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J. C. M.


J. A. K. T.



The important question whether, in discussing the constitution
of matter, the atom or the molecule should be first considered,
is one regarding which there has been considerable difference of
opinion among chemists.

Formerly, few would have disputed the claim of the atom to
prior consideration. Not only did Dalton's atomic hypothesis
precede Avogadro's molecular hypothesis in order of time, but
this chronological order seemed also to be the natural order,
involving, as it did, only the usual transition from the simpler to
the more complex conception.

But the history of the science shows that, enormous as
were the services which Dalton's atomic hypothesis rendered to
chemistry, the chief object of that hypothesis the determination
of a set of consistent atomic weights remained for a long time
merely a pious hope. Avogadro's rule supplied a means of
determining the molecular weights of substances, and, from these
molecular weights, of ascertaining which of several possible
atomic weights of a contained element was the correct one.
Until this step had been taken, the marvellous developments of
theoretical chemistry which have characterised the last fifty years
would have been impossible.

In the study of the constitution of matter, therefore, we are
compelled, by the very nature of the particular problems of
scientific measurement and calculation involved, to reverse what
is apparently the natural order of things and to proceed from the
more complex to the simpler from highly complex objects of
sense to successively simpler and simpler conceptual structures
underlying these. Thus the order of quantitative determination
is : (i) relative weights of comparable amounts of matter in bulk
(gaseous or dissolved) ; (2) relative weights of molecules ; (3) relative
weights of atoms ; and (4), if subsequent experiment should justify
the most recent speculations, mass of electrons.

The view here stated as to the true ratiocinative order of
precedence of the molecular and atomic hypotheses has been
held by various chemists ; but I have nowhere else seen it
expounded with such wealth of illustration and with so exhaustive
a knowledge of the fundamental literature of the subject, as in
the present monograph by Dr. Meldrum.

September* 1904.


Some of the books required for the purposes of this essay
were purchased by means of a grant from the Carnegie Trustees.
The publication of the essay has been made possible by another
grant from the same body.

I am indebted to Mr. Joseph Knox, B.Sc., who went over
the essay in a friendly, critical way, and canvassed difficulties
with me till a solution was reached.




Part I. The Standing in Chemistry of Avogadro's

Hypothesis, - 9

Chapter I. Introduction, - 9

., II. The relation between the Hypothesis and Gay-

Lussac's Law, - 14

,, III. The relation between the Hypothesis and the

Kinetic Theory of Gases, - 20

,, IV. The Hypothesis as a Principle of Chemistry : the

Molecule, - 25

,, V. The Hypothesis as a Principle of Chemistry

(continued) : the Atom, - 29

,, VI, The Molecular Formulae of the Elements, - 39

,, VII. The Hypothesis in relation to " Purely Chemical "

Methods, - - 43

Part II. The Standing in Chemistry of Dalton's Atomic

Theory, - 50

Chap. VIII. Introduction,- - -5

IX. The Essentials of Dalton's Theory, - 56

X. The Atomic Weight Systems of Berzelius, - 68

,, XI. The Atomic Weight System of Gmelin, - - 76

,, XII. The Chemical System of Gerhardt and Laurent, 83

XIII. The Chemical System of Cannizzaro, - 95

,, XIV. The Relative Standing of Dalton's Atomic

Theory and Avogadro's Hypothesis, - 102'


A. C. R.,

Chemical Philosophy
Cooke, -
C. N., -
Delametherie, -
Divers. -

E. B.,
Essai, 1819,

Essai, 1835, -
Gmelin, -

Heat, -
Henry, -
J. C. S., -

Von Meyer.
Morley, -

Nernst, -
Roscoe, -
Short History, -

Thorpe, -



Alembic Club Reprints.

Tilden's Chemical Philosophy, 1901.

Cooke's New Chemistry, 1874.

Chemical News.

Delame'therie's Journal de Physique.

British Association, 1902, Section B,
President's Address, Separate Reprint.

Encyclopaedia Britannica, 9th Ed.

Berzelius' Essai sur la The'orie des Propor-
tions Chimiques, 1819.

Berzelius' Essai sur la Theorie des Propor-
tions Chimiques, 1835.

Gmelin's Handbook of Chemistry, Watt's


Clerk Maxwell's Theory of Heat, loth Ed.
Henry's Memoirs of Dalton, 1854.
Journal of the Chemical Society of London.
Ostwald's Klassiker.
Ladenburg's History of the Development of

Chemistry, Dobbin's Translation, 1900.
Ernst von Meyer's History of Chemistry,

McGowan's Translation, 1898.
Smithsonian Contributions to Knowledge,

980, The Densities of Oxygen and

Hydrogen, Morley.
Nernst's Theoretical Chemistry, Palmer's

Translation, 1895.
Ostwald's Principles of Inorganic Chemistry,

Findlay's Translation, 1902.
Roscoe's John Dalton and the Rise of

Modern Chemistry, 1895.
Tilden's Short History of the Progress of

Scientific Chemistry, 1899.
Essays in Historical Chemistry, 1902.
Gerhardt's Traite de Chimie Organique.
Zeitschrift fur Physikalische Chc-mic.


The Standing in Chemistry of
Avogadro's Hypothesis*


Truth on these subjects is militant and can only establish itself by
means of conflict. f. S. MILL.

At the outset of this essay, it is well to state an axiom
which is much used in the course of the argument. It is
assumed that there is an essential distinction between what
are known on the one hand as laws and on the other hand as
hypotheses. A hypothesis is the creation of the mind, and is
of service in interpreting a law. There is good ground for
the belief that in science the recognition of this distinction
between law and hypothesis is an indispensable condition of
clear thinking.

The distinction has been insisted on by Faraday. His
words are : " It is always safe and philosophic to distinguish,
as much as is in our power, fact from theory ; the experi-
ence of past ages is sufficient to show us the wisdom of such
a course ; and considering the constant tendency of the mind
to rest on an assumption, and, when it answers every present
purpose, to forget that it is an assumption, we ought to
remember that it, in such cases, becomes a prejudice, and
inevitably interferes, more or less, with a clear-sighted judg-
ment. I cannot doubt but that he who, as a wise philosopher,
has most power of penetrating the secrets of nature, and
guessing by hypothesis at her mode of working, will also be
most careful, for his own safe progress and that of others, to
distinguish that knowledge which consists of assumption, by
B 9

io Standing in Chemistry of Avogadrtfs Hypothesis.

which I mean theory and hypothesis, from that which is the
knowledge of facts and laws ; never raising the former to the
dignity or authority of the latter, nor confusing the latter more
than is inevitable with the former." l

Very recently Richards, his views on a question of the day
having been much misunderstood, had occasion to emphasise
the distinction. He refers to a question the discussion
of which, " as of so many scientific questions, has been much
confused by the inability of many writers to distinguish
between fact and hypothesis. . . . Facts are determined
by observation and experiment, and their truth depends only
upon the accuracy of the observation and experiment. Their
discovery is a lasting addition to the knowledge of mankind.
On the other hand, hypotheses are attempts to interpret the
facts ; and many hypotheses, from their very nature, can never
be proved." 2

Obvious as this distinction may seem, it is necessary to lay
emphasis on it here, in view of the persistence with which
certain chemists use the term Avogadro's law, instead of
Avogadro's hypothesis. In this essay, Avogadro's hypothesis
is regarded as an interpretation put upon Gay-Lussac's law.
The law, unlike the hypothesis, is matter of fact, and must
remain so, even should the hypotheses which are made to
explain it be multiplied.

Science is coming more and more into use in education.
So used, one of the benefits of science is understood to be that
it inculcates logical ways of thinking.

" What a retrospect," says Gibbon, " is it to a genius truly
philosophical ... to find true consequences falsely
deduced from the most erroneous principles." As a training
in thinking, the study of experimental science presents one
risk : logic is one thing, and experiment is another. The
chemist habitually examines how far his conclusions square
with the facts, and as to the facts, need not go very far wrong.
Nevertheless, " true consequences may be falsely deduced from
the most erroneous principles." The conclusions squaring

1 Kxperiincntnl Researches in Klertricity, vol. II., 184/1, p. 285.
-T.N., 88. 69.'

Introduction. 1 1

with the facts, it does not follow that the logic which yields
the conclusions is sound.

To show that the logic of chemistry is not always sound,
it is sufficient to consider the treatment, in many of the books
on chemistry, of the subjects of molecular-weight and atomic-
weight determination. The connection between the several
molecular-weight methods and the definition of the molecule
is left in obscurity. How different is the treatment in physics
of the subject of specific-gravity, for instance ! Specific-
gravity having been defined, some effort is made to show that
the several specific-gravity methods are in accordance with the
definition. On the other hand, the molecular-weight methods
are stated in such a way as to leave on the student's mind the
impression that each of these methods stands on its own
footing, and is independent of the definition of the molecule.
The treatment of the subject of atomic-weight methods is
similar ; the books give the impression that the different
atomic-weight methods have no connection that can be shown
with one another, or with the definition of atomic-weight, and
that they yield concordant results for all that.

The " Theoretical Chemistry " of Nernst is written, as the
title-page states, " from the standpoint of Avogadro's Rule and
Thermodynamics." The subject of Thermodynamics may
be regarded as non-hypothetical, since it consists essentially
of a development by the aid of mathematics and dynamics of
the two fundamental laws of Thermodynamics, and makes no
assumption, as to the continuity or discontinuity of matter.
The theoretical basis of Nernst's system of chemistry is
Avogadro's hypothesis.

Nernst's book is a comprehensive one, suitable for the
student of research. It goes as far as the debatable ground
between the known and the unknown. It was doubtless
foreign to Nernst's purpose to expatiate on the rudiments of
chemistry. There is reason to believe that it would be of
interest, and even of value, to trace the development, in logical
order, of the cardinal doctrines of chemistry on the basis of
Avogadro's hypothesis.

The standing of Avogadro's hypothesis in chemistry is
still an open question. Strange as this may seem, it can,

12 Standing in Chemistry of A vogadro's Hypothesis.

easily be made manifest by reference to the literature of
chemistry. For instance, I quote the verdicts on this
question of Cooke and Divers.

Cooke states that in writing " The New Chemistry " lie
made it his object " to present the modern theories of
chemistry," and " to give to the philosophy of the science a
logical consistency, by resting it on the law of Avogadro." l

Divers, as President of the Chemical Section of the British
Association in 1902, took a very different view from Cooke.
The credit given to Avogadro by Cooke, is given by Divers to
Dalton. In the Presidential Address, Divers had occasion
" to restate and examine most of the fundamental and familiar
principles of our science." 2 Accordingly, Divers expounds
" the theory of chemistry, which, with all its modern develop-
ments, I take to be indisputably the theory of Dalton." 3
Again, " the theory of chemical molecules was brought to
light . . . not by Avogadro's hypothesis," he says,.
" but in the first place by Dalton's atomic theory and Gay-
Lussac's law . . . ; and then, much more fully in the
middle of the last century, through the brilliant work of
Gerhardt, Williamson, Laurent, Odling, Wurtz, and others, in
the purely chemical field." 4 Apparently, in Divers' judg-
ment, the historical importance of Avogadro's hypothesis is

Not only so, but speaking of the same hypothesis, Div-ers
says, " unfortunately it does not hold good in the case of not a
few simple substances." 5

True, chemical theory did not stand still in the interval
between 18/3, when Cooko was writing, and 1902, the date of
Divers' address. There was in the interval development and
expansion of the old ideas ; but nobody maintains that there
has been, since 1870, a revolution in chemical ideas. It is
impossible to maintain that this contradiction between Cooke
and Divers is significant of some change, amounting to an
upheaval, in chemical theory.

If a sound method for the advancement of a science con-
sists in " constant recurrence to first principles," in what a

1 Cooke, p. 5. * Divers, p. 2. :i Loc. at., p. 3. 4 Lor. dt.. p. 8.
"' Loc. cit.. p. 12.

Introduction. 1 3

position of difficulty and embarrassment are the devotees of
chemistry placed In regard to first principles, here are the
high-priests of chemistry giving decisions which, to use plain
language, are in flat contradiction to one another.

Controversy is not always a bad thing. Subjects there
are on which " truth is militant, and can only establish itself by
means of conflict." Surely chemists would do well to make
up their minds about first principles, and to make their reasons
known, even at the risk of raising controversy.

No further explanation can be given for the attempt in the
following essay to consider the questions of the standing in
chemistry first of Avogadro's hypothesis, and afterwards of
Dalton's atomic theory. Reasons will be given later for
taking the questions in this order.

Avogadro's 'hypothesis is the subject of the first part of
this essay. After consideration of the hypothesis as such, it
is taken as a starting-point, from which to develop, as logically
as may be, the ideas such as molecular-weight, atomic-weight,
valency, radicals, etc., which are second nature to the chemist.



SiHcc all progress of mind consists for the most part in differential ion, in
the resolution of an ohscure and complex ohject into its component
aspects, it is surely the stupidest of losses to confute tilings rsliich right
reason has put asunder. I'ATKR.

Gay-Lussac's " Memoir on the Combination of Gaseous
Substances with each other" was read in 1808 and issued in
print in 1809. The subject of this paper is what is known as
Gay-Lussac's law. The law is : " Not only do gases combine
in very simple proportions " by volume, " but the apparent
contraction of volume which they experience on combination
has also a simple relation to the volume of the gases, or at
least to that of one of them." l

Rich in experimental discoveries, Gay-Lussac's memoir is
comparatively destitute of speculations and hypotheses. Ber-
zelius remarks on this : " M. Gay-Lussac was satisfied with
having determined the ratios in which gaseous substances
combine, but he made no wider application of this discovery." ;

In iSil, on consideration of this law, Avogadro published
his hypothesis, namely, '' That the number of (integral) mole-
cules in any gases is always the same for equal volumes, or
always proportional to the volumes "

It is surprising that Gay-Lussac did not himself anticipate
Avogadro. The reason why can only be guessed at. \Yith
some men of science, with Dalton, for instance, the faculty of
speculation is predominant ; with others, with Bunsen, for
instance, the ruling passion is the making of experiments. It
may be that Gay-Lussac resembled Bunsen. But whatever
the explanation, a division of labour there was between Gay-
Lussac and Avogadro. Stronger witness there could hardly
be to the distinction between law and hypothesis, than the

1 A.C.R., 4, 15.

" " M. Gay-Lussac se contenta d' avoir demontre les rapports dans lesquels.

se combinent les substances gazeiformes, rnais il ne fit point

<!' application plus generate de cette decouverte." Essai, 1819, p. 14.

3 A.C.R., 4, 29.

The Relation of 'the Hypothesis to Gay-Lussac's Law. 15

enunciation of a law in 1808 by Gay-Lussac, and the enuncia-
tion of a 'hypothesis, by way of explanation of the law, in 181 1
by Avogadro. 1

Plain as is the above distinction between Gay-Lussac's
teaching and Avogadro's, all the more surprising is the amount
of established error on the subject in the books, and the extent
to which the distinction 'has been ignored by men of science.
Error has arisen in three several ways.

In the first place, the assertion is made that the object of
Avogadro's hypothesis was other than the interpretation of
Gay-Lussac's law. One of the traditions of chemistry is that
Avogadro formed his hypothesis on contemplation of the
physical properties of gases and as an interpretation of these
properties. Among the authorities who maintain and diffuse
this tradition is the great Encyclopaedia Britannica. " In
1811, Avogadro, remarking that equal variations of tempera-
ture and pressure produce in all gases and vapours the same
change of volume, enunciated the hypothesis that equal
volumes of any gas or vapour contain the same number of
atoms." 2

According to this account of the genesis of the hypothesis,
the physical properties of gases, i.e., Boyle's law and Charles'
law, formed the main consideration with Avogadro, so that
Gay-Lussac's law was at most a minor consideration, if it was
considered at all. This account is in no way confirmed by a
scrutiny of Avogadro's paper ; the contrary is evidently the
case, that what suggested the hypothesis to Avogadro was
Gay-Lussac's law. What Avogadro had in view when he
formulated his hypothesis, what he refers to at the outset of
his paper and takes into consideration throughout, is Gay-
Lussac's law.

This erroneous account was corrected by Ostwald in iSSp. 3
Nevertheless Ladenburg, in a book published in 1900, persists

1 The statement, that Avogadro's hypothesis is an explanation of the
properties of gases, does not mean that Avogadro explained why one gas
combines with another. There is little need to emphasise this, so far as the
main purpose of this essay is concerned, because chemical affinity was explained
just as little by Dalton as by Avogadro.

2 E. B., Article Chemistry Historical Introduction by F.H.B.

3 Klassiker, 8, 48.

1 6 Standing in Chemistry of Avogadro's Hypothesis.

in the error. r ' The physical properties of the gases (especi-
ally the similarity in their behaviour towards changes of
pressure and of temperature) lead Avogadro to assume in equal
volumes of all gases, the same number of molecules." x

The matter can be put beyond doubt by quoting Avo-
gadro's own statement, in his second paper on the subject.
" In my essay on ' A Method of Determining the Relative
Masses of the Molecules of Substances, etc.,' I have advanced
a hypothesis ... in order to explain the fact discovered
by M. Gay-Lussac, that the volumes of the gaseous sub-
stances which combine with one another, and of the compound
gases which are produced, are always in simple ratios to one
another." 2

In the second place, Gay-Lussac's law and Avogadro's
hypothesis have been regarded as the same thing. Clerk
Maxwell mentions " a very important law established by Gay-
Lussac, that the densities of gases are proportional to their
molecular weights." 3 The statement which Clerk Maxwell
here describes as Gay-Lussac's law is familiar to chemists as
the equivalent of Avogadro's hypothesis.

Nevertheless, Gay-Lussac's law and Avogadro's hypothesis
are not the same thing. The two generalisations are distinct,
no matter how natural the step from the law to the hypo-
thesis may seem, and no matter how obvious a corollary of
the hypothesis the law may be. On this point the history
of the subject affords a decisive verdict. The two generalisa-
tions were enunciated at different times by different men.
Again, while the law came at once into almost, if not quite,
universal acceptance with chemists, the hypothesis for long-
met with neglect, or was revived only to be rejected.
Revived, and applied successfully at last to organic chemistry
by Gerhardt and Laurent, the hypothesis was accepted

1 Ladenburg, p. 61.

- "Dans nion Essai a' uuc Mann'rc tie- determiner Us Masses relatives des
Molecules des corps , etc., j'ai propose une hypothese pour expliquer le fait
decouvert par M. Gay-Lussac, que les volumes des substances gazeuses
combinent entre elles, et des gaz composes qui en resultent, sent loujours dans
des rapports tres simples entre eux." Delametherie, 1814, 78, 131. The
reference to the first paper is Delametherie, 1811, 73, 58

:; 1 leat, p. 326.

TJie Relation of tJie Hypothesis to Gay-Lussac's Law. 17

without reserve, and applied successfully to both organic and
inorganic chemistry, first by Cannizzaro about the year 1858.

In the third place, Avogadro's hypothesis is frequently
described as a law. Tilden, for instance, under the heading,
" the law of Avogadro," remarks, 4< This statement, originally
enunciated by an Italian physicist, Avogadro, . . . may
now be regarded as a well-established truth." x

This is not a mere matter of words. The point lies in the
statement that this particular doctrine, whether it be called
Avogadro's hypothesis or Avogadro's law, is " now a well-
established truth." It is one of the tenets of this essay that
the doctrine, far from being a " well-established truth" is, on
the contrary, one of the hypotheses, which, from their very
nature, have never been proved.

Avogadro himself, presumably, regarded the doctrine as an
assumption ; he uses the term " hypothesis." To use the term
" law " is only to give way to what Faraday calls " the constant
tendency of the mind to rest on an assumption, and, when it
answers every present purpose, to forget that it is an assump-

The use of the term " law " in this connection has two
results. First, it tends to keep the hypotheses which form
the basis of nineteenth century science out of sight Second,
and this will be considered in the next chapter, it is likely to
conceal the truth that hypotheses are of a transient nature.

About the constitution of matter, there are, according to
Clerk Maxwell, " two modes of thinking, which have had their
adherents both in ancient and in modern times. They corre-
spond to the two methods of regarding quantity the arith-
metical and the geometrical. To the atomist the true method
of estimating the quantity of matter in a body is to count the
atoms in it. The void spaces between the atoms count for
nothing. To those who identify matter with extension, the
volume of space occupied by a body is the only measure of
the quantity of matter in it." 2

From this point of view it is of much interest to consider
the measurement of matter in chemistry. The method is, to

1 Chemical Philosophy, p. 16. ' 2 E. B., Article Atom.

1 8 Standing in Chemistry of Avogadrrf s- Hypothesis.

measure matter in the gaseous state, by taking equal volumes
of the different gases. At the present time, the use of this
method pure and simple is being inculcated by Ostwald.
Chemistry, as expounded by him, is a science which " identifies
matter with extension."

On the contrary, as understood by the chemists of the
school of Dalton and of Avogadro, chemistry is a science of
molecules and atoms. Yet, so far as results go, there is no
difference between the opposing schools ; they both measure
matter in the same way, by taking equal volumes of different

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