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HELGE KRAGH
THE FIRST SUBATOMIC EXPLANATIONS OF THE
PERIODIC SYSTEM
ABSTRACT. Attempts to explain the periodic system as a manifestation of regularities in the structure of the atoms of the elements are as old as the system itself.
The paper analyses some of the most important of these attempts, in particular
such works that are historically connected with the recognition of the electron as
a fundamental building block of all matter. The history of the periodic system,
the discovery of the electron, and ideas of early atomic structure are closely interwoven and transcend the physics–chemistry boundary. It is pointed out that J. J.
Thomson’s discovery of the electron in 1897 included a first version of his electron atomic model and that it was used to suggest how the periodic system could
be understood microphysically. Thomson’s theory did not hold what it promised,
but elements of it were included in Niels Bohr’s first atomic model. In both cases,
Thomson’s and Bohr’s, the periodic system played an important role, heuristically
as well as justificatory.
1. INTRODUCTION
From an early date, many chemists saw in the periodic system of
the elements an indication that the atoms are complex bodies with a
constitution that somehow is reflected macroscopically in the properties of the elements that the system summarises.1 Not content with
accepting the periodic system as merely an empirical classification,
they wanted to explain it in terms of atomic constitution and the idea
of the unity of matter. Among the chemists who saw a profound
connection between the periodic law and atomic structure were
Lothar Meyer in Germany, Gustavus Hinrichs in the United States,
William Crookes in England, Julius Thomsen in Denmark, and
Thomas Carnelley in Ireland, to mention but a few. The conviction
resulted in numerous numerological proposals, more or less fanciful
periodic tables, and vague speculations concerning the constitution of atoms (Rudorf, 1904; van Spronsen, 1969). However, these
Foundations of Chemistry 3: 129–143, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
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HELGE KRAGH
attempts of explanation were all hypothetical and speculative in the
sense that they built on the assumption of some (usually unspecified)
kind of subatomic unit for which there was no empirical evidence.
We know that the periodic system does, in fact, reflect the internal
constitution of the atoms, namely, the configuration of electrons in
various shells or quantum states. This is how the system is presently
explained in textbooks of chemistry. Whether the system can also
be reduced to atomic physics, or completely accounted for in this
way, is a different question that I shall not consider here. (For
this question, and a brief history of electron explanations of the
periodic table, see Scerri, 1997.) Perhaps the first ‘modern’ and
successful explanation along this line was Niels Bohr’s theory of
1922, at the time widely acclaimed as a breakthrough in the understanding of the periodic system in terms of atomic structure (Kragh,
1979). However, although Bohr’s theory was the first quantitative (or
semi-quantitative) quantum theory of the periodic system, it built in
important respects on earlier models that anticipated the presently
accepted theory. In this essay I focus on the first explanations of
the system that were framed in terms of a known subatomic particle
and, in this sense, were realistic explanations. In 1895, the German
chemist Victor Meyer expressed the view of many scientists when
he wrote that “The knowledge that all chemical elements belong to
a common series (which, since the discovery of the periodic law,
practically no chemist denies) has established . . . that a common
something is present in all the elements” (Meyer, 1895: p. 96). Two
years later, J. J. Thomson identified the “common something” with
the electrons he had identified in cathode rays and thereby laid the
foundation for the modern explanation of the periodic system.
2. FROM VORTEX THEORY TO THE ELECTRON
J. J. Thomson’s ‘plum pudding model’ of the atom is usually dated
1904, the year when he gave a detailed and mathematically elaborate
version of it. However, the essence of the model can be found, if only
qualitatively, in his famous paper of 1897 in which he announced
the discovery of the ‘corpuscle’ – Thomson’s name for what would
soon be called the electron, a name introduced by George Johnstone
Stoney in 1891 to denote an elementary quantity of electricity. By
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131
and large, the difference between the 1904 conception of the atom
and the original one of 1897 was that in his first version Thomson
did not introduce the positive, spherical distribution of positive electrification as an electrical container of the electrons. It is also in
the 1897 paper that we find the first electronic explanation sketch
of the periodic system. Today it is generally recognised among
historians that Thomson’s model of the atom, and his conception
of the electron (as I shall call the corpuscle), was greatly indebted to
an earlier tradition in theoretical Victorian chemistry that has been
called ‘vortex chemistry’ or ‘knot chemistry’ (Chayut, 1991).
The idea that matter and forces can be understood as manifestations of the vortical motions of an underlying, continuous quasisubstance, the ether, was introduced in 1867 by William Thomson
(the later Lord Kelvin), who built on an earlier hydrodynamical
theory of Hermann von Helmholtz. In the 1870s and 1880s the
vortex atomic theory attracted much attention among British mathematical physicists, who were impressed by the theory’s unitary
features and fascinated by its mathematical challenges (Siegel,
1981; Epple, 1998). For more than two decades it was highly
regarded and developed by physicists such as J. Clerk Maxwell,
Peter G. Tait, John Tyndall, Augustus Love, William Hicks, and
J. J. Thomson. It is less well known that Kelvin’s dynamical
atomism in the shape of the mathematically abstruse vortex theory
was sought applied also to chemical problems. The theory was
favourably received by a few theoretically inclined chemists who
believed that it might furnish a foundation of a theoretical, indeed
a deductive chemistry. This kind of vortex chemistry was advocated by Tait in 1876 and taken up a few years later by young J. J.
Thomson, one of Tait’s former students. The topological approach
to chemistry was developed by the Edinburgh chemist Alexander
Crum Brown, who used it in his graphic representations of chemical compounds and thereby contributed to the early conception
of valency. The fascinating, but short-lived tradition of British
vortex chemistry was mainly concerned with structural formulae
and chemical combination, and did not explicitly address the periodic system of the elements. Nonetheless, indirectly it provided an
important source not only for the first electron atomic theory, but
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HELGE KRAGH
also for an explanation of the periodic system in terms of subatomic
particles.
J. J. Thomson’s early work on the vortex atomic theory provided
him with a conceptual framework that would prove essential to his
later interpretation of cathode rays as streams of electrons liberated
from matter (Kragh, 2000). In his Adams Prize essay of 1882, 25year-old Thomson greatly developed Kelvin’s theory and applied it
to a number of chemical problems, including affinity and chemical
combination. Although he did not mention the periodic system by
name, he did suggest that “the atoms of the elements called by the
chemists monads, dyads, triads, tetrads, and so on, consist of one,
two, three, four, &c., vortex rings linked together”. Furthermore:
“Atomicity corresponds to complexity of atomic arrangement; and
the elements of high atomicity consist of more vortex rings than
those whose atomicity is low; thus high atomicity corresponds to
complicated atomic arrangement” (Thomson, 1883: pp. 120 and
124). For a small number of interacting vortex rings, Thomson
determined the stability of the atomic system by means of elaborate
perturbation calculations, but for more than six rings he relied on
the analogy with an interesting experiment with floating magnets
that the American physicist Alfred Mayer had published in 1878
(Snelders, 1976). Subjecting equally magnetised needles floating
in water to the attractive force of a central electromagnet, Mayer
noticed that the needles took up equilibrium positions on concentric
circles. His purpose with the experiment was primarily didactical,
and he used it to illustrate phenomena of molecular structure such
as allotropy and isomerism.
Mayer’s experiment is a beautiful illustration of the role of
analogies in scientific thinking. Whereas Mayer did not relate his
findings to atomic structure, Kelvin was quick to point out that
the experimentally determined configurations of equilibrium would
correspond to those of an atom made up of columnar vortices. As
he wrote, “Mr. Mayer’s beautiful experiment brings us very near an
experimental solution of a problem which has for years been before
me unsolved – of vital importance in the theory of vortex atoms
– to find the greatest number of bars which a vortex mouse-mill
can have” (Kelvin, 1878: p. 14). J. J. Thomson carried the analogy
further and elaborated it greatly in his Adams Prize essay. We should
THE PERIODIC SYSTEM
133
not be surprised that neither Mayer, Kelvin nor Thomson pointed
out the similarity between the patterns of magnetised needles and
the structure of the periodic system. Explicit references to the periodic system were rare in the 1870s, even in the chemistry literature,
and only by the late 1880s had Mendeleev’s system become widely
accepted and incorporated into most textbooks (Brush, 1996).
In 1892 Thomson pointed out, for the first time, the suggestive
similarity between Mayer’s configurations of magnetised needles,
the arrangement of interacting vortices, and the periodicity of the
properties of the chemical elements: “If we imagine the molecules
[atoms] of all elements to be made up of the same primordial atom,
and interpret increasing atomic weight to indicate an increase in the
number of such atoms, then, on this view, as the number of [primordial] atoms is continually increased, certain peculiarities will recur”
(Thomson, 1892: p. 410). At the time, Thomson no longer identified the primordial particle with an ether vortex, but his thinking
about atomic constitution continued to be guided by the vortex
atom theory even after the announcement of the true primordial
atom, the electron or corpuscle. “Personally I generally endeavour
(often without success) to picture to myself some kind of vortex-ring
mechanism”, he wrote in a letter of 1898; “I regard . . . the vortexatom explanation as the goal at which to aim” (Holman, 1898: p.
226). The conceptual framework of the vortex theory was clearly
exhibited in his 1897 work, where he pictured the electron in the
shape of the vortex theory that he held in such esteem.
Thomson’s corpuscle of 1897 differed in certain respects from
the ‘electron’ that Joseph Larmor had introduced three years earlier
as a singularity in the electromagnetic ether. However, the two
versions of the electron had in common their indebtedness to the
theory of vortex atoms, at the time abandoned by most physicists.
Moreover, Larmor’s electron had in common with Thomson’s that
it was seen as a building block of all chemical elements. In 1895,
two years before the celebrated discovery of the electron, Larmor
suggested “a molecule [atom] to be made up of, or to involve,
a steady configuration of revolving electrons” (Larmor, 1927: p.
595). However, Larmor was uninterested in chemistry and did not
consider the periodic system or other chemical phenomena. By
contrast, Thomson was well informed about chemistry, a field that
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HELGE KRAGH
greatly interested him and acted as a source of inspiration for his
atomic theory.2 Conversely, from 1897 onward he sought eagerly to
apply his new atomic theory to chemical phenomena, of which he
considered the periodic system to be particularly important.
3. THE THOMSON ATOM AND THE PERIODIC SYSTEM
In his first announcement of the identification of cathode rays as
streams of electrons, in a Royal Institution lecture of April 1897,
Thomson did not mention the periodic system. But he did introduce the basic features of a new conception of the atom, as a vast
conglomeration of electrons; and he explicitly connected the picture
with the Proutean tradition of composite elements, as “has been
put forward from time to time by various chemists” (Davis and
Falconer, 1997: p. 151). As Thomson was well aware, advocates of
this tradition considered the periodic system to be a strong argument
in favour of their cause. Thomson made the connection explicit half
a year later, in his paper in Philosophical Magazine of October 1897
where he presented a better argued and more detailed version of his
electron hypothesis. As far as the arrangement of intra-atomic electrons was concerned, Thomson made use of Mayer’s experiment,
just as he had done fifteen years earlier in the context of the vortex
atomic theory. “A study of the forms taken by these magnets seems
to me to be suggestive in relation to the periodic law”, he wrote.
Assuming that a certain chemical property was associated with a
group of magnets, that the magnets corresponded to electrons, and
that the atomic weight was expressed by the number of electrons, he
suggested:
Now suppose that a certain property is associated with two magnets forming a
group by themselves; we should have this property with 2 magnets, again with 8
and 9, again with 19 and 20, and again with 34, 35, and so on. If we regard the
system of magnets as a model of an atom, the number of magnets being proportional to the atomic weight, we should have this property occurring in elements
of atomic weight 2, (8,9), 19, 20, (34,35). . . . [I]n fact, we should have something
quite analogous to the periodic law . . . (Thomson, 1897: p. 314).
Here we have the essential features of Thomson’s explanation of
the periodic system, features that did not change much over the
next decade. Although by 1904 a sphere of positive electrification
THE PERIODIC SYSTEM
135
had been added in order to keep the electrons together, this did
not change the equilibrium configurations and the validity of the
analogy to Mayer’s experiment. In his works from 1904 to about
1912, Thomson repeatedly referred to his explanation of the periodic
system as a major triumph of his atomic model. For example, in
a Royal Institution lecture of 1905 he mentioned that atoms with
the same inner groups of electrons would “have much in common,
and we might therefore expect the physical as well as the chemical
properties of the atoms to have a general resemblance to each other”.
This property, he added, was “analogous to that indicated by the
periodic law in chemistry” (Davis and Falconer, 1997: p. 218).
As an example, consider the electron configurations in select
Thomson atoms with three to six rings. The configurations are
denoted with the symbol n(x1 , x2 , . . . ), meaning a total of n electrons
distributed with x1 electrons in the innermost ring, x2 electrons in the
second ring, etc.:
21(1,8,12)
37(1,8,12,16)
56(1,8,12,16,19)
78(1,8,12,16,19,22)
22(2,8,12)
38(2,8,12,16)
57(2,8,12,16,19)
79(2,8,12,16,19,22)
23(2,8,13)
39(2,8,13,16)
58(2,8,13,16,19)
80(2,8,13,16,19,22)
Here, the atoms in the same columns will correspond to elements
of the same chemical group because they have electron groups in
common. Contrary to the later explanation of the periodic system,
in Thomson’s view the similarity between elements was the result
of common internal groups of electrons.
Thomson’s account of the periodic system was a suggestion or an
explanation sketch, not a quantitative explanation. His model was
unable to associate real elements with definite electron configurations. Not only was his model a two-dimensional representation of
the three-dimensional atom, the number of electrons in real atoms
was also unknown. Therefore, although Thomson’s atomic model
furnished a striking analogy to the periodic system, it was no more
than an analogy. Thomson believed originally that the entire mass
of the atom was made up of electrons, which meant that even the
lightest atoms would consist of thousands of electrons. For this
reason alone, realistic atomic models could not be constructed.
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However, in 1906 he concluded from various experimental evidence
that the number of electrons was probably of the same order as the
atomic weight A; and four years later he was inclined to believe
that the number was between A and A/2. The new insight changed
the status of Thomson’s model, for now it would be possible to
construct a realistic model of, say, helium (with 2, 3 or 4 electrons) and confront the predictions of the model with the known
physical and chemical properties of helium. It should be possible
to explain, for example, the similarity between helium and neon.
Although Thomson himself did not make such (three-dimensional)
calculations and compare the results with the empirical data, a few
other physicists did (Haas, 1911; Föppl, 1912). The result was not
encouraging: It turned out that the Thomson model was unable to
account for the real structure of atoms and hence also of the periodic
system.3
The failure of Thomson’s model to reproduce the properties of
real atoms was not much noted and did not seriously damage the
reputation of the model; for a period, its suggestive explanation
of the periodic system was broadly accepted or at least considered
interesting. According to the chemist Ida Freund, Thomson’s explanation “supply an explanation for the empirical relations between
atomic weight and atomic properties embodied in the periodic
law” (Freund, 1904: p. 624). The Cambridge chemist Matthew M.
Pattison Muir similarly concluded that “[Thomson’s] electrocorpuscular theory of the structure of atoms leads to the recognition of a
periodic connexion between the atomic weights and the properties
of the elements” (Pattison Muir, 1907: p. 374). Also Harry Clary
Jones, an American physical chemist, was impressed by the chemical merits of the Thomson model and praised its explanation of
the periodic system (Jones, 1907). Although no one believed that
Thomson had actually explained the periodic system, many believed
that his approach was a step in the right direction and that it might
one day lead to a complete understanding of the system in terms
of electron physics. As early as 1901, the German physicist Walter
Kaufmann, himself a pioneer of electron research, wrote (1901:
p. 97):
We might assume, for instance, that among the innumerable possible groupings
of electrons only a relatively limited number would be sufficiently stable to occur
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137
in larger quantities. These stable groupings would then be the elements as known
to us. Perhaps a mathematical treatment of this question will one day succeed
in presenting the relative frequency of the elements as a function of their atomic
weights and in solving many another problem of the periodic system.
It was such a mathematical treatment that Thomson offered in 1904,
but without solving the problems that Kaufmann alluded to and
without being able to reproduce models of “the elements as known
to us”.
Although Thomson’s model was the only electron-based theory
of the periodic system that attracted wide attention, it was not the
only one.4 Thus, Gilbert N. Lewis’s model of the cubic atom had
its origin in an attempt to explain the periodic system and was used
for this purpose as early as 1902, although it was published only
in 1916 (Lewis, 1966: p. 29; Kohler, 1971). Another example is
provided by H. Strache, a German chemist who in 1908 claimed to
have explained the periodic system in terms of a speculative conception of the atom as made up of electrons (which he conceived as
the elementary particles of the world ether). Contrary to Thomson,
Strache undertook to use his explanation to predict (or postulate)
new chemical elements, namely, of atomic weights 99, 176, 233 and
235 (Strache, 1908). It is unclear how he arrived at these predictions.
4. THE PERIODIC SYSTEM IN BOHR’S 1913 THEORY
Niels Bohr’s famous atomic theory of 1913 was based on Rutherford’s new nuclear atom, but in many respects also indebted to J. J.
Thomson’s rival model which furnished the natural starting point for
Bohr’s treatment of many-electron atoms. In fact, there is a striking
similarity between Bohr’s calculations in the second (and less well
known) part of the 1913 trilogy and those performed almost a
decade earlier by Thomson (Heilbron, 1977). Bohr was well aware
of Thomson’s theory of the periodic system, but believed that the
theory was incorrect. In the so-called Manchester memorandum
from the summer of 1912, a draft version of his theory that he sent
to Rutherford, he mentioned in a footnote that “it [is] impossible,
to give a satisfactory explanation of the periodic law from the last
mentioned [Thomson’s] atom-model” (Bohr, 1981: p. 136). Bohr
considered an explanation of the periodic system to be an important
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HELGE KRAGH
part of his theory. In February 1913, he wrote to the chemist George
de Hevesy that his still unpublished theory would include “a very
suggestive indication of an understanding of the periodic system of
the elements” (ibid.: p. 530).
In building up atomic models, Bohr had the advantage over
Thomson that he could make use of the recent introduction of the
atomic number as the ordinal number of the periodic system, equal
to the number of electrons in a neutral atom. Hence he was able to
offer realistic models of the atoms. Bohr had developed the idea of
the atomic number independently of the Dutch scientist Antonius
J. van den Broek. In early 1913, Bohr wrote to the Swedish physicist Carl Oseen that he had come across the work of van den
Broek, “who empirically had arrived at conceptions of the periodic system similar to those I have arrived at deductively from
my theoretical speculations” (ibid.: p. 552). I shall not go into the
details of Bohr’s theory, which has been treated elsewhere (Kragh,
1977; Heilbron, 1977). As far as the reconstruction of the periodic system is concerned, Bohr summarised his results in a table
including electron configurations for the first 24 elements:
1(1)
2(2)
3(2,1)
4(2,2)
...
8(4,2,2)
9(4,4,1)
10(8,2)
11(8,2,1)
12(8,2,2)
17(8,4,4,1)
18(8,8,2)
19(8,8,2,1)
20(8,8,2,2)
16(8,4,2,2) 24(8,8,4,2,2)
The cautious Bohr did not explicitly identify the electron structures
with definite elements but merely noted that “it seems not unlikely
that this constitution of the atoms will correspond to properties of
the elements similar with those observed” (ibid.: p. 209). On the
other hand, it would be quite clear to his readers that the structure
6(2,4) referred to carbon, 11(8,2,1) to sodium, and so on.
Comparing Bohr’s explanation with that offered by Thomson,
there are similarities as well as dissimilarities to be noticed.
The general features of Bohr’s theory were clearly indebted to
Thomson’s reasoning, but according to Bohr the chemical similarity
between elements in the same group was associated with the same
THE PERIODIC SYSTEM
139
number of electrons in the outermost ring. As mentioned, whereas
Thomson’s structures did not claim to represent real atoms, those
proposed by Bohr were realistic models. Also with regard to method
and approach, the two physicists differed. Thomson’s theory was, or
can be regarded as, an attempt to establish a deductive or ‘mathematical chemistry’, at least in principle.5 His electron structures
were the result of calculations, and empirical considerations of the
properties of elements did not enter. Bohr, on the other hand, was
well aware that he could not do without empirical input. In spite of
what he told in his letter to Oseen, his theory of the periodic system
was not obtained “deductively”. As he admitted, physical principles,
whether classical or based on the new quantum theory, “[are] in most
cases not sufficient to determine completely the constitution of the
system” (ibid.: p. 198). He therefore followed an eclectic methodology, freely mixing mathematical calculations and general principles
with knowledge of the physical and chemical properties of the
elements. The latter considerations were no less important than the
first, and if the two approaches collided he usually gave priority
to the results suggested by empirical knowledge. This particular
eclecticism was not only a characteristic methodological feature in
Bohr’s 1913 theory, but also in his later theory of 1922 (Kragh,
1979).
5. DISCUSSION AND CONCLUSIONS
The historical roots of the modern theory of atomic structure are
to be found not only in the development of physics, but also in
the development of chemistry. Among the chemical phenomena that
have influenced atomic theory, the periodic system of the elements
is perhaps the most important. The existence of regularities in the
properties of the elements, such as summarised in the periodic table,
was a source of puzzle as well as inspiration to many scientists
who wanted to know the underlying mechanisms and causes they
assumed to exist. Mendeleev’s classification scheme played a heuristic role in early views of atomic structure: a good atomic theory
was expected to give some kind of explanation of the periodic
system, or, at least, be consistent with it. Of course, an atomic model
could not be derived from the periodic system alone and then be
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HELGE KRAGH
used (circularly) to explain the system. The early atomic models
of Thomson, Bohr and others rested on many sources, theoretical
as well as empirical, and the periodicity of the elements was only
one source among several others. Between 1897 and 1913 the new
electron-based atomic models were used, with more or less success,
to explain the periodic system. The period can be seen as leading up
to the much more satisfactory explanations that were formulated in
the 1920s on the basis of principles of quantum theory.
According to Dudley Shapere (1977: p. 538), the expectation of
an underlying, deeper explanation of the periodic system in terms
of atomic contituents reached the status of a demand as more and
more phenomena came under the domain of atomistic explanation.
Considering that many eminent chemists (including Mendeleev)
denied the value of such explanations, this is probably an exaggeration. On the other hand, it is undoubtedly true that expectations
of what Shapere calls a ‘compositional theory’ increased during
the two last decades of the nineteenth century. These expectations
were not easily shaken, nor were they abandoned simply because
the proposed theories were not very satisfactory. In this respect,
they had the character of a research programme in the sense of
Imre Lakatos. Shapere (1977: p. 540) writes about the atomistic
expectations:
Nor were they shaken by the failure of successive atomistic theories to account
successfully for the features of the periodic table, . . . Considerations [of the
validity of atomistic explanations in other domains] . . . were strong enough to
constitute reasons in favor of a search for such a theory. That the reasons were
not logically conclusive did not make them any the less reasons, and good ones,
relative to the state of science at the time, nor did it make action in accordance
with them any the less rational.
This assessment seems to agree well with the first phase of electronbased explanations of the periodic system, from Thomson to Bohr.
The theories were suggestive, perhaps even promising, but can
hardly be called successful. Yet, with the general success of electron theories in other domains of both physics and chemistry it was
natural to expect that the periodic system, too, would find its explanation in terms of the electrons of which the atoms were composed.
Indeed, by the mid-1920s, the expectation turned out to be justified.
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NOTES
1. I shall mostly refer to the periodic ‘system’ rather than ‘table’ or ‘law’,
although ‘periodic law’ was frequently used at the time and can still be met in
the literature. For a philosophically oriented discussion of the various terms,
see Shapere (1977: pp. 535–536). Whereas the periodic table is one form of
representation of the concept of the periodic system, neither the table nor
the system qualify (or, in the past, qualified) as a causal and fundamental
law of nature. Yet the periodic system of the elements can be ascribed the
status of a law. Like several other statements of regularities (such as the
Dulong-Petit law), it can be described as a semi-quantitative, functional and
phenomenological law of nature (Weinert, 1995).
2. Thomson’s continual interest in chemistry, and the continuity of his ideas
about atomic structure from the 1880s to the electron atom of 1897 and
beyond, is richly documented in Sinclair (1987) and Chayut (1991).
3. After lengthy calculations, Ludwig Föppl, a German physicist, concluded
that the periods of the periodic system would correspond to either 24 or 48
electrons, a result that did not harmonise with the properties of the chemical
elements (Föppl, 1912: p. 300).
4. Among the many ideas of atomic structure in the period 1900–1912 were
proposals by James Jeans, Rayleigh, Jean Perrin, Philipp Lenard, Hantaro
Nagaoka, Ernest Rutherford, and John Nicholson. Except for Nicholson’s
system of 1911, the periodic system played no great role in these atomic
hypotheses.
5. “It will be the task of the future”, wrote Arnold Sommerfeld in 1922, “to
sketch a complete topology of the interior of the atom and, in addition, a
mathematical chemistry, that is, to show the exact position of the electrons
in the shell of the atom” (Sommerfeld, 1922: p. 88). The ultimate aim of
Thomson’s programme was a mathematical chemistry in this reductionist
sense.
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