight of hydrogen. Suppose the density of the vapour of water to be
determined at a temperature above that at which it is decomposed,
then, if not all, at any rate a large proportion of the water will be
decomposed into hydrogen and oxygen. The density of such a mixture of
gases, or of detonating gas, will be less than that of aqueous vapour;
it will be equal to 6 (compared with hydrogen), because 1 volume of
oxygen weighs 16, and 2 volumes of hydrogen 2; and, consequently, 3
volumes of detonating gas weigh 18 and 1 volume 6, while the density
of aqueous vapour = 9. Hence, if the density of aqueous vapour be
determined after its decomposition, the quotient M/D would be found
to be 3 and not 2. This phenomenon might be considered as a deviation
from Gerhardt's law, but this would not be correct, because it may be
shown by means of diffusion through porous substances, as described in
Chapter II., that water is decomposed at such high temperatures. In the
case of water itself there can naturally be no doubt, because its vapour
density agrees with the law at all temperatures at which it has been
determined.[12] But there are many substances which decompose with great
ease directly they are volatilised, and therefore only exist as solids
or liquids, and not in a state of vapour. There are, for example, many
salts of this kind, besides all definite solutions having a constant
boiling point, all the compounds of ammonia for example, all ammonium
salts--&c. Their vapour densities, determined by Bineau, Deville, and
others, show that they do not agree with Gerhardt's law. Thus the
vapour density of sal-ammoniac, NH_{4}Cl, is nearly 14 (compared with
hydrogen), whilst its molecular weight is not less than 53·5, whence the
vapour density should be nearly 27, according to the law. The molecule
of sal-ammoniac cannot be less than NH_{4}Cl, because it is formed from
the molecules NH_{3} and HCl, and contains single atoms of nitrogen
and chlorine, and therefore cannot be divided; it further never enters
into reactions with the molecules of other substances (for instance,
potassium hydroxide, or nitric acid) in quantities of less than 53·5
parts by weight, &c. The calculated density (about 27) is here double
the observed density (about 13·4); hence M/D = 4 and not 2. For this
reason the vapour density of sal-ammoniac for a long time served as an
argument for doubting the truth of the law. But it proved otherwise,
after the matter had been fully investigated. The low density depends
on the decomposition of sal-ammoniac, on volatilising, into ammonia and
hydrogen chloride. The observed density is not that of sal-ammoniac, but
of a mixture of NH_{3} and HCl, which should be nearly 14, because the
density of NH_{3} = 8·5 and of HCl = 18·2, and therefore the density
of their mixture (in equal volumes) should be about 13·4.[13] The
actual decomposition of the vapours of sal-ammoniac was demonstrated
by Pebal and Than by the same method as the decomposition of water,
by passing the vapour of sal-ammoniac through a porous substance. The
experiment demonstrating the decomposition during volatilisation of
sal-ammoniac may be made very easily, and is a very instructive point
in the history of the law of Avogadro-Gerhardt, because without its
aid it would never have been imagined that sal-ammoniac decomposed
in volatilising, as this decomposition bears all the signs of simple
sublimation; consequently the knowledge of the decomposition itself
was forestalled by the law. The whole aim and practical use of the
discovery of the laws of nature consists in, and is shown by, the fact
that they enable the unknown to be foretold, the unobserved to be
foreseen. The arrangement of the experiment is based on the following
reasoning.[14] According to the law and to experiment, the density of
ammonia, NH_{3}, is 8-1/2, and of hydrochloric acid, HCl, 18-1/4, if
the density of hydrogen = 1. Consequently, in a mixture of NH_{3} and
HCl, the ammonia will penetrate much more rapidly through a porous
mass, or a fine orifice, than the heavier hydrochloric acid, just as
in a former experiment the hydrogen penetrated more rapidly than the
oxygen. Therefore, if the vapour of sal-ammoniac comes into contact with
a porous mass, the ammonia will pass through it in greater quantities
than the hydrochloric acid, and this excess of ammonia may be detected
by means of moist red litmus paper, which should be turned blue. If the
vapour of sal-ammoniac were not decomposed, it would pass through the
porous mass as a whole, and the colour of the litmus paper would not
be altered, because sal-ammoniac is a neutral salt. Thus, by testing
with litmus the substances passing through the porous mass, it may be
decided whether the sal-ammoniac is decomposed or not when passing into
vapour. Sal-ammoniac volatilises at so moderate a temperature that the
experiment may be conducted in a glass tube heated by means of a lamp,
an asbestos plug being placed near the centre of the tube.[15] The
asbestos forms a porous mass, which is unaltered at a high temperature.
A piece of dry sal-ammoniac is placed at one side of the asbestos
plug, and is heated by a Bunsen burner. The vapours formed are driven
by a current of air forced from a gasometer or bag through two tubes
containing pieces of moist litmus paper, one blue and one red paper
in each. If the sal-ammoniac be heated, then the ammonia appears on
the opposite side of the asbestos plug, and the litmus there turns
blue. And as an excess of hydrochloric acid remains on the side where
the sal-ammoniac is heated, it turns the litmus at that end red. This
proves that the sal-ammoniac, when converted into vapour, splits up into
ammonia and hydrochloric acid, and at the same time gives an instance of
the possibility of correctly conjecturing a fact on the basis of the law
of Avogadro-Gerhardt.[15 bis]

  [12] As the density of aqueous vapour remains constant within the
       limits of experimental accuracy, even at 1,000°, when
       dissociation has certainly commenced, it would appear that only a
       very small amount of water is decomposed at these temperatures.
       If even 10 p.c. of water were decomposed, the density would be
       8·57 and the quotient M/D = 2·1, but at the high temperatures
       here concerned the error of experiment is not greater than the
       difference between this quantity and 2. And probably at 1,000°
       the dissociation is far from being equal to 10 p.c. _Hence the
       variation in the vapour density of water does not give us the
       means of ascertaining the amount of its dissociation._

  [13] This explanation of the vapour density of sal-ammoniac, sulphuric
       acid, and similar substances which decompose in being distilled
       was the most natural to resort to as soon as the application of
       the law of Avogadro-Gerhardt to chemical relations was begun; it
       was, for instance, given in my work on _Specific Volumes_, 1856,
       p. 99. The formula, M/D = 2, which was applied later by many
       other investigators, had already been made use of in that work.

  [14] The beginner must remember that an experiment and the mode in
       which it is carried out must be determined by the principle or
       fact which it is intended to illustrate, and not _vice versa_,
       as some suppose. The idea which determines the necessity of an
       experiment is the chief consideration.

  [15] It is important that the tubes, asbestos, and sal-ammoniac should
       be dry, as otherwise the moisture retains the ammonia and
       hydrogen chloride.

  [15 bis] Baker (1894) showed that the decomposition of NH_{4}Cl in
       the act of volatilising only takes place in the presence of water,
       traces of which are amply sufficient, but that in the total
       absence of moisture (attained by carefully drying with P_{2}O_{5})
       there is no decomposition, and the vapour density of the
       sal-ammoniac is found to be normal, _i.e._, nearly 27. It is not
       yet quite clear what part the trace of moisture plays here, and it
       must be presumed that the phenomenon belongs to the category of
       electrical and contact phenomena, which have not yet been fully
       explained (_see_ Chapter IX., Note 29).

So also the fact of a decomposition may be proved in the other instances
where M/D proved greater than 2, and hence the apparent deviations
appear in reality as an excellent proof of the general application and
significance of the law of Avogadro-Gerhardt.

In those cases where the _quotient_ M/D proves to be _less_ than 2,
or the observed density _greater_ than that calculated, by a multiple
number of times, the matter is evidently more simple, and the fact
observed only indicates that the weight of the molecule is as many times
greater as that taken as the quotient obtained is less than 2. So, for
instance, in the case of ethylene, whose composition is expressed by
CH_{2}, the density was found by experiment to be 14, and in the case
of amylene, whose composition is also CH_{2}, the density proved to be
35, and consequently the quotient for ethylene = 1, and for amylene =
2/5. If the molecular weight of ethylene be taken, not as 14, as might
be imagined from its composition, but as twice as great--namely, as
28--and for amylene as five times greater--that is as 70--then the
molecular composition of the first will be C_{2}H_{4}, and of the
second C_{5}H_{10}, and for both of them M/D will be equal to 2. This
application of the law, which at first sight may appear perfectly
arbitrary, is nevertheless strictly correct, because the amount of
ethylene which reacts--for example, with sulphuric and other acids--is
not equal to 14, but to 28 parts by weight. Thus with H_{2}SO_{4},
Br_{2}, or HI, &c., ethylene combines in a quantity C_{2}H_{4}, and
amylene in a quantity C_{5}H_{10}, and not CH_{2}. On the other hand,
ethylene is a gas which liquefies with difficulty (absolute boiling
point = +10°), whilst amylene is a liquid boiling at 35° (absolute
boiling point = +192°), and by admitting the greater density of the
molecules of amylene (M = 70) its difference from the lighter molecules
of ethylene (M = 28) becomes clear. Thus, the smaller quotient M/D
is _an indication of polymerisation_, as the larger quotient is of
decomposition. The difference between the densities of oxygen and ozone
is a case in point.

On turning to the elements, it is found in certain cases, especially
with metals--for instance, mercury, zinc, and cadmium--that that weight
of the atoms which must be acknowledged in their compounds (of which
mention will be afterwards made) appears to be also the molecular
weight. Thus, the atomic weight of mercury must be taken as = 200,
but the vapour density = 100, and the quotient = 2. Consequently the
_molecule of mercury contains one atom_, Hg. It is the same with sodium,
cadmium, and zinc. This is the simplest possible molecule, which
necessarily is only possible in the case of elements, as the molecule
of a compound must contain at least two atoms. However, the molecules
of many of the elements prove to be complex--for instance, the weight
of an atom of oxygen = 16, and its density = 16, so that its molecule
must contain two atoms, O_{2}, which might already be concluded by
comparing its density with that of ozone, whose molecule contains O_{3}
(Chapter IV.) So also the molecule of hydrogen equals H_{2}, of chlorine
Cl_{2}, of nitrogen N_{2}, &c. If chlorine react with hydrogen, the
volume remains unaltered after the formation of hydrochloric acid,
H_{2} + Cl_{2} = HCl + HCl. It is a case of substitution between the
one and the other, and therefore the volumes remain constant. There
are elements whose molecules are much more complex--for instance,
sulphur, S_{6}--although, by heating, the density is reduced to a third,
and S_{2} is formed. Judging from the vapour density of phosphorus
(D = 62) the molecule contains four atoms P_{4}. Hence many elements
when polymerised appear in molecules which are more complex than the
simplest possible. In carbon, as we shall afterwards find, a very
complex molecule must be admitted, as otherwise its non-volatility and
other properties cannot be understood. And if compounds are decomposed
by a more or less powerful heat, and if polymeric substances are
depolymerised (that is, the weight of the molecule diminishes) by a rise
of temperature, as N_{2}O_{4} passes into NO_{2}, or ozone, O_{3}, into
ordinary oxygen, O_{2}, then we might expect to find the splitting-up of
the complex molecules of elements into the simplest molecule containing
a single atom only--that is to say, if O_{2} be obtained from O_{3},
then the formation of O might also be looked for. The possibility but
not proof of such a proposition is indicated by the vapour of iodine.
Its normal density = 127 (Dumas, Deville, and others), which corresponds
with the molecule I_{2}. At temperatures above 800° (up to which the
density remains almost constant), this density distinctly decreases, as
is seen from the verified results obtained by Victor Meyer, Crafts, and
Troost. At the ordinary pressure and 1,000° it is about 100, at 1,250°
about 80, at 1,400° about 75, and apparently it strives to reduce itself
to one-half--that is, to 63. Under a reduced pressure this splitting-up,
or depolymerisation, of iodine vapour actually reaches a density[16]
of 66, as Crafts demonstrated by reducing the pressure to 100 mm. and
raising the temperature to 1,500°. From this it may be concluded that
at high temperatures and low pressures the molecule I_{2} gradually
passes into the molecule I containing one atom like mercury, and that
something similar occurs with other elements at a considerable rise of
temperature, which tends to bring about the disunion of compounds and
the decomposition of complex molecules.[17]

  [16] Just as we saw (Chapter VI. Note 46) an increase of the
       dissociation of N_{2}O_{4} and the formation of a large
       proportion of NO_{2}, with a decrease of pressure. The
       decomposition of I_{2} into I + I is a similar dissociation.

  [17] Although at first there appeared to be a similar phenomenon in the
       case of chlorine, it was afterwards proved that if there is
       a decrease of density it is only a small one. In the case of
       bromine it is not much greater, and is far from being equal to
       that for iodine.

       As in general we very often involuntarily confuse chemical
       processes with physical, it may be that a physical process
       of change in the coefficient of expansion with a change of
       temperature participates with a change in molecular weight,
       and partially, if not wholly, accounts for the decrease of the
       density of chlorine, bromine, and iodine. Thus, I have remarked
       (Comptes Rendus, 1876) that the coefficient of expansion of
       gases increases with their molecular weight, and (Chapter II.,
       Note 26) the results of direct experiment show the coefficient
       of expansion of hydrobromic acid (M = 81) to be 0·00386 instead
       of 0·00367, which is that of hydrogen (M = 2). Hence, in the
       case of the vapour of iodine (M = 254) a very large coefficient
       of expansion is to be expected, and from this cause alone
       the relative density would fall. As the molecule of chlorine
       Cl_{2} is lighter (= 71) than that of bromine (= 160), which is
       lighter than that of iodine (= 254), we see that the order in
       which the decomposability of the vapours of these haloids is
       observed corresponds with the expected rise in the coefficient of
       expansion. Taking the coefficient of expansion of iodine vapour
       as 0·004, then at 1,000° its density would be 116. Therefore
       the dissociation of iodine may be only an apparent phenomenon.
       However, on the other hand, the heavy vapour of mercury (M = 200,
       D = 100) scarcely decreases in density at a temperature of 1,500°
       (D = 98, according to Victor Meyer); but it must not be forgotten
       that the molecule of mercury contains only one atom, whilst that
       of iodine contains two, and this is very important. Questions
       of this kind which are difficult to decide by experimental
       methods must long remain without a certain explanation, owing to
       the difficulty, and sometimes impossibility, of distinguishing
       between physical and chemical changes.

Besides these cases of apparent discrepancy from the law of
Avogadro-Gerhardt there is yet a third, which is the last, and is very
instructive. In the investigation of separate substances they have to be
isolated in the purest possible form, and their chemical and physical
properties, and among them the vapour density, then determined. If
it be normal--that is, if D = M/2--it often serves as a proof of the
purity of the substance, _i.e._ of its freedom from all foreign matter.
If it be abnormal--that is, if D be not equal to M/2--then for those
who do not believe in the law it appears as a new argument against it
and nothing more; but to those who have already grasped the important
significance of the law it becomes clear that there is some error in
the observation, or that the density was determined under conditions in
which the vapour does not follow the laws of Boyle or Gay-Lussac, or
else that the substance has not been sufficiently purified, and contains
other substances. The law of Avogadro-Gerhardt in that case furnishes
convincing evidence of the necessity of a fresh and more exact research.
And as yet the causes of error have always been found. There are not a
few examples in point in the recent history of chemistry. We will cite
one instance. In the case of pyrosulphuryl chloride, S_{2}O_{5}Cl_{2},
M = 215, and consequently D should = 107·5, instead of which Ogier and
others obtained 53·8--that is, a density half as great; and further,
Ogier (1882) demonstrated clearly that the substance is not dissociated
by distillation into SO_{3} and SO_{2}Cl_{2}, or any other two products,
and thus the abnormal density of S_{2}O_{5}Cl_{2} remained unexplained
until D. P. Konovaloff (1885) showed that the previous investigators
were working with a mixture (containing SO_{3}HCl), and that
pyrosulphuryl chloride has a normal density of approximately 107. Had
not the law of Avogadro-Gerhardt served as a guide, the impure liquid
would have still passed as pure; the more so since the determination of
the amount of chlorine could not aid in the discovery of the impurity.
Thus, by following a true law of nature we are led to true deductions.

All cases which have been studied confirm the law of Avogadro-Gerhardt,
and as by it a deduction is obtained, from the determination of the
vapour density (a purely physical property), as to the weight of the
molecule or quantity of a substance entering into chemical reaction,
this law links together the two provinces of learning--physics and
chemistry--in the most intimate manner. Besides which, the law of
Avogadro-Gerhardt places the conceptions of _molecules_ and _atoms_ on
a firm foundation, which was previously wanting. Although since the
days of Dalton it had become evident that it was necessary to admit the
existence of the elementary atom (the chemical individual indivisible
by chemical or other forces), and of the groups of atoms (or molecules)
of compounds, indivisible by mechanical and physical forces; still
the relative magnitude of the molecule and atom was not defined with
sufficient clearness. Thus, for instance, the atomic weight of oxygen
might be taken as 8 or 16, or any multiple of these numbers, and nothing
indicated a reason for the acceptation of one rather than another of
these magnitudes;[18] whilst as regards the weights of the molecules of
elements and compounds there was no trustworthy knowledge whatever. With
the establishment of Gerhardt's law the idea of the molecule was fully
defined, as well as the relative magnitude of the elementary atom.

  [18] And so it was in the fifties. Some took O = 8, others O = 16.
       Water in the first case would be HO and hydrogen peroxide HO_{2},
       and in the second case, as is now generally accepted, water
       H_{2}O and hydrogen peroxide H_{2}O_{2} or HO. Disagreement
       and confusion reigned. In 1860 the chemists of the whole world
       met at Carlsruhe for the purpose of arriving at some agreement
       and uniformity of opinion. I was present at this Congress, and
       well remember how great was the difference of opinion, and how
       a compromise was advocated with great acumen by many scientific
       men, and with what warmth the followers of Gerhardt, at whose
       head stood the Italian professor, Canizzaro, followed up the
       consequences of the law of Avogadro. In the spirit of scientific
       freedom, without which science would make no progress, and would
       remain petrified as in the middle ages, and with the simultaneous
       necessity of scientific conservatism, without which the roots
       of past study could give no fruit, a compromise was not arrived
       at, nor ought it to have been, but instead of it truth, in the
       form of the law of Avogadro-Gerhardt, received by means of the
       Congress a wider development, and soon afterwards conquered all
       minds. Then the new so-called Gerhardt atomic weights established
       themselves, and in the seventies they were already in general use.

The chemical particle or _molecule must be considered as the quantity
of a substance which enters into chemical reaction with other molecules,
and occupies in a state of vapour the same volume as two parts by weight
of hydrogen_.

The molecular weight (which has been indicated by M) of a substance is
determined by its composition, transformations, and vapour density.

The molecule is not divisible by the mechanical and physical changes
of substances, but in chemical reaction it is either altered in its
properties, or quantity, or structure, or in the nature of the motion of
its parts.

An agglomeration of molecules, which are alike in all chemical respects,
makes up the masses of homogeneous substances in all states.[19]

  [19] A bubble of gas, a drop of liquid, or the smallest crystal,
       presents an agglomeration of a number of molecules, in a state of
       continual motion (like the stars of the Milky Way), distributing
       themselves evenly or forming new systems. If the aggregation of
       all kinds of heterogeneous molecules be possible in a gaseous
       state, where the molecules are considerably removed from each
       other, then in a liquid state, where they are already close
       together, such an aggregation becomes possible only in the
       sense of the mutual reaction between them which results from
       their chemical attraction, and especially in the aptitude of
       heterogeneous molecules for combining together. Solutions and
       other so-called indefinite chemical compounds should be regarded
       in this light. According to the principles developed in this
       work we should regard them as containing both the compounds of
       the heterogeneous molecules themselves and the products of their
       decomposition, as in peroxide of nitrogen, N_{2}O_{4} and NO_{2}.
       And we must consider that those molecules A, which at a given
       moment are combined with B in AB, will in the following moment
       become free in order to again enter into a combined form. The
       laws of chemical equilibrium proper to dissociated systems cannot
       be regarded in any other light.

Molecules consist of atoms in a certain state of distribution and
motion, just as the solar system[20] is made up of inseparable parts
(the sun, planets, satellites, comets, &c.) The greater the number of
atoms in a molecule, the more complex is the resultant substance. The
equilibrium between the dissimilar atoms may be more or less stable,
and may for this reason give more or less stable substances. Physical
and mechanical transformations alter the velocity of the motion and
the distances between the individual molecules, or of the atoms in the
molecules, or of their sum total, but they do not alter the original
equilibrium of the system; whilst chemical changes, on the other hand,
alter the molecules themselves, that is, the velocity of motion, the
relative distribution, and the quality and quantity of the atoms in the
molecules.

  [20] This strengthens the fundamental idea of the unity and harmony of
       type of all creation and is one of those ideas which impress
       themselves on man in all ages, and give rise to a hope of
       arriving in time, by means of a laborious series of discoveries,
       observations, experiments, laws, hypotheses, and theories, at
       a comprehension of the internal and invisible structure of
       concrete substances with that same degree of clearness and
       exactitude which has been attained in the visible structure of
       the heavenly bodies. It is not many years ago since the law of
       Avogadro-Gerhardt took root in science. It is within the memory
       of many living scientific men, and of mine amongst others. It is
       not surprising, therefore, that as yet little progress has been
       made in the province of molecular mechanics; but the theory of
       gases alone, which is intimately connected with the conception of
       molecules, shows by its success that the time is approaching when
       our knowledge of the internal structure of matter will be defined
       and established.

_Atoms are the smallest quantities_ or chemically indivisible masses _of
the elements forming the molecules_ of elements and compounds.

Atoms have weight, the sum of their weights forms the weight of the
molecule, and the sum of the weights of the molecules forms the weight
of masses, and is the cause of gravity, and of all the phenomena which
depend on the mass of a substance.

The elements are characterised, not only by their independent existence,
their incapacity of being converted into each other, &c., but also by
the weight of their atoms.

Chemical and physical properties depend on the weight, composition, and
properties of the molecules forming a substance, and on the weight and
properties of the atoms forming the molecules.

This is the substance of those principles of molecular mechanics which
lie at the basis of all contemporary physical and chemical constructions
since the establishment of the law of Avogadro-Gerhardt. The fecundity
of the principles enunciated is seen at every step in all the particular
cases forming the present store of chemical data. We will here cite a
few examples of the application of the law.

As the weight of an atom must be understood as the minimum quantity of
an element entering into the composition of all the molecules formed
by it, therefore, in order to find the weight of an atom of oxygen,
let us take the molecules of those of its compounds which have already
been described, together with the molecules of certain of those carbon
compounds which will be described in the following chapter:

                 Molecular  Amount of          Molecular  Amount of
                   Weight     Oxygen             Weight     Oxygen

         H_{2}O     18         16      HNO_{3}    63         48
         N_{2}O     44         16      CO         28         16
         NO         30         16      CO_{2}     44         32
         NO_{2}     46         32

The number of substances taken might be considerably increased, but
the result would be the same--that is, the molecules of the compounds
of oxygen would never be found to contain less than 16 parts by weight
of this element, but always _n_16, where _n_ is a whole number. The
molecular weights of the above compounds are found either directly from
the density of their vapour or gas, or from their reactions. Thus, the
vapour density of nitric acid (as a substance which easily decomposes
above its boiling point) cannot be accurately determined, but the
fact of its containing one part by weight of hydrogen, and all its
properties and reactions, indicate the above molecular composition and
no other. In this manner it is very easy to find the atomic weight of
all the elements, knowing the molecular weight and composition of their
compounds. It may, for instance, be easily proved that less than _n_12
parts of carbon never enters into the molecules of carbon compounds,
and therefore C must be taken as 12, and not as 6 which was the number
in use before Gerhardt. In a similar manner the atomic weights now
accepted for the elements oxygen, nitrogen, carbon, chlorine, sulphur,
&c., were found and indubitably established, and they are even now
termed the Gerhardt atomic weights. As regards the metals, many of
which do not give a single volatile compound, we shall afterwards
see that there are also methods by which their atomic weights may be
established, but nevertheless the law of Avogadro-Gerhardt is here
also ultimately resorted to, in order to remove any doubt which may be
encountered. Thus, for instance, although much that was known concerning
the compounds of beryllium necessitated its atomic weight being taken
as Be = 9--that is, the oxide as BeO and the chloride BeCl_{2}--still
certain analogies gave reason for considering its atomic weight to be Be
= 13·5, in which case its oxide would be expressed by the composition
Be_{2}O_{3}, and the chloride by BeCl_{3}.[21] It was then found that
the vapour density of beryllium chloride was approximately 40, when
it became quite clear that its molecular weight was 80, and as this
satisfies the formula BeCl_{2}, but does not suit the formula BeCl_{3},
it therefore became necessary to regard the atomic weight of Be as 9 and
not as 13-1/2.

  [21] If Be = 9, and beryllium chloride be BeCl_{2}, then for every 9
       parts of beryllium there are 71 parts of chlorine, and the
       molecular weight of BeCl_{2} = 80; hence the vapour density
       should be 40 or _n_{4}0. If Be = 13·5, and beryllium chloride be
       BeCl_{3}, then to 13·5 of beryllium there are 106·5 of chlorine;
       hence the molecular weight would be 120, and the vapour density
       60 or _n_60. The composition is evidently the same in both cases,
       because 9 : 71 :: 13·5 : 106·5. Thus, if the symbol of an element
       designate different atomic weights, apparently very different
       formulæ may equally well express both the percentage composition
       of compounds, and those properties which are required by the laws
       of multiple proportions and equivalents. The chemists of former
       days accurately expressed the composition of substances, and
       accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6,
       Si = 14, &c. The Gerhardt equivalents are also satisfied by them,
       because O = 16, C = 12, Si = 28, &c., are multiples of them.
       The choice of one or the other multiple quantity for the atomic
       weight is impossible without a firm and concrete conception of
       the molecule and atom, and this is only obtained as a consequence
       of the law of Avogadro-Gerhardt, and hence the modern atomic
       weights are the results of this law (_see_ Note 28).

With the establishment of a true conception of molecules and atoms,
chemical formulæ became direct expressions, not only of composition,[22]
but also of molecular weight or _vapour density_, and consequently of a
series of fundamental chemical and physical data, inasmuch as a number
of the properties of substances are dependent on their vapour density,
or molecular weight and composition. The vapour density D = M/2. For
instance, the formula of ethyl ether is C_{4}H_{10}O, corresponding
with the molecular weight 74, and the vapour density 37, which is the
fact. Therefore, the density of vapours and gases has ceased to be
an empirical magnitude obtained by experiment only, and has acquired
a rational meaning. It is only necessary to remember that 2 grams
of hydrogen, or the molecular weight of this primary gas in grams,
occupies, at 0° and 760 mm. pressure, a volume of 22·3 litres (or
22,300 cubic centimetres), in order to directly determine the weights
of cubical measures of gases and vapours from their formulæ, because
_the molecular weights in grams of all other vapours at 0° and 760 mm.
occupy the same volume, 22·3 litres_. Thus, for example, in the case
of carbonic anhydride, CO_{2}, the molecular weight M = 44, hence 44
grams of carbonic anhydride at 0° and 760 mm. occupy a volume of 22·3
litres--consequently, a litre weighs 1·97 gram. By combining the laws of
gases--Gay-Lussac's, Mariotte's, and Avogadro-Gerhardt's--we obtain[23]
a general formula for gases

                        6200_s_(273 + _t_) = M_p_

where _s_ is the weight in grams of a cubic centimetre of a vapour or
gas at a temperature _t_ and pressure _p_ (expressed in centimetres of
mercury) if the molecular weight of the gas = M. Thus, for instance, at
100° and 760 millimetres pressure (_i.e._ at the atmospheric pressure)
the weight of a cubic centimetre of the vapour of ether (M = 74) is _s_
= 0·0024.[24]

  [22] The percentage amounts of the elements contained in a given
       compound may be calculated from its formula by a simple
       proportion. Thus, for example, to find the percentage amount of
       hydrogen in hydrochloric acid we reason as follows:--HCl shows
       that hydrochloric acid contains 35·5 of chlorine and 1 part of
       hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1
       part by weight of hydrogen, consequently 100 parts by weight of
       hydrochloric acid will contain as many more units of hydrogen as
       100 is greater than 36·5; therefore, the proportion is as
       follows--_x_ : 1 :: 100 : 36·5 or _x_ = 100/36·5 = 2·739.
       Therefore 100 parts of hydrochloric acid contain 2·739 parts of
       hydrogen. In general, when it is required to transfer a formula
       into its percentage composition, we must replace the symbols by
       their corresponding atomic weights and find their sum, and knowing
       the amount by weight of a given element in it, it is easy by
       proportion to find the amount of this element in 100 or any other
       quantity of parts by weight. If, on the contrary, it be required
       to find the formula from a given percentage composition, we must
       proceed as follows: Divide the percentage amount of each element
       entering into the composition of a substance by its atomic weight,
       and compare the figures thus obtained--they should be in simple
       multiple proportion to each other. Thus, for instance, from the
       percentage composition of hydrogen peroxide, 5·88 of hydrogen and
       94·12 of oxygen, it is easy to find its formula; it is only
       necessary to divide the amount of hydrogen by unity and the amount
       of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained,
       which are in the ratio 1 : 1, which means that in hydrogen
       peroxide there is one atom of hydrogen to one atom of oxygen.

       The following is a proof of the practical rule given above _that
       to find the ratio of the number of atoms from the percentage
       composition, it is necessary to divide the percentage amounts
       by the atomic weights of the corresponding substances, and to
       find the ratio which these numbers bear to each other_. Let us
       suppose that two radicles (simple or compound), whose symbols
       and combining weights are A and B, combine together, forming
       a compound composed of _x_ atoms of A and _y_ atoms of B. The
       formula of the substance will be A_x_B_y_. From this formula we
       know that our compound contains _x_A parts by weight of the first
       element, and _y_B of the second. In 100 parts of our compound
       there will be (by proportion) (100. _x_A)/(_x_A + _y_B) of the
       first element, and (100. _y_B)/(_x_A + _y_B) of the second. Let
       us divide these quantities, expressing the percentage amounts by
       the corresponding combining weights; we then obtain 100_x_/(_x_A
       + _y_B) for the first element and 100_y_/(_x_A + _y_B) for the
       second element. And these numbers are in the ratio _x_ : _y_--that
       is, in the ratio of the number of atoms of the two substances.

       It may be further observed that even the very language or
       nomenclature of chemistry acquires a particular clearness and
       conciseness by means of the conception of molecules, because then
       the names of substances may directly indicate their composition.
       Thus the term 'carbon dioxide' tells more about and expresses
       CO_{2} better than carbonic acid gas, or even carbonic anhydride.
       Such nomenclature is already employed by many. But expressing
       the composition without an indication or even hint as to the
       properties, would be neglecting the advantageous side of the
       present nomenclature. Sulphur dioxide, SO_{2}, expresses the same
       as barium dioxide, BaO_{2}, but sulphurous anhydride indicates
       the acid properties of SO_{2}. Probably in time one harmonious
       chemical language will succeed in embracing both advantages.

  [23] This formula (which is given in my work on 'The Tension of
       Gases,' and in a somewhat modified form in the 'Comptes Rendus,'
       Feb. 1876) is deduced in the following manner. According to the
       law of Avogadro-Gerhardt, M = 2D for all gases, where M is the
       molecular weight and D the density referred to hydrogen. But it is
       equal to the weight _s__{0} of a cubic centimetre of a gas in
       grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is
       the weight in grams of a cubic centimetre of hydrogen. But the
       weight _s_ of a cubic centimetre of a gas at a temperature _t_ and
       under a pressure _p_ (in centimetres) is equal to _s__{0}_p_/76(1
       + _at_). Therefore, _s__{0} = _s_.76(1 + _at_)/_p_; hence D =
       76._s_(1 + _at_)/0·0000898_p_, whence M = 152_s_(1 +
       _at_)/0·0000898_p_, which gives the above expression, because
       1/_a_ = 273, and 152 multiplied by 273 and divided by 0·0000898 is
       nearly 6200. In place of _s_, _m/v_ may be taken, where _m_ is the
       weight and _v_ the volume of a vapour.

  [24] The above formula may be directly applied in order to ascertain
       the molecular weight from the data; weight of vapour _m_ grms.,
       its volume _v_ c.c., pressure _p_ cm., and temperature _t_°; for
       _s_ = the weight of vapour _m_, divided by the volume _v_, and
       consequently M = 6,200_m_(273 + _t_)/_pv_. Therefore, instead
       of the formula (_see_ Chapter II., Note 34), _pv_ = R(273 +
       _t_), where R varies with the mass and nature of a gas, we
       may apply the formula _pv_ = 6,200(_m_/M)(273 + _t_). These
       formulæ simplify the calculations in many cases. For example,
       required the volume _v_ occupied by 5 grms. of aqueous vapour
       at a temperature _t_ = 127° and under a pressure _p_ = 76 cm.
       According to the formula M = 6,200_m_(273 + _t_)/_pv_, we find
       that _v_ = 9,064 c.c., as in the case of water M = 18, _m_ in
       this instance = 5 grms. (These formulæ, however, like the laws of
       gases, are only approximate.)

As the molecules of many elements (hydrogen, oxygen, nitrogen, chlorine,
bromine, sulphur--at least at high temperatures) are of uniform
composition, the formulæ of the compounds formed by them directly
indicate the composition by volume. So, for example, the formula HNO_{3}
directly shows that in the decomposition of nitric acid there is
obtained 1 vol. of hydrogen, 1 vol. of nitrogen, and 3 vols. of oxygen.

And since a great number of mechanical, physical, and chemical
properties are directly dependent on the elementary and volumetric
composition, and on the vapour density, the accepted system of atoms
and molecules gives the possibility of simplifying a number of most
complex relations. For instance, it may be easily demonstrated _that
the vis viva of the molecules of all vapours and gases is alike_. For
it is proved by mechanics that the _vis viva_ of a moving mass = (1/2)
_mv_^2, where _m_ is the mass and _v_ the velocity. For a molecule,
_m_ = M, or the molecular weight, and the velocity of the motion of
gaseous molecules = a constant which we will designate by C, divided
by the square root of the density of the gas[25] = C/[sqrt]D, and as D
= M/2, the _vis viva_ of molecules = C^2--that is, a constant for all
molecules. _Q.E.D._[26] The specific heat of gases (Chapter XIV.), and
many other of their properties, are determined by their density, and
consequently by their molecular weight. Gases and vapours in passing
into a liquid state evolve the so-called _latent heat_, which also
proves to be in connection with the molecular weight. The observed
latent heats of carbon bisulphide, CS_{2} = 90, of ether, C_{4}H_{10}O,
= 94, of benzene, C_{6}H_{6}, = 109, of alcohol, C_{2}H_{6}O, = 200,
of chloroform, CHCl_{3}, = 67, &c., show the amount of heat expended
in converting one part by weight of the above substances into vapour.
A great uniformity is observed if the measure of this heat he referred
to the weight of the molecule. For carbon bisulphide the formula CS_{2}
expresses a weight 76, hence the latent heat of evaporation referred to
the molecular quantity CS_{2} = 76 x 90 = 6,840, for ether = 9,656, for
benzene = 8,502, for alcohol = 9,200, for chloroform = 8,007, for water
= 9,620, &c. That is, for molecular quantities, the latent heat varies
comparatively little, from 7,000 to 10,000 heat units, whilst for equal
parts by weight it is ten times greater for water than for chloroform
and many other substances.[27]

  [25] Chapter I., Note 34.

  [26] _The velocity of the transmission of sound through gases and
       vapours_ closely bears on this. It = [sqrt](_Kpg_)/D(1 +
       [Greek: a]_t_), where _K_ is the ratio between the two specific
       heats (it is approximately 1·4 for gases containing two atoms in a
       molecule), _p_ the pressure of the gas expressed by weight (that
       is, the pressure expressed by the height of a column of mercury
       multiplied by the density of mercury), _g_ the acceleration of
       gravity, D the weight of a cubic measure of the gas, [Greek: a] =
       0·00367, and _t_ the temperature. Hence, if _K_ be known, and as D
       can he found from the composition of a gas, we can calculate the
       velocity of the transmission of sound in that gas. Or if this
       velocity be known, we can find _K_. The relative velocities of
       sound in two gases can he easily determined (Kundt).

       If a horizontal glass tube (about 1 metre long and closed at
       both ends) be full of a gas, and be firmly fixed at its middle
       point, then it is easy to bring the tube and gas into a state
       of vibration, by rubbing it from centre to end with a damp
       cloth. The vibration of the gas is easily rendered visible, if
       the interior of the tube be dusted with lycopodium (the yellow
       powder-dust or spores of the lycopodium plant is often employed
       in medicine), before the gas is introduced and the tube fused
       up. The fine lycopodium powder arranges itself in patches, whose
       number depends on the velocity of sound in the gas. If there
       be 10 patches, then the velocity of sound in the gas is ten
       times slower than in glass. It is evident that this is an easy
       method of comparing the velocity of sound in gases. It has been
       demonstrated by experiment that the velocity of sound in oxygen
       is four times less than in hydrogen, and the square roots of the
       densities and molecular weights of hydrogen and oxygen stand in
       this ratio.

  [27] If the conception of the molecular weights of substances does not
       give an exact law when applied to the latent heat of evaporation,
       at all events it brings to light a certain uniformity in
       figures, which otherwise only represent the simple result of
       observation. Molecular quantities of liquids appear to expend
       almost equal amounts of heat in their evaporation. It may be said
       that the latent heat of evaporation of molecular quantities is
       approximately constant, because the _vis viva_ of the motion of
       the molecules is, as we saw above, a constant quantity. According
       to thermodynamics the latent heat of evaporation is equal to
       ((_t_ + 273)/E)(_n_´-_n_)_dp_/_d_T × 13·59, where _t_ is the
       boiling point, _n_´ the specific volume (_i.e._ the volume of a
       unit of weight) of the vapour, and _n_ the specific volume of
       the liquid, _dp_/_d_T the variation of the tension with a rise
       of temperature per 1°, and 13·89 the density of the mercury
       according to which the pressure is measured. Thus the latent heat
       of evaporation increases not only with a decrease in the vapour
       density (_i.e._ the molecular weight), but also with an increase
       in the boiling point, and therefore depends on different factors.

Generalising from the above, the weight of the molecule determines the
properties of a substance _independently of its composition_--_i.e._ of
the number and quality of the atoms entering into the molecule--whenever
the substance is in a gaseous state (for instance, the density of
gases and vapours, the velocity of sound in them, their specific heat,
&c.), or passes into that state, as we see in the latent heat of
evaporation. This is intelligible from the point of view of the atomic
theory in its present form, for, besides a rapid motion proper to the
molecules of gaseous bodies, it is further necessary to postulate that
these molecules are dispersed in space (filled throughout with the
luminiferous ether) like the heavenly bodies distributed throughout
the universe. Here, as there, it is only the degree of removal (the
distance) and the masses of substances which take effect, while
those peculiarities of a substance which are expressed in chemical
transformations, and only come into action on near approach or on
contact, are in abeyance by reason of the dispersal. Hence it is at once
obvious, in the first place, that in the case of solids and liquids,
in which the molecules are closer together than in gases and vapours,
a greater complexity is to be expected, _i.e._ a dependence of all
the properties not only upon the weight of the molecule but also upon
its composition and quality, or upon the properties of the individual
chemical atoms forming the molecule; and, in the second place, that,
in the case of a small number of molecules of any substance being
disseminated through a mass of another substance--for example, in the
formation of weak (dilute) solutions (although in this case there is
an act of chemical reaction--_i.e._ a combination, decomposition, or
substitution)--the dispersed molecules will alter the properties of
the medium in which they are dissolved, almost in proportion to the
molecular weight and almost independently of their composition. The
greater the number of molecules disseminated--_i.e._ the stronger the
solution--the more clearly defined will those properties become which
depend upon the composition of the dissolved substance and its relation
to the molecules of the solvent, for the distribution of one kind of
molecules in the sphere of attraction of others cannot but be influenced
by their mutual chemical reaction. These general considerations give
a starting point for explaining why, since the appearance of Van't
Hoff's memoir (1886), 'The Laws of Chemical Equilibrium in a Diffused
Gaseous or Liquid State' (_see_ Chapter I., Note 19), it has been found
more and more that _dilute_ (weak) solutions exhibit such variations
of properties as depend wholly upon the weight and number of the
molecules and not upon their composition, and even give the means of
determining the weight of molecules by studying the variations of the
properties of a solvent on the introduction of a small quantity of a
substance passing into solution. Although this subject has been already
partially considered in the first chapter (in speaking of solutions),
and properly belongs to a special (physical) branch of chemistry, we
touch upon it here because the meaning and importance of molecular
weights are seen in it in a new and peculiar light, and because it gives
a method for determining them whenever it is possible to obtain dilute
solutions. Among the numerous properties of dilute solutions which have
been investigated (for instance, the osmotic pressure, vapour tension,
boiling point, internal friction, capillarity, variation with change of
temperature, specific heat, electroconductivity, index of refraction,
&c.) we will select one--the 'depression' or fall of the temperature of
freezing (Raoult's cryoscopic method), not only because this method has
been the most studied, but also because it is the most easily carried
out and most frequently applied for determining the weight of the
molecules of substances in solution, although here, owing to the novelty
of the subject there are also many experimental discrepancies which
cannot as yet be explained by theory.[27 bis]

  [27 bis] The osmotic pressure, vapour tension of the solvent, and
       several other means applied like the cryoscopic method to dilute
       solutions for determining the molecular weight of a substance in
       solution, are more difficult to carry out in practice, and only
       the method of _determining the rise of the boiling point_ of
       dilute solutions can from its facility be placed parallel with the
       cryoscopic method, to which it bears a strong resemblance, as in
       both the solvent changes its state and is partially separated. In
       the boiling point method it passes off in the form of a vapour,
       while in cryoscopic determinations it separates out in the form of
       a solid body.

       Van't Hoff, starting from the second law of thermodynamics, showed
       that the dependence of the rise of pressure (_dp_) upon a rise of
       temperature (_d_T) is determined by the equation _dp_ =
       (_kmp_/2T^2)_d_T, where _k_ is the latent heat of evaporation of
       the solvent, _m_ its molecular weight, _p_ the tension of the
       saturated vapour of the solvent at T, and T the absolute
       temperature (T = 273 + _t_), while Raoult found that the quantity
       (_p_-_p´_)/_p_ (Chapter I., Note 50) or the measure of the
       relative fall of tension (_p_ the tension of the solvent or water,
       and _p´_ of the solution) is found by the ratio of the number of
       molecules, _n_ of the substance dissolved, and N of the solvent,
       so that (_p_-_p´_)/_p_ = C_n_/(N + _n_) where C is a constant.
       With very dilute solutions _p_ _-p´_ may be taken as equal to
       _dp_, and the fraction _n_/(N + _n_) as equal to _n_/N (because in
       that case the value of N is very much greater than _n_), and then,
       judging from experiment, C is nearly unity--hence: _dp/p_ = _n_/N
       or _dp_ = _np_/N, and on substituting this in the above equation
       we have (_kmp_/2T^2)_d_T = _np_/N. Taking a weight of the solvent
       _m_/N = 100, and of the substance dissolved (per 100 of the
       solvent) _q_, where _q_ evidently = _n_M, if M be the molecular
       weight of the substance dissolved, we find that _n_/N = _qm_/100M,
       and hence, according to the preceding equation, we have M =
       (0·02T^2/_k_)·(_q_/_d_T), that is, by taking a solution of _q_
       grms. of a substance in 100 grms. of a solvent, and determining by
       experiment the rise of the boiling point _d_T, we find the
       molecular weight M of the substance dissolved, because the
       fraction 0·02T^2/_k_ is (for a given pressure and solvent) a
       constant; for water at 100° (T = 373°) when _k_ = 534 (Chapter I.,
       Note 11), it is nearly 5·2, for ether nearly 21, for bisulphide of
       carbon nearly 24, for alcohol nearly 11·5, &c. As an example, we
       will cite from the determinations made by Professor Sakurai, of
       Japan (1893), that when water was the solvent and the substance
       dissolved, corrosive sublimate, HgCl_{2}, was taken in the
       quantity _q_ = 8·978 and 4·253 grms., the rise in the boiling
       point _d_T was = O°·179 and 0°·084, whence M = 261 and 263, and
       when alcohol was the solvent, _q_ = 10·873 and 8·765 and _d_T =
       0°·471 and 0°·380, whence M = 266 and 265, whilst the actual
       molecular weight of corrosive sublimate = 271, which is very near
       to that given by this method. In the same manner for aqueous
       solutions of sugar (M = 342), when _q_ varied from 14 to 2·4, and
       the rise of the boiling point from 0°·21 to 0°·035, M was found to
       vary between 339 and 364. For solutions of iodine I_{2} in ether,
       the molecular weight was found by this method to be between 255
       and 262, and I_{2} = 254. Sakurai obtained similar results
       (between 247 and 262) for solutions of iodine in bisulphide of
       carbon.

       We will here remark that in determining M (the molecular weight of
       the substance dissolved) at small but increasing concentrations
       (per 100 grms. of water), the results obtained by Julio Baroni
       (1893) show that the value of M found by the formula may either
       increase or decrease. An increase, for instance, takes place in
       aqueous solutions of HgCl_{2} (from 255 to 334 instead of 271),
       KNO_{3} (57-66 instead of 101), AgNO_{3} (104-107 instead of 170),
       K_{2}SO_{4} (55-89 instead of 174), sugar (328-348 instead of
       342), &c. On the contrary the calculated value of M decreases as
       the concentration increases, for solutions of KCl (40-39 instead
       of 74·5), NaCl (33-28 instead of 58·5), NaBr (60-49 instead of
       103), &c. In this case (as also for LiCl, NaI, C_{2}H_{3}NaO_{2},
       &c.) the value of _i_ (Chapter I., Note 49), or the ratio between
       the actual molecular weight and that found by the rise of the
       boiling point, was found to increase with the concentration,
       _i.e._ to be greater than 1, and to differ more and more from
       unity as the strength of the solution becomes greater. For
       example, according to Schlamp (1894), for LiCl, with a variation
       of from 1·1 to 6·7 grm. LiCl per 100 of water, _i_ varies from
       1·63 to 1·89. But for substances of the first series (HgCl_{2},
       &c.), although in very dilute solutions _i_ is greater than 1, it
       approximates to 1 as the concentration increases, and this is the
       normal phenomenon for solutions which do not conduct an electric
       current, as, for instance, of sugar. And with certain
       electrolytes, such as HgCl_{2}, MgSO_{4}, &c., _i_ exhibits a
       similar variation; thus, for HgCl_{2} the value of M is found to
       vary between 255 and 334; that is, _i_ (as the molecular weight =
       271) varies between 1·06 and 0·81. Hence I do not believe that the
       difference between _i_ and unity (for instance, for CaCl_{2}, _i_
       is about 3, for KI about 2, and decreases with the concentration)
       can at present be placed at the basis of any general chemical
       conclusions, and it requires further experimental research. Among
       other methods by which the value of _i_ is now determined for
       dilute solutions is the study of their electroconductivity,
       admitting that _i_ = 1 + _a_(_k_-1), where _a_ = the ratio of the
       molecular conductivity to the limiting conductivity corresponding
       to an infinitely large dilution (_see_ Physical Chemistry), and
       _k_ is the number of ions into which the substance dissolved can
       split up. Without entering upon a criticism of this method of
       determining _i_, I will only remark that it frequently gives
       values of _i_ very close to those found by the depression of the
       freezing point and rise of the boiling point; but that this
       accordance of results is sometimes very doubtful. Thus for a
       solution containing 5·67 grms. CaCl_{2} per 100 grms. of water,
       _i_, according to the vapour tension = 2·52, according to the
       boiling point = 2·71, according to the electroconductivity = 2·28,
       while for solutions in propyl alcohol (Schlamp 1894) _i_ is near
       to 1·33. In a word, although these methods of determining the
       molecular weight of substances in solution show an undoubted
       progress in the general chemical principles of the molecular
       theory, there are still many points which require explanation.

       We will add certain general relations which apply to these
       problems. Isotonic (Chapter I., Note 19) solutions exhibit not
       only similar osmotic pressures, but also the same vapour tension,
       boiling point and freezing temperature. The osmotic pressure bears
       the same relation to the fall of the vapour tension as the
       specific gravity of a solution does to the specific gravity of the
       vapour of the solvent. The general formulæ underlying the whole
       doctrine of the influence of the molecular weight upon the
       properties of solutions considered above, are: 1. Raoult in
       1886-1890 showed that

             ((_p_-_p_´)/_p_) × (100/_a_) × (M/_m_) = a constant C

       where _p_ and _p_´ are the vapour tensions of the solvent and
       substance dissolved, _a_ the amount in grms. of the substance
       dissolved per 100 grms. of solvent, M and _m_ the molecular
       weights of the substance dissolved and solvent. 2. Raoult and
       Recoura in 1890 showed that the constant above C = the ratio of
       the actual vapour density _d_´ of the solvent to the theoretical
       density _d_ calculated according to the molecular weight. This
       deduction may now be considered proved, because both the fall of
       tension and the ratio of the vapour densities _d_´/_d_ give, for
       water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of
       carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By
       applying the principles of thermodynamics and calling L_{1} the
       latent heat of fusion and T_{1} the absolute (= _t_ + 273)
       temperature of fusion of the solvent, and L_{2} and T_{2} the
       corresponding values for the boiling point, Van't Hoff in
       1886-1890 deduced:--

         (Depression of freezing point)/(Rise of boiling point)
                                    = (L_{2}/L_{1}) × (T_{1}^2/T_{2}^2)

          Depression of freezing point = (AT_{1}^{2}_a_)/(L_{1}M_{1})

              Rise of boiling point = (AT_{2}^{2}_a_)/(L_{2}M_{1})

       where A = 0·01988 (or nearly 0·02 as we took it above), _a_ is
       the weight in grms. of the substance dissolved per 100 grms. of
       the solvent, M_{1} the molecular weight of the dissolved substance
       (in the solution), and M the molecular weight of this substance
       according to its composition and vapour density, then _i_ =
       M/M_{1}. The experimental data and theoretical considerations upon
       which these formulæ are based will be found in text-books of
       physical and theoretical chemistry.

If 100 gram-molecules of water, _i.e._ 1,800 grms, be taken and _n_
gram-molecules of sugar, C_{12}H_{22}O_{11}, _i.e._ _n_ 342 grms., be
dissolved in them, then the depression _d_, or fall (counting from
0°) of the temperature of the formation of ice will be (according to
Pickering)

          _n_ = 0    0·010    0·025    0·100    0·250    1·000
          _d_ = 0°  0°·0103  0°·0280  0°·1115  0°·2758  1°·1412

which shows that for high degrees of dilution (up to 0·25_n_) _d_
approximately (estimating the possible errors of experiment at ±0°·005)
= _n_1·10, because then _d_ = 0°, 0°·0110, 0°·0275, 0°·1100, 0°·2750,
1°·1000, and the difference between these figures and the results
of experiment for very dilute solutions is less than the possible
errors of experiment (for _n_ = 1 the difference is already greater)
and therefore for dilute solutions of sugar it may be said that _n_
molecules of sugar in dissolving in 100 molecules of water give a
depression of about 1°·1_n_. Similar data for acetone (Chapter I., Note
49) give a depression of 1°·006_n_ for _n_ molecules of acetone per 100
molecules of water. And in general, for indifferent substances (the
majority of organic bodies) the depression per 100H_{2}O is _nearly
n_1°·1 to _n_1°·0 (ether, for instance, gives the last number), and
consequently in dissolving in 100 grms. of water it is about 18°·0_n_
to 19°·0_n_, taking this rule to apply to the case of a small number
of _n_ (not over 0·2_n_). If instead of water, other liquid or fused
solvents (for example, benzene, acetic acid, acetone, nitrobenzene or
molten naphthaline, metals, &c.) be taken and in the proportion of 100
molecules of the solvent to _n_ molecules of a dissolved indifferent
(neither acid nor saline) substance, then the depression is found to be
equal to from 0°·62_n_ to 0°·65_n_ and in general K_n_. If the molecular
weight of the solvent = _m_, then 100 gram-molecules will weigh 100_m_
grms., and the depression will be approximately (taking 0·63_n_) equal
to _m_0·63_n_ degrees for _n_ molecules of the substance dissolved in
100 grms. of the solvent, or in general the depression for 100 grms.
of a given solvent = _kn_ where _k_ is almost a constant quantity (for
water nearly 18, for acetone nearly 37, &c.) for all dilute solutions.
Thus, having found a convenient solvent for a given substance and
prepared a definite (by weight) solution (_i.e._ knowing how many grms.
_r_ of the solvent there are to _q_ grms. of the substance dissolved)
and having determined the depression _d_--_i.e._ the fall in temperature
of freezing for the solvent--it is possible to determine the molecular
weight of the substance dissolved, because _d_ = _kn_ where _d_ is found
by experiment and _k_ is determined by the nature of the solvent, and
therefore _n_ or the number of molecules of the substance dissolved can
be found. But if _r_ grms. of the solvent and _q_ grms. of the substance
dissolved are taken, then there are 100_q_/_r_ of the latter per 100
grms. of the former, and this quantity = _n_X, where _n_ is found from
the depression and = _d_/_k_ and X is the molecular weight of the
substance dissolved. Hence X = 100_qk_/_rd_, which gives the molecular
weight, naturally only approximately, but still with sufficient accuracy
to easily indicate, for instance, whether in peroxide of hydrogen the
molecule contains HO or H_{2}O_{2} or H_{3}O_{3}, &c. (H_{2}O_{2} is
obtained). Moreover, attention should be drawn to the fact that a great
many substances taken as solvents give per 100 molecules a depression of
about 0·63_n_, whilst water gives about 1·05_n_, _i.e._ a larger
quantity, as though the molecules of liquid water were more complex than
is expressed by the formula H_{2}O.[28] A similar phenomenon which
repeats itself in the osmotic pressure, vapour tension of the solvent,
&c. (_see_ Chapter I., Notes 19 and 49), _i.e._ a variation of the
constant (_k_ for 100 grms. of the solvent or K for 100 molecules of it),
is also observed in passing from indifferent substances to saline (to
acids, alkalis and salts) both in aqueous and other solutions as we will
show (according to Pickering's data 1892) for solutions of NaCl and
CuSO_{4} in water. For

                    _n_ = 0·01  0·03  0·05  0·1  0·5

molecules of NaCl the depression is

            _d_ = 0°·0177  0°·0598  0°·0992  0°·1958  0°·9544

which corresponds to a depression per molecule

                    K = 1·77  1·96  1·98  1·96  1·91

_i.e._ here in the most dilute solutions (when _n_ is nearly 0) _d_ is
obtained about 1·7_n_, while in the case of sugar it was about 1·1_n_.
For CuSO_{4} for the same values of _n_, experiment gave:

            _d_ = 0°·0164  0°·0451  0°·0621  0°·1321  0°·5245
              K =  1·64     1·50     1·44     1·32     1·05

_i.e._ here again _d_ for very dilute solutions is nearly 1·7_n_, but
the value of K falls as the solution becomes more concentrated, while
for NaCl it at first increased and only fell for the more concentrated
solutions. The value of K in the solution of _n_ molecules of a body
in 100H_{2}O, when _d_ = K_n_, for very dilute solutions of CaCl_{2}
is nearly 2·6, for Ca(NO_{3})_{2} nearly 2·5, for HNO_{3}, KI and KHO
nearly 1·9-2·O, for borax Na_{2}B_{4}O_{7} nearly 3·7, &c., while for
sugar and similar substances it is, as has been already mentioned,
nearly 1·0-1·1. Although these figures are very different[28 bis] still
_k_ and K may be considered constant for analogous substances, and
therefore the weight of the molecule of the body in solution can be
found from _d_. And as the vapour tension of solutions and their boiling
points (_see_ Note 27 bis and Chapter I., Note 51) vary in the same
manner as the freezing point depression, so they also may serve as means
for determining the molecular weight of a substance in solution.[29]

  [28] A similar conclusion respecting the molecular weight of liquid
       water (_i.e._ that its molecule in a liquid state is more
       complex than in a gaseous state, or polymerized into H_{8}O_{4},
       H_{6}O_{3} or in general into _n_H_{2}O) is frequently met
       in chemico-physical literature, but as yet there is no basis
       for its being fully admitted, although it is possible that a
       polymerization or aggregation of several molecules into one
       takes place in the passage of water into a liquid or solid
       state, and that there is a converse depolymerization in the
       act of evaporation. Recently, particular attention has been
       drawn to this subject owing to the researches of Eötvös (1886)
       and Ramsay and Shields (1893) on the variation of the surface
       tension N with the temperature (N = the capillary constant _a_^2
       multiplied by the specific gravity and divided by 2, for example,
       for water at 0° and 100° the value of _a_^2 = 15·41 and 12·58
       sq. mm., and the surface tension 7·92 and 6·04). Starting from
       the absolute boiling point (Chapter II., Note 29) and adding 6°,
       as was necessary from all the data obtained, and calling this
       temperature T, it is found that AS = _k_T, where S is the surface
       of a gram-molecule of the liquid (if M is its weight in grams,
       _s_ its sp. gr., then its sp. volume = M/_s_, and the surface
       S = [3root](M/_s_)^2), A the surface tension (determined by
       experiment at T), and _k_ a constant which is independent of
       the composition of the molecule. The equation AS = _k_T is in
       complete agreement with the well-known equation for gases _vp_
       = RT (p. 140) which serves for deducing the molecular weight
       from the vapour density. Ramsay's researches led him to the
       conclusion that the liquid molecules of CS_{2}, ether, benzene,
       and of many other substances, have the same value as in a state
       of vapour, whilst with other liquids this is not the case, and
       that to obtain an accordance, that is, that _k_ shall be a
       constant, it is necessary to assume the molecular weight in the
       liquid state to be _n_ times as great. For the fatty alcohols and
       acids _n_ varies from 1-1/2 to 3-1/2, for water from 2-1/4 to 4,
       according to the temperature (at which the depolymerization takes
       place). Hence, although this subject offers a great theoretical
       interest, it cannot be regarded as firmly established, the more
       so since the fundamental observations are difficult to make and
       not sufficiently numerous; should, however, further experiments
       confirm the conclusions arrived at by Professor Ramsay, this will
       give another method of determining molecular weights.

  [28 bis] Their variance is expressed in the same manner as was done by
       Van't Hoff (Chapter I., Notes 19 and 49) by the quantity _i_,
       taking it as = 1 when _k_ = 1·05, in that case for KI, _i_ is
       nearly 2, for borax about 4, &c.

  [29] We will cite one more example, showing the direct dependence of
       the properties of a substance on the molecular weight. If one
       molecular part by weight of the various chlorides--for instance,
       of sodium, calcium, barium, &c.--be dissolved in 200 molecular
       parts by weight of water (for instance, in 3,600 grams) then
       it is found that the greater the molecular weight of the salt
       dissolved, the greater is the specific gravity of the resultant
       solution.

                  Molecular    Sp. gr.                Molecular   Sp. gr.
                   weight       at 15°                 weight      at 15°
         HCl         36·5       1·0041       CaCl_{2}   111        1·0236
         NaCl        58·5       1·0106       NiCl_{2}   130        1·0328
         KCl         74·5       1·0121       ZnCl_{2}   136        1·0331
         BeCl_{2}    80         1·0138       BaCl_{2}   208        1·0489
         MgCl_{2}    95         1·0203

Thus not only in vapours and gases, but also in dilute solutions
of solid and liquid substances, we see that if not all, still many
properties are wholly dependent upon the molecular weight and not upon
the quality of a substance, and that this gives the possibility of
determining the weight of molecules by studying these properties (for
instance, the vapour density, depression of the freezing point, &c.) It
is apparent from the foregoing that the physical and even more so the
chemical properties of homogeneous substances, more especially solid and
liquid, do not depend exclusively upon the weights of their molecules,
but that many are in definite (_see_ Chapter XV.) dependence upon the
weights of the atoms of the elements entering into their composition,
and are determined by their quantitative and individual peculiarities.
Thus the density of solids and liquids (as will afterwards be shown) is
chiefly determined by the weights of the atoms of the elements entering
into their composition, inasmuch as dense elements (in a free state) and
compounds are only met with among substances containing elements with
large atomic weights, such as gold, platinum, and uranium. And these
elements themselves, in a free state, are the heaviest of all elements.
Substances containing such light elements as hydrogen, carbon, oxygen
and nitrogen (like many organic substances) never have a high specific
gravity; in the majority of cases it scarcely exceeds that of water. The
density generally decreases with the increase of the amount of hydrogen,
as the lightest element, and a substance is often obtained lighter than
water. The refractive power of substances also entirely depends on the
composition and the properties of the component elements.[29 bis] The
history of chemistry presents a striking example in point--Newton
foresaw from the high refractive index of the diamond that it would
contain a combustible substance since so many combustible oils have a
high refractive power. We shall afterwards see (Chapter XV.) that many
of those properties of substances which are in direct dependence not
upon the weight of the molecules but upon their composition, or, in
other words, upon the properties and quantities of the elements entering
into them, stand in a peculiar (periodic) dependence upon the atomic
weight of the elements; that is, the mass (of molecules and atoms),
proportional to the weight, determines the properties of substances
as it also determines (with the distance) the motions of the heavenly
bodies.

  [29 bis] With respect to the optical refractive power of substances, it
       must first be observed that the coefficient of refraction is
       determined by two methods: (_a_) either all the data are referred
       to one definite ray--for instance, to the Fraunhofer (sodium) line
       D of the solar spectrum--that is, to a ray of definite wave
       length, and often to that red ray (of the hydrogen spectrum) whose
       wave length is 656 millionths of a millimetre; (_b_) or Cauchy's
       formula is used, showing the relation between the coefficient of
       refraction and dispersion to the wave length _n_ = A +
       (B/([Greek: l]^2)), where A and B are two constants varying for
       every substance but constant for all rays of the spectrum, and
       [Greek: l] is the wave length of that ray whose coefficient of
       refraction is _n_. In the latter method the investigation usually
       concerns the magnitudes of A, which are independent of dispersion.
       We shall afterwards cite the data, investigated by the first
       method, by which Gladstone, Landolt, and others established the
       conception of the refraction equivalent.

       It has long been known that the _coefficient of refraction n_
       for a given substance decreases with the density of a substance D,
       so that the magnitude (_n_-1) ÷ D = C is almost constant for a
       given ray (having a definite wave length) and for a given
       substance. This constant is called the _refractive energy_, and
       its product with the atomic or molecular weight of a substance the
       _refraction equivalent_. The coefficient of refraction of oxygen
       is 1·00021, of hydrogen 1·00014, their densities (referred to
       water) are 0·00143 and 0·00009, and their atomic weights, O = 16,
       H = 1; hence their refraction equivalents are 3 and 1·5. Water
       contains H_{2}O, consequently the sum of the equivalents of
       refraction is (2 × 1·5) + 3 = 6. But as the coefficient of
       refraction of water = 1·331, its refraction equivalent = 5·958, or
       nearly 6. Comparison shows that, approximately, the sum of the
       refraction equivalents of the atoms forming compounds (or
       mixtures) is equal to the refraction equivalent of the compound.
       According to the researches of Gladstone, Landolt, Hagen, Brühl
       and others, the refraction equivalents of the elements are--H =
       1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of
       oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4,
       Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn =
       12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co =
       10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd =
       13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The
       refraction equivalents of many elements could only be calculated
       from the solutions of their compounds. The composition of a
       solution being known it is possible to calculate the refraction
       equivalent of one of its component parts, those for all its other
       components being known. The results are founded on the acceptance
       of a law which cannot be strictly applied. Nevertheless the
       representation of the refraction equivalents gives an easy means
       for directly, although only approximately, obtaining the
       coefficient of refraction from the chemical composition of a
       substance. For instance, the composition of carbon bisulphide is
       CS_{2} = 76, and from its density, 1·27, we find its coefficient
       of refraction to be 1·618 (because the refraction equivalent = 5 +
       2 × 16 = 37), which is very near the actual figure. It is evident
       that in the above representation compounds are looked on as simple
       mixtures of atoms, and the physical properties of a compound as
       the sum of the properties present in the elementary atoms forming
       it. If this representation of the presence of simple atoms in
       compounds had not existed, the idea of combining by a few figures
       a whole mass of data relating to the coefficient of refraction of
       different substances could hardly have arisen. For further details
       on this subject, see works on _Physical Chemistry_.

                              CHAPTER VIII

                       CARBON AND THE HYDROCARBONS

It is necessary to clearly distinguish between the two closely-allied
terms, charcoal and carbon. Charcoal is well known to everybody,
although it is no easy matter to obtain it in a chemically pure state.
Pure charcoal is a simple, insoluble, infusible, combustible substance
produced by heating organic matter, and has the familiar aspect of
a black mass, devoid of any crystalline structure, and completely
insoluble. Charcoal is a substance possessing a peculiar combination
of physical and chemical properties. This substance, whilst in a state
of ignition, combines directly with oxygen; in organic substances it
is found in combination with hydrogen, oxygen, nitrogen, and sulphur.
But in all these combinations there is no real charcoal, as in the same
sense there is no ice in steam. What is found in such combinations
is termed 'carbon'--that is, an element common to charcoal, to those
substances which can be formed from it, and also to those substances
from which it can be obtained. Carbon may take the form of charcoal, but
occurs also as diamond and as graphite. Truly no other element has such
a wide terminology. Oxygen is always called 'oxygen,' whether it is in a
free gaseous state, or in the form of ozone, or oxygen in water, or in
nitric acid or in carbonic anhydride. But here there is some confusion.
In water it is evident that there is no oxygen in a gaseous form, such
as can be obtained in a free state, no oxygen in the form of ozone, but
a substance which is capable of producing both oxygen, ozone, and water.
As an element, oxygen possesses a known chemical individuality, and an
influence on the properties of those combinations into which it enters.
Hydrogen gas is a substance which reacts with difficulty, but the
element hydrogen represents in its combinations an easily displaceable
component part. Carbon may be considered as an atom of carbon matter,
and charcoal as a collection of such atoms forming a whole substance,
or mass of molecules of the substance. The accepted atomic weight
of carbon is 12, because that is the least quantity of carbon which
enters into combination in molecules of its compounds; but the weight
of the molecules of charcoal is probably very much greater. This weight
remains unknown because charcoal is capable of but few direct reactions
and those only at a high temperature (when the weight of its molecules
probably changes, as when ozone changes into oxygen), and it does not
turn into vapour. Carbon exists in nature, both in a free and combined
state, in most varied forms and aspects. Carbon in a free state is
found in at least three different forms, as charcoal, graphite, and the
diamond. In a combined state it enters into the composition of what are
called organic substances--a multitude of substances which are found in
all plants and animals. It exists as carbonic anhydride both in air and
in water, and in the soil and crust of the earth as salts of carbonic
acid and as organic remains.

The variety of the substances of which the structure of plants and
animals is built up is familiar to all. Wax, oil, turpentine, and
tar, cotton and albumin, the tissue of plants and the muscular fibre
of animals, vinegar and starch, are all vegetable and animal matters,
and all carbon compounds.[1] The class of carbon compounds is so vast
that it forms a separate branch of chemistry, known under the name of
organic chemistry--that is, the chemistry of carbon compounds, or, more
strictly, of the hydrocarbons and their derivatives.

  [1] Wood is the non-vital part of ligneous plants: the vital part of
      ordinary trees is situated between the bark and the lignin. Every
      year a layer of lignin is deposited on this part by the juices
      which are absorbed by the roots and drawn up by the leaves; for
      this reason the age of trees may be determined by the number of
      lignin layers deposited. The woody matter consists principally
      of fibrous tissue on to which the lignin or so-called incrusting
      matter has been deposited. The tissue has the composition
      C_{6}H_{10}O_{5}, the substance deposited on it contains more
      carbon and hydrogen and less oxygen. This matter is saturated
      with moisture when the wood is in a fresh state. Fresh birch wood
      contains about 31 p.c. of water, lime wood 47 p.c., oak 35 p.c.,
      pine and fir about 37 p.c. When dried in the air the wood loses a
      considerable quantity of water and not more than 19 p.c. remains.
      By artificial means this loss of water may be increased. If water
      be driven into the pores of wood the latter becomes heavier than
      water, as the lignin of which it is composed has a density of
      about 1·6. One cubic centimetre of birch wood does not weigh more
      than 0·901 gram, fir 0·894, lime tree 0·817, poplar 0·765 when
      in a fresh state; when in a dry state birch weighs 0·622, pine
      0·550, fir 0·355, lime 0·430, guaiacum 1·342, ebony 1·226. On one
      hectare (2·7 acres) of woodland the yearly growth averages the
      amount of 3,000 kilograms (or about 3 tons) of wood, but rarely
      reaches as much as 5,000 kilos. The average chemical composition
      of wood dried in air may be expressed as follows:--Hygroscopic
      water 15 p.c., carbon 42 p.c., hydrogen 5 p.c., oxygen and
      nitrogen 37 p.c., ash 1 p.c. Wood parts with its hygroscopic water
      at 150°, and decomposes at about 300°, giving a brown, brittle,
      so-called red charcoal; above 350° black charcoal is produced.
      As the hydrogen contained in wood requires for its combustion
      about forty parts by weight of oxygen, which is present to the
      amount of about 36 p.c., all that burns of the wood is the carbon
      which it contains, 100 parts of wood only giving out as much heat
      as forty parts of charcoal, and therefore it would be far more
      profitable to use charcoal for heating purposes than wood, if it
      were possible to obtain it in such quantities as correspond with
      its percentage ratio--that is forty parts per 100 parts of wood.
      Generally, however, the quantity produced is far less, not more
      than 30 p.c., because part of the carbon is given off as gas, tar,
      &c. If wood has to be transported great distances, or if it is
      necessary to obtain a very high temperature by burning it, then
      even as little as 25 p.c. of charcoal from 100 parts of wood may be
      advantageous. Charcoal (from wood) develops on burning 8,000 heat
      units, whilst wood dried in air does not develop more than 2,800
      units of heat; therefore seven parts of charcoal give as much heat
      as twenty parts of wood. As regards the temperature of combustion,
      it is far higher with charcoal than with wood, because twenty parts
      of burning wood give, besides the carbonic anhydride which is also
      formed together with charcoal, eleven parts of water, the
      evaporation of which requires a considerable amount of heat.

      [Illustration: FIG. 57.--Apparatus for the dry distillation of
      wood. The retort _a_ containing the wood is heated by the flues _c
      e_. The steam and volatile products of distillation pass along the
      tube g through the condenser _m_, where they are condensed. The
      form, distribution, and dimensions of the apparatus vary.]

      The composition of the growing parts of plants, the leaves, young
      branches, shoots, &c., differs from the composition of the wood
      in that these vital parts contain a considerable quantity of sap
      which contains much nitrogenous matter (in the wood itself there
      is very little), mineral salts, and a large amount of water.
      Taking, for example, the composition of clover and pasture hay in
      the green and dry state; in 100 parts of green clover there is
      about 80 p.c. of water and 20 p.c. of dry matter, in which there
      are about 3·5 parts of nitrogenous albuminous matter, about 9·5
      parts of soluble and about 5 parts of insoluble non-nitrogenous
      matter, and about 2 p.c. of ash. In dry clover or clover-hay there
      is about 15 p.c. of water, 13 p.c. of nitrogenous matter, and 7
      p.c. of ash. This composition of grassy substances shows that they
      are capable of forming the same sort of charcoal as wood itself.
      It also shows the difference of nutritive properties existing
      between wood and the substances mentioned. These latter serve as
      food for animals, because they contain those substances which are
      capable of being dissolved (entering into the blood) and forming
      the body of animals; such substances are proteids, starch, &c. Let
      us remark here that with a good harvest an acre of land gives in
      the form of grass as much organic substance as it yields in the
      form of wood.

      One hundred parts of dry wood are capable of giving, on dry
      distillation, besides 25 p.c. of charcoal and 10 p.c. or more of
      tar, 40 p.c. of watery liquid, containing acetic acid and wood
      spirit, and about 25 p.c. of gases, which may be used for heating
      or lighting purposes, because they do not differ from ordinary
      illuminating gas, which can indeed be obtained from wood. As
      wood-charcoal and tar are valuable products, in some cases the
      dry distillation of wood is carried on principally for producing
      them. For this purpose those kinds of woods are particularly
      advantageous which contain resinous substances, especially
      coniferous trees, such as fir, pine, &c.; birch, oak, and ash
      give much less tar, but on the other hand they yield more aqueous
      liquor. The latter is used for the manufacture of wood spirit,
      CH_{4}O, and acetic acid, C_{2}H_{4}O_{2}. In such cases, the
      dry distillation is carried on in stills. The stills are nothing
      more than horizontal or vertical cylindrical retorts, made of
      boiler plate, heated with fuel and having apertures at the top
      and sometimes also at the bottom for the exit of the light and
      heavy products of distillation. The dry distillation of wood in
      stoves is carried on in two ways, either by burning a portion of
      the wood inside the stove in order to submit the remainder to dry
      distillation by means of the heat obtained in this manner, or by
      placing the wood in a stove the thin sides of which are surrounded
      with a flue leading from the fuel, placed in a space below.

      The first method does not give such a large amount of liquid
      products of the dry distillation as the latter. In the latter
      process there is generally an outlet below for emptying out the
      charcoal at the close of the operation. For the dry distillation
      of 100 parts of wood from forty to twenty parts of fuel are used.

      In the north of Russia wood is so plentiful and cheap that this
      locality is admirably fitted to become the centre of a general
      trade in the products of its dry distillation. Coal (Note 6),
      sea-weed, turf, animal substances (Chapter VI.), &c., are also
      submitted to the process of dry distillation.

If any one of these organic compounds be strongly heated without free
access of air--or, better still, in a vacuum--it decomposes with more or
less facility. If the supply of air be insufficient, or the temperature
be too low for combustion (_see_ Chapter III.), and if the first
volatile products of transformation of the organic matter are subjected
to condensation (for example, if the door of a stove be opened), an
imperfect combustion takes place, and smoke, with charcoal or soot,
is formed.[2] The nature of the phenomenon, and the products arising
from it, are the same as those produced by heating alone, since that
part which is in a state of combustion serves to heat the remainder of
the fuel. The decomposition which takes place on heating a compound
composed of carbon, hydrogen, and oxygen is as follows:--A part of the
hydrogen is separated in a gaseous state, another part in combination
with oxygen, and a third part separates in combination with carbon, and
sometimes in combination with carbon and oxygen in the form of gaseous
or volatile products, or, as they are also called, the products of
dry distillation. If the vapours of these products are passed through
a strongly heated tube, they are changed again in a similar manner
and finally resolve themselves into hydrogen and charcoal. Altogether
these various products of decomposition contain a smaller amount of
carbon than the original organic matter; part of the carbon remains
in a free state, forming charcoal.[3] It remains in that space where
the decomposition took place, in the shape of the black, infusible,
non-volatile charcoal familiar to all. The earthy matter and all
non-volatile substances (ash) forming a part of the organic matter,
remain behind with the charcoal. The tar-like substances, which require
a high temperature in order to decompose them, also remain mixed with
charcoal. If a volatile organic substance, such as a gaseous compound
containing oxygen and hydrogen, be taken, the carbon separates on
passing the vapour through a tube heated to a high temperature. Organic
substances when burning with an insufficient supply of air give off
soot--that is, charcoal--proceeding from carbon compounds in a state of
vapour, the hydrogen of which has, by combustion, been converted into
water; so, for instance, turpentine, naphthalene, and other hydrocarbons
which are with difficulty decomposed by heat, easily yield carbon in the
form of soot during combustion. Chlorine and other substances which,
like oxygen, are capable of taking up hydrogen, and also substances
which are capable of taking up water, can also separate carbon from (or
char) most organic substances.