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Chapter 1Order in the Chemical Elements

1.1 An Early Start

The idea of atoms as forming the ultimate constituents of matter already arosein the great speculative or philosophical minds of the ancient world, although noexact chemical or physical atomic theory actually evolved from it at the time, andalthough, most importantly, there was no direct evidence for it. The fundamentalquestions were: What are the chemical elements? What are the basic units whichcarry the identity of a chemical element? Can matter be divided indefinitely whilestill preserving its identity?

Such questions already bothered Greek philosophers, including for exampleAristotle (384–322 BCm), Leucippus (flourished circa 440 BCm), and Democri-tus (circa 460–370 BCm). According to the doctrines of Leucippus and Democritus,matter could not be divided indefinitely. Democritus believed in the existence of twotypes of reality: atoms and void. According to this hypothesis, the world consists ofa collection of simple particles, of one kind of matter, and of indivisible smallness,as the name indicates. Indeed, the term ‘atom’ emerged from the Greek adjectiveatomos or atomon, which means ‘indivisible’. According to this view, the atoms areinfinite in number and have various sizes and shapes. They move about in an infinitevoid, interacting with one another to form clusters by mechanical means resemblinghooks.

A variation on this idea was suggested by Anaxagoras (500–428 BCm), whoproposed the Homoiomeria. According to this, material things consist of particlesthat are homogeneous in each kind of body, but dissimilar in different bodies. On theother hand, some 60 years later, Aristotle1 suggested that matter might be indefinitelydivisible. None of these ideas were put to a physical test, so they were just purehypothesis. However, it is not clear what else they could have done, since the physical

1 In some places it is claimed that Aristotle preached that we have to learn from experience. Expe-rience is, however, not the same as an experiment which is carried out under controlled conditions.The ratio between the frequencies of string vibrations was probably found by Pythagoras and hisstudents, and this is considered by many to constitute the first experiment.

G. Shaviv, The Synthesis of the Elements, Astrophysics and Space Science Library 387, 1DOI: 10.1007/978-3-642-28385-7_1, © Springer-Verlag Berlin Heidelberg 2012

2 1 Order in the Chemical Elements

and technical basis for experimentation did not yet exist, even if they had wanted todo it.

With the lack of good tests, and centuries before Ockham’s razor2 was invented,an hypothesis was accepted or rejected according to the reputation of the philoso-pher who proposed it. In the present case, the later Aristotle came out best, and hishypothesis became a common conviction, irrespective of the fact that it was com-pletely wrong and gave rise to more questions and problems than it solved.3 However,Aristotle’s reputation carried it through for centuries to come. The Greeks masteredlogic, but logic without experiment or observation may lead us astray.4

1.2 Ideas in the Far East

Ideas about the ultimate indivisibility of matter evolved in China and India, but theywere not expressed explicitly and must be inferred from contemporary writings.An atomic theory was proposed by Kanada, the founder of the Nyaya system ofphilosophy.5 The technical term ‘atom’ or its equivalent was not invented, but can beinferred. According to Kanada, atoms are eternal but may compose more complexsubstances, although they themselves are simple and non-composite. Aggregates ofatoms can be separated into the fundamental atoms.

1.3 Alchemy

It is an amazing fact that, through all the centuries of believing in and workingon the possibility of transforming ordinary metals into gold, for example, none ofthe alchemists ever came up with a theory to explain how such a change could bebrought about. Alchemists made innumerable attempts, and it is well known that allwere in vain. And yet there was never a word, not a single idea about the fundamentalconstituents of matter they wanted to transform, or a theory that could be used as aguide. Every attempt was just a shot in the dark.

Despite its esoteric foundations, alchemy is in fact a precursor of practicalchemistry, even though absolutely no new concept was invented over the many

2 The so-called razor due to William of Ockham (1285?–1349) is the philosophical principle that,of all possible explanations of a phenomenon, the simplest is most probably the best one. Of course,this principle cannot be proven rigorously. We must ‘take it or leave it’.3 Even today, an hypothesis is often accepted or rejected by popular vote, i.e., according to thenumber of scientists who believe it. See, for example, the idea that anthropogenic CO2 causesglobal warming, while no evidence exists to support this quite common conjecture, and one groupof scientists even tried to massage the data so as to ‘prove’ it. On the other hand, scientific revolutionsare caused just when a single scientist attempts to disclaim a scientific dogma.4 For more detail on the ancient atomic theory, see Partington, J.R., Annals of Science 4, 245 (1939).5 Ray, P.C., A History Of Hindu Chemistry V1: From The Earliest Times to the Middle of the SixteenthCentury A.D., Calcutta, The Bengal Chemical and Pharmaceutical Works, Ltd., 1903. The bookcontains translations of relevant texts from oriental languages to English.

1.3 Alchemy 3

years during which ‘alchemistry’ was practised. Anyway we should not forget thatNewton was a disciple of the alchemist movement, and that physics has alreadyturned the old fantasy of element transmutation into a reality by transforming onenucleus into another.

It is instructive at this point to mention Ben Johnson’s hilarious play The Alchemist,first performed in 1610, in which the author exploited the profession of alchemist asa platform on which to satirize about human greed and the partly scientific, partlypretentious language of the alchemist.6

1.4 Lavoisier and the Beginning of the Modern Era

The modern era of chemistry started in 1789 when the ‘father of chemistry’, Antoine-Laurent de Lavoisier (1743–1794m),7 attempted to classify the elements.8

Lavoisier9 defined what we call today a chemical element as une substance simplen’étant susceptible d’être divisée par aucune méthode connue d’analyse chimique.In other words, a chemical element was a substance that could not be further dividedby any known method of chemical analysis, and this is the definition that we shalluse here.10 Lavoisier was unbelievably precise in his definition, almost predictingdiscoveries to be made 150 years on, when he restricted the definition to objects thatwere ‘indivisible by analytical chemistry’, as though suggesting that other methodscould possibly further split the element. On the other hand, Lavoisier, who onceand for all eliminated the imaginary phlogiston from chemistry, assumed the equallyimaginary caloric to be a ‘simple substance’.11

6 Craig, D.H., Ben Johnson: The Critical Heritage, London, Routledge, 1999.7 Lavoisier, A., Traité Elémentaire de Chimie, Cuchet, Paris, 1789.8 As scientists could not make a living from doing research alone, Lavoisier, like Fourierafter him, became a member of the Fermiers Généraux. This General Farmers association wasa private company with 60 members which had at its disposal a fortune of about 100 millionpounds. Every 6 years, the company negotiated with the royal treasury the right to collect tax andcustoms duties. Obviously, this company and its members were not very popular, to put it mildly.Lavoisier’s immense scientific reputation did not save him on Judgement Day, and his job as taxcollector cost him his life: he was guillotined in 1794, during the French revolution.9 There is a controversial claim regarding the extent to which Robert Boyle (1627–1691m) recog-nized the fundamental nature of a chemical element. See Knight, D., Ideas in Chemistry: A Historyof the Science, Cambridge University Press, 1992.10 One sometimes sees erroneous definitions of chemical elements as ‘pure chemical substance’(see, for example, in Wikipedia). We adopted Lavoisier’s definition here, although we did not definewhat exactly was meant by ‘a method of chemical analysis’. The atoms of an element are complexsystems that exist over a certain range of temperatures and densities, and in certain environments.So a chemical element can exist only if chemistry itself actually exists. In the cores of stars, forexample, all atoms are crushed by the pressure, and there is no chemistry to speak of.11 On the other hand, it is not clear today whether the dark energy and dark matter postulated toexplain the structure of galaxies and the expansion of the Universe are matter in the normal senseor merely an expression for our ignorance of some fundamental physical law.


Fig. 1.1 Lavoisier’s originalclassification of 33 ‘simplesubstances’, including light(the first on the list) and heat(the second on the list) underthe name ‘calorique’, whichat that time was assumed tobe a liquid that carries heat.Lavoisier, 1787

Lavoisier included all entities he could not split in his list of elements (seeFig. 1.1), including light, heat, and metal oxides. In addition, Lavoisier did notuse the name ‘element’, but preferred ‘simple substances’. Five of the substanceslisted by Lavoisier were discovered by Carl Wilhelm Scheele (1742–1786m), whowas a German–Swedish pharmaceutical chemist. It was Scheele who discovered thechemical elements oxygen and nitrogen (in 1772–1773),12 although it was Lavoisierwho first named these gases.

1.5 Wenzel and Richter: Quantitative Chemistry

Quantitative chemistry was actually initiated by two German chemists, Karl FriedrichWenzel (1740–1793)13 and Jeremias Benjamin Richter (1762–1807),14 who coinedthe word ‘stöichiometrie’ or ‘stoichiometry’ (from the Greek word stoicheion for

12 Scheele, C.W., Chemische Abhandlung von der Luft und dem Feuer, Upsala und Leipzig, Verlegtvon Magn. Swederus, Buchhändler; zu finden bey S.L. Crusius 1777.13 Wenzel, K.F., Lehre von der Verwandtschaft der Körper, Dresden, 1777.14 Richter, J.B., Anfangsgründe der Stöchyometrie oder Messkunst chymischer Elemente, Breslauund Hirschberg 1792–1793. Reprint Hildesheim 1968.

1.5 Wenzel and Richter: Quantitative Chemistry 5

element). The main finding was that elements combine to form compounds in fixedmass ratios.15 But the ideas of Wenzel and Richter apparently came too early, andinvolved some errors. As a result, the scientific community refused to recognize thediscovery and it was mainly forgotten.16

1.6 Proust and Gay-Lussac Versus Berthollet: 1800–1808

Claude-Louis Berthollet (1748–1822) was a member of Lavoisier’s entourage17 anda leading French chemist in his own right. From the historical perspective, Bertholletis best known for his ideas on ‘reverse chemical reactions’, which led to Guldbergand Waage’s ‘law of mass action’.18

Berthollet’s most remarkable contribution to chemistry was his Essai de StatiqueChimique (Essay on Chemical Equilibria, 1803), which was the first systematicattempt to cope with the problems of chemical physics and chemical reactions.According to Berthollet’s theory, the physical conditions surrounding reagents,including temperature and solubility, often offset the effect of affinities, therebydetermining the direction of the reaction. Borrowing a physical term, he assertedthat chemical reactions seek a ‘static equilibrium’, hence the title of his essay.Because it was thought that the molecules in a gaseous reaction were separated bycaloric (a hypothetical weightless substance thought to account for the flow of heat),

15 Note that we stress mass ratios and not number ratios. This is a fundamental point. Fixed massratios do not necessarily lead to the atomic hypothesis, but fixed ratios of integers do.16 Wenzel and later Richter published some inaccurate results and interpretations. This had to dowith the conservation of electric charge in the dissociation of salts. See, for example, Wollaston,W.H., Phil. Trans. Roy. Soc. London 104, 1 (1814). Consequently, they lost their credentials aschemists and it was only Berzelius who recognized their achievements about twenty years later.It is not absolutely clear to whom the credit for the discovery of the law of proportionality shouldgo. Does the announcement of a correct law on the basis of incorrect experimental interpretationdeserve full recognition? See A History of Chemical Theory, Wurtz, MacMillam and Co. London,1869. But the idea was good so why was it ignored? Szabadváy (Szabadváy, F., J. Chem. Educ. 39,267, 1962) suggests that Richter began his book with an attempt to teach chemists simple arithmetic,e.g., explaining things like the simple plus sign. If you treat your fellow practitioners with suchdisdain, do not be surprised to find they ignore you.17 In contrast to Lavoisier, Berthollet served the revolutionary government as an adviser and emergedfrom the French Revolution unharmed. Later he joined Napoleon on his trip to Egypt, where he didthe research reported later in his book Essay on Chemical Equilibria.18 Cato Maximilian Guldberg (1836–1902) and Peter Waage (1833–1900) suggested the lawof mass action in 1864 (Forhandlinger: Videnskabs-Selskabet i Christiana 35, 1864). In 1877,van ’t Hoff (1852–1911m) (Berichte der Berliner Chem. Ges. 10, 1877) rediscovered the law with-out knowing about the earlier discovery by Guldberg and Waage, which was published in Norwegian.In 1879, Guldberg and Waage decided to republish the paper in German (Erdmann’s J. für Prac.Chem. 127, 69, 1879) in order to claim the discovery. The law of mass action says that, when achemical reaction is in dynamic equilibrium, e.g., A + B � C , then K (T ) = [A][B]/[C] is aconstant which depends only on the temperature and pressure. Here [X ] denotes the concentrationof the species X .


Berthollet insisted that they had to be carried out at certain temperatures in orderto be successful.19 Berthollet’s thesis did not meet with general approval among hiscontemporaries, partly perhaps because he pushed it too far. For instance, he claimedthat two elements might combine in varying proportions. Berthollet’s experimentsshowed that the concentration of the species affects how the reaction ends, which isof course true for reactions in equilibrium. This result is at variance with the cases inwhich the affinity of the elements determines the outcome in an elementary reactionlike A + B → C.

1.7 Berthollet Was Both Right and Wrong

The confusion between reactions in equilibrium and regular chemical reactions,where the reacting species consume each other completely, worked against Bertholletand caused him to think that all chemical compounds exist in indefinite proportionsin solution. When the acceptance of John Dalton’s atomic theory discredited thisthesis, some of Berthollet’s contemporaries unjustifiably inferred that his views onmass action were erroneous. If partly wrong, then completely wrong! Others, how-ever, notably Berzelius, distinguished between these two different situations. Forseveral decades the prevailing belief was that Berthollet’s mass action presented analternative hypothesis to the affinities of elements as an interpretation for chemicalreactions. The issue appeared chemically indeterminate because the relative quanti-ties of each substance present in a solution could not be determined without applyingreagents that themselves disturbed the equilibrium.

Joseph Louis Gay-Lussac (1778–1850m)20 was quite prolific in his researchinterests, from the structure of the atmosphere to magnetism. However, Gay-Lussacis best known for the ‘law of combining volumes’: The compounds of gaseoussubstances with each other are always formed in very simple ratios by volume.21

In a brilliant move, Gay-Lussac took Davy’s (1778–1829m) results, in which theelements making up a compound were given as a ratio of weights (see Table 1.1),

19 In conducting this research, Berthollet was assisted by his student Joseph Louis Gay-Lussac,with whom he was engaged in experiments in the laboratory as well as in a balloon flight toa then record height of 23,000 feet. Gay-Lussac and others, including Louis-Jacques Thenard,Jean-Baptiste Biot, Pierre-Louis Dulong, and ultimately Jacques-Etienne Bérard, constituted theactive chemical group of the Société d‘Arcueil, all inspired by the older academicians Bertholletand Laplace. The proceedings of the society were published in three volumes between 1807 and1817 as Mémoires de la Société d‘Arcueil.20 Gay-Lussac grew up during the French Revolution, and his education was disrupted when hisprivate tutor ran away and his father was imprisoned. However, Gay-Lussac took advantage of thenew order when he was chosen to attend the Ecole Polytechnique, the institution that the FrenchRevolution designed to create the leading scientific and technical cadre, especially for the military.Gay-Lussac’s mentors at the Polytechnique, Laplace and Berthollet, urged him to pursue a research-academic career, which he began shortly after graduation in 1800.21 Gay-Lussac, J.L., Mém. de la Soc. d’Arcueil 2, 207 (1809)

1.7 Berthollet Was Both Right and Wrong 7

Table 1.1 Davy’s results for the relative masses of nitrogen and oxygen in various compounds ofthese two elements, and Gay-Lussac’s conversion to volumes, 1809

Compound Nitrogen mass Oxygen mass Nitrogen volume Oxygen volume Gay-Lussacà la Davy à la Davy à la G-L à la G-L assumed ratio

Nitrous oxide 63.30 36.70 100 49.5 2:1Nitrous gas 44.05 55.95 100 108.9 1:1Nitric acid 29.50 70.50 100 204.7 1:2

and converted them into volumes, thereby neutralizing the role of the weight of eachatom.

No estimate of the error in the measurements was given by Davy. But Gay-Lussacunderstood the existence of an error in the measurements and ingeniously overlookedit. Gay-Lussac gave more examples before he summarized his conclusions:

I have shown in this Memoir that the compounds of gaseous substances with each other arealways formed in very simple ratios, so that representing one of the terms by unity, the otheris 1, or 2, or at most 3.

But Gay-Lussac went on to conclude that:

These ratios by volume are not observed with solid or liquid substances, nor when we considerweights, and they form a new proof that it is only in the gaseous state that substances are inthe same circumstances and obey regular laws.

In 1805 Gay-Lussac and Alexander von Humboldt (1767–1835m) showed, forexample, that hydrogen and oxygen combine in a ratio of 2:1 to form water.22

Gay-Lussac the scientist was uncompromising with regard to his mentor, pointingout that:

The numerous results I have brought forward in this Memoir are also very favorable to thetheory. But M. Berthollet, who thinks that combinations are made continuously, cites inproof of his opinion the acid sulphates, glass alloys, mixtures of various liquids, all of whichare compounds with very variable proportions, and he insists principally on the identity ofthe force which produces chemical compounds and solutions.

Note that none of the counterexamples are gases. Did he mean that in the other casesBerthollet was right? Moreover, Berthollet spoke about mixtures while Gay-Lussacdid not specifically eliminate this possibility.

Gay-Lussac turned against the view of his old mentor Berthollet, as it wasexpressed in the introduction Berthollet wrote to the French translation of the thirdedition of Thomson’s (1773–1852) textbook, published in 1807.23 In this book,Thomson presented Dalton’s atomic hypothesis before Dalton published it,24 and itis easy to imagine that Berthollet did not approve of it. Gay-Lussac referred in a very

22 von Humboldt, A. and Gay-Lussac, J.F., Ann. der Physik 20, 129, 1805.23 Thomson, T., A System of Chemistry, Edinburgh, 1807.24 Thomson had private communication with Dalton, in which Dalton provided him with a copy ofA New System of Chemical Philosophy, which he published only a year later. Thomson gave all thecredit to Dalton.


polite way to Berthollet’s claims in the introduction, arguing that they did not agreewith experiment:

M. Berthollet has already strongly opposed it in the Introduction he has written to Thomson’sChemistry, and we shall see that in reality it is not entirely exact.

Berthollet did not allow the facts to confuse him again, claiming that the gaseouscompounds were not the rule but the exception.

In 1785, after serving in different positions in Paris, Joseph Louis Proust (1754–1826) accepted a prestigious teaching position offered by the Spanish government.He spent the next twenty years in Madrid and Segovia, thereby completely ‘missing’the French Revolution and the rise to power of Napoleon Bonaparte, with their variousconsequences for French science. While in Spain, Proust began studying differenttypes of sugar, and was the first to identify glucose and study it.

Proust also studied copper carbonate,25 the two tin oxides, and the two ironsulfides. In particular, he prepared artificial copper carbonate and compared it tothe natural one. In this way he demonstrated that each compound has the same pro-portion of weights between the three elements involved (Cu, C, O). Moreover, Proustshowed that no indeterminate intermediate compound exists between them. Conse-quently, Proust was able to formulate his law that compounds are formed by certainbut fixed mass proportions. Although Proust published this paper in 1799, the law,let alone its implications, was not accepted by the scientific community until 1811,when Berzelius credited Proust with the discovery of the law and endowed it withhis approval. No doubt, this was Proust’s greatest achievement in chemistry. The lawand its conclusions contradicted what Berthollet thought and wrote in his book, andunavoidably became the center of a long controversy between Berthollet and Proustwhich lasted from 1800 to 1808.

Proust owed nothing to Berthollet and expressed himself more critically thanGay-Lussac, although he remained friendly. For about eight years, Proust andBerthollet were immersed in a controversy over this issue, but in the end the truth ofProust’s arguments prevailed. A frequently expressed view is that Berthollet treatedmixtures, solutions, and compounds equally, and that this was the source of his error.However, things were a bit more complicated than that. Apart from discovering reac-tions in chemical equilibrium, Berthollet actually discovered the berthollites, that isto say, nonstoichiometric compounds in which the numbers of atoms of the elementspresent cannot be expressed as a ratio of integers.26 It was ingenious on the part of

25 Proust, J.L., Ann. de Chim. 23, 101 (1797), ibid. 32 (1799).26 Nonstoichiometric compounds appear mainly among the transition elements which are used insolid-state electronic devices, such as rectifiers, thermoelectric generators, photodetectors, thermis-tors, and magnets useful in high-frequency circuits.

The existence of nonstoichiometric compounds which led Berthollet astray is related to thepresence of defects in the lattice structures of crystalline substances. For example, a sodium chloridecrystal in which one of the locations is occupied by a neutral sodium atom rather than a sodium ion.Another example is the FeO crystal with some vacancies (missing oxygen atoms at some location)leading to Fe0.95O. Most nonstoichiometric compounds have compositions that are close to thoseof stoichiometric compounds.

1.7 Berthollet Was Both Right and Wrong 9

Proust to disregard Berthollet’s confusing non-true chemical compounds, although,like Gay-Lussac before him, he did not explain why the crystals, for example, do notobey his law. The problem for Proust was to demonstrate in a convincing way thedifference between a compound and a mixture or an alloy. Still, Proust succeededin showing27 that the sulfurous compounds of copper were not true compounds, butmixtures of copper sulphide in sulphur.

Proust then went on to show how Berthollet was incorrect in his own chemicalanalyses, by showing that Berthollet treated some of the chemicals he used as oxides,when they were actually hydrates, i.e., they contained chemically-bonded water. This‘unpleasant discovery’ completely pulled the rug from under Berthollet’s claim.

On the other hand, Berthollet rejected the experiments carried out by Proust bystating that they did not have a general validity. Worse than that, Gay-Lussac, whoworked on gaseous compounds under the directorship of Berthollet, managed todemonstrate that the gases combine in fixed ratios, but Berthollet simply refusedto accept Gay-Lussac’s results. Berthollet did not go as far as rejecting what hecalled ‘Dalton’s ingenious atomic idea’, which was published during the ongoingcontroversy.

Berthollet also engaged in a long controversy with other chemists about the natureof the force acting between two atoms and making a compound, but this issue, knowntoday as the chemical bond, goes beyond our scope here.

Berthollet insisted that Proust define a compound and a solution, definitions whichProust had difficulty in providing. He eventually defined a compound by saying that itwas a privileged product to which nature assigns fixed proportions. But his definitionwas logically circular, hence useless.

Berthollet was famous for the controversy in which he was wrong, and Proustbecame famous for the controversy in which he was right. For more details aboutthe Proust–Berthollet controversy, see Kapoor.28 Berthollet’s fundamental contribu-tions which led to the law of mass action were unjustifiably overshadowed by thecontroversy. Here is that stupid law again: wrong once, wrong all the time. Similarly,Berthollet’s contributions to the chemistry of dyes and bleaching agents, in particu-lar, the suggestion that chlorine could be used as a bleaching agent, did not receiveadequate recognition by his contemporaries.

1.8 Dalton and the Revival of the Atomic Theory

At the same time as the Berthollet–Proust controversy was taking place in France,Dalton proposed his seminal hypothesis about the structure of matter. It was in1802 that John Dalton (1766–1844m),29 professor of chemistry in Manchester,

27 Proust, J.L., J. de Phys. 55, 335 (1802).28 Kapoor, S.K., Berthollet, Proust, and proportions, Chymia 10, 53 (1965).29 Dalton was also known for his extensive meteorological observations and the rediscovery of theHadley circulation in the atmosphere, as well as research on color blindness.


resuscitated the old Greek atomic theory, but this time with good, or at least cir-cumstantial, evidence. It must be admitted that similar ideas had been announcedbefore by Wenzel and Richter.30 Dalton had in hand the quantitative measurementsof mass fractions of elements making up different compounds, as carried out byLavoisier some two decades earlier, as well as the books by Richter and Wenzel.Atoms were defined by Dalton as:

[. . .] the smallest parts of which bodies are composed. An atom therefore, must be mechan-ically indivisible and of course a fraction of an atom cannot exist.

Note the term ‘mechanical’, which is a physical term (as opposed to a chemical one).As we know today, Dalton’s statement was too general (unless we add the clause ‘forthe energies available at the time’).

In 1803, Dalton realized that carbon and oxygen can form two chemical com-pounds, CO and CO2, and the ratio of oxygen between the two compounds isexactly 2.31 It was this observation that led him to propose the ‘law of simple propor-tions’, which was later confirmed by Jöns Jacob Berzelius (1779–1848m). The keyfact was that compounds are made of fixed proportions of the constituents. But at thispoint Dalton made a major step forward and interpreted the result as follows: eachelement has its unique atoms and the atoms of each element have a unique atomicweight. When an atom of element 1 combines with an atom of element 2 the massratio is always the mass ratio between atom 1 and atom 2 or a simple product of it.Questions such as how the chemical bond forms or why the properties of the thusformed molecule are not the average between the properties of the two atoms whichcomposed it, were not asked. In the case of water it was clear that hydrogen and oxy-gen unite in no other proportions than two hydrogen atoms with one oxygen atom.32

One may claim that the idea of atoms of matter can be traced back to the ancientGreek philosophers, but it was Dalton who based it on chemical facts. Moreover,Dalton essentially made a prediction, viz., in all chemical compounds, the elementsthat combine to form a compound combine in an integer(1):integer(2) ratio. Thereare no two elements which combine with a ratio of

√2 : 1, for example. Assuming

Dalton’s hypothesis, the mass ratio of the atoms of oxygen to hydrogen, is 5.5:1 (seeTable 1.2). If this is the mass ratio of the two atoms, then they combine either in a1:1 or a 1:2 ratio, but not say in a 1:1.67 ratio.

In 1808, Dalton33 published a new table in which all the weights were roundedoff. The comparison between the two tables shows that the atomic weight of several

30 Richter, J.B., Ueber die Neuren Gegenstande der Chimie, Breslau, 1791, Anfangsgrunden derStoichiometrie, 1792–1794 (Basics of Stoichiometry).31 Dalton, J., Memoirs Literary Phil. Soc. Manchester, Second Ser. 1, 271 (1805); reprinted inFoundations of the Atomic Theory: Comprising Papers and Extracts by Dalton, William Wollaston,and Thomas Thomson, Alembic Club Reprints No. 2, The Alembic Club, Edinburgh (1899) p. 15.32 Hydrogen peroxide, H2O2, was first discovered by Louis-Jacques Thenard (1777–1857) in 1818.However, it did not change the fact that the ratio of volumes is 2:1 or 1:1, i.e., always a ratio of twointegers.33 Dalton, J., A New System of Chemical Philosophy 1, Manchester, London, printed by S. Russelfor R. Bickerstaff, 1808.

1.8 Dalton and the Revival of the Atomic Theory 11

Table 1.2 Dalton’s relative-to-hydrogen weights of the ultimate particles of gaseous and otherbodies

Element Dalton Accurate

Hydrogen 1 1Azote (nitrogen) 4.2 7Carbon 4.3 6Ammonia 5.2 5Oxygen 5.5 8Water 6.5 9Phosphorus 7.2 15.5Sulphur 14.4 14

From Dalton, read before the Philosophical Society of Manchester in 1803, but published in 1808.Our table here contains only the known elements. However, Dalton included many compounds, ofwhich we include only water.

elements had ‘changed’ over the five years. The reason was the poor determination,impurities in the samples, and above all different methods used by various chemists.Furthermore, the comparison with present day values highlights the inaccuracies inthe results. The admirable thing is that, despite the very poor available data for theatomic weights, the abstraction needed to get the law was nevertheless successfullymade. Dalton disregarded the fact that two elements had the same atomic weight,and did not ask what made their atoms different.

A different classification of atoms was proposed by Berzelius,34 namely, elemen-tary atoms and compound atoms. The compound atoms divide into three types: atomsformed from two elementary substances united, which Berzelius called compoundatoms of the first order, atoms composed of more than two elementary substances,which he found mostly to be organic compounds, so he called them organic atoms,and atoms formed by the union of two or more compound atoms, such as salts. TheseBerzelius called compound atoms of the second kind.

Most chemists accepted Dalton’s hypothesis favorably. Thomson was even soenthusiastic as to argue that his own experiments were not accurate. Most of hispapers were published in the journal he himself edited, which is quite convenientif you do not have accurate results. Thomson’s estimates of atomic weights wereworse than those of Dalton. Moreover, his estimates were influenced by Proust’shypothesis, something we might call theoretically biased experimental results.

Fundamental imperfections in Dalton’s ideas were the lack of a definition of an‘ideal indivisible atom’ (which caused Dalton to reject the work of Gay-Lussac) andsome way to find the number of atoms in a given compound. The question of whatthe atoms were made of was not raised.

In the 1808 theory, Dalton rephrased Proust’s law, calling it the ‘law of multipleproportions’. Although it is unclear whether Dalton was directly influenced by Proust,the law of constant proportions provided evidence for Dalton’s atomic theory, whichin turn provided an explanation for Proust’s observations.

34 Berzelius, J.J., Annals of Phil. 2, 443 (1813).


As Proust stated, after learning about Dalton’s atomic hypothesis:

According to Dalton’s ingenious idea, that combinations are formed from atom to atom, thevarious compounds which two substances can form would be produced by the union of onemolecule of the one with one molecule of the other, or with two, or with a greater number,but always without intermediate compounds. Thomson and Wollaston have indeed describedexperiments which appear to confirm this theory. Thomson has found that super-oxalate ofpotash contains twice as much acid as is necessary to saturate the alkali; and Wollaston, thatthe sub-carbonate of potash contains, on the other hand, twice as much alkali as is necessaryto saturate the acid.

Dalton did not at first accept the results of Gay-Lussac concerning the fixed volumeratios of combining gases, and even claimed that he had had this idea earlier andfound it untenable, despite the obvious support that Gay-Lussac’s results providedto his hypothesis. He claimed that Gay-Lussac,35 who was considered a very carefulchemist and developed accurate methods, got inaccurate results. As an example,Dalton took HCl (or hydrogen chloride). If the supposition that equal volumes ofgases contain equal numbers of particles is correct, equal volumes of hydrogen andchlorine should yield one volume of hydrogen chloride. But on the contrary, Daltonwrongly claimed, the yield is two volumes of hydrogen chloride.36 It was clear thatthere was a missing link between the number of particles, the mass of particles, andthe volume they occupy. It was Avogadro who showed how wrong Dalton was andhow right Gay-Lussac was.

Berthollet eventually also attacked Dalton, who did not remain silent. Indeed,Dalton replied to Berthollet in the first part of his New System of Chemical Philoso-phy, which was published in 1808.37 In Dalton’s words, Berthollet’s claim, both inreason and observation, cannot fail to strike everyone who takes a proper view ofthe phenomenon. In other words, Berthollet’s conclusions, according to Dalton, hadnothing to do with experiment. In the controversy, each protagonist referred to thoseexperiments that agreed with his hypothesis. While Dalton knew of Berthollet’s pub-lication in France, he was apparently unaware of Proust’s very correct publications inFrench. But summaries of Proust’s papers were published in English,38 so it is diffi-cult to believe that Dalton was unaware of Proust’s results. Furthermore, Proust’sideas appeared in Thomson’s English textbook.39 If the reader doubts whetherDalton read Thomson’s description of Proust’s results, then note that Dalton stressedin his book that Thomson failed to understand his hypothesis from 1802.40 As forproper reference, there were so few chemists and publications in those days that itwould have required a special effort to miss a publication!

35 There is a long discussion and some surprises in Dumas’ book Lecons sur la Philosophie Chim-ique, Bechet Jeune, Paris, 1837, based on his lectures at the Collège de France.36 Another source of conflict was the equation for water. Berzelius said H2O, while Daltonassumed HO.37 Dalton, J., A New System of Chemical Philosophy, Manchester, 1808.38 Proust J.L., Ann. de Chim. 28, 213 (1798), and the English abstract Nicholson J. 2, 515 (1799).39 Thomson, T., A System of Chemistry, 4 vols. Edinburgh, 1802.40 Dalton, J., Phil. Mag. 14, 169 (1802).

1.8 Dalton and the Revival of the Atomic Theory 13

A burning question was: what is the weight of a hydrogen atom, or should thenumbers be divided by the weight of oxygen? Various attempts by Thomson failedand led him to conclude that: The above experiments (to find the common divisorwhich yields integers) will neither succeed with Dalton’s, Wollaston’s, nor Berzelius’numbers—a sufficient proof that none of them is absolutely correct. Thomson there-fore concluded that there was no proof for the atomic hypothesis.

1.9 Higgins and an Unjustified Claim for Priority

In 1814, William Higgins (1763–1825), who was a professor of chemistry in Dublin,published a book41 in which he claimed priority for the atomic idea, giving as areference his book from 1789.42 The book dealt basically with the theory of phlo-giston, which Higgins correctly claimed to be a wrong idea. Interestingly, Higginswrote that:

When I commenced my investigation [. . .] all the chemical philosophers were phlogistians.Under these circumstances, a very young man, such as I was at that time, might well besupposed to be intimidated, and even deterred from offering an opinion on the subject ofchemical philosophy; however, the new view which I fortunately adopted furnished me withsome degree of confidence.43

Regarding the atomic theory, Higgins wrote that chemical attraction only prevailedbetween the ultimate particles of simple elementary matter, and also between com-pound atoms, and he explained that the term ‘ultimate particles’ means the lastdivision of elementary matter. This is more like an attempt at the chemical bondtheory. Higgins continued: Dalton repeats experiments formerly made by me, hedoes not even glance at the source from whence he derived his information. ButHiggins introduced the atomic hypothesis only as an additional argument againstphlogiston and not as a basic argument on its own.

Dalton was probably unaware of Higgins’ publication. A close examination showsthat, even in 1814, Higgins assumed that all atoms have the same weight, while inDalton’s theory the atomic weight played the dominant role. According to Higgins,

41 Higgins, W., Experiments and Observations on the Atomic Theory and Electrical Phenomena,Graisberry and Campbell, Dublin, 1814.42 Higgins, W., A Comparative View of the Phlogistic and Antiphlogistic Theories: With Inductions.To which is annexed, An Analysis of the Human Calculus, Publisher Murray, 1789. In this book,Higgins suggested marking the bonding interaction between atoms and within molecules by astraight line. Like Lavoisier, Higgins did not give up the caloric as he hypothesizes that even whentwo atoms unite, the compound becomes surrounded with one common atmosphere of caloric [. . .]and this description is continually mixed with the bonding of atoms.43 At this point Higgins cited the letter he got from the editor: I shall be glad to see your book thoughI hope you have not taken Lavoisier’s side of the question or else have defended it by argumentstotally unlike any thing that has yet appeared. Dr. Priesley’s late admirable experiments have in myopinion totally overset that doctrine and re-established the existence of phlogiston. Yours faithfully,Thos. Beddoes. The editor was ready to publish only what he believed in!


atoms differ only in the atmosphere of caloric which surrounds them. But whatdoes caloric have to do with the atomic theory? Thomson, who was a professor ofchemistry in Glasgow, just on the other side of the Irish Sea, published right awayin the journal he edited, Annals of Philosophy, a memoir44 claiming that: I havehad that book (he refers to Higgins 1789) since the year 1798, and have pursued itcarefully; yet I did not find anything in it which suggested to me the Atomic Theory.[. . .] and I still consider myself as the first person who gave the world an outlineof the Daltonian theory. Higgins complained that Dalton did not even bother toanswer him. Only Thomson responded.45 Alas, Higgins’ attempts to shake Dalton’spriority failed completely.46 Dalton’s ideas were not immediately accepted by all.Sir Humphrey Davy, for example, was among the notable objectors, yet he eventuallyyielded to the evidence.

1.10 If You Dislike a Theory, Reinvent it Under Another Name

On 4 November 1813 William Wollaston (1766–1828m) lectured before the RoyalSociety47 and reviewed the work of his predecessors. Wollaston argued that:

When the nature of any saline compound is proposed as the subject of inquiry to an analyticalchemist, the questions that occur for his consideration are so varied and so numerous, that hewill seldom be disposed of satisfying his inquiries, so long as he can rely upon the accuracyof those results that have been obtained by the labor of others, who have preceded him inthis field of patient investigation.

In short, Wollaston was bothered by the fact that many published results were notidentical, and even contradictory, which meant that it was a problem to sort outthe results or repeat all the measurements. Indeed, Wollaston did not repeat all themeasurements and a quick look at his table reveals that his results were not free oferrors either (see Table 1.3).

So Wollaston devised a new scale which he called the synoptic scale. This scalewas intended to answer at one view all these questions, and he meant questionsconcerning the properties of elements and compounds. You can see some hints ofelement classification. The rationale behind the need for a new scale was:

44 Thomson, T., Annal. Phil. 3, 329 (1814).45 Higgins, W., The Phil. Mag. XLIX, 241, 1817. The letter to the editor is amazing for its strangestyle of English: It is stated that this paper, referring to Dalton’s paper, was read before the Literaryand Philosophical Society of Manchester in the year 1816. That should lie by since is not to bewondered at, as containing nothing new; it relate to a hackneyed subject, which chemists havelately gone over repeatedly. In that part of my paper which appeared in your excellent Magazinefor December 1816, I observed that Dr. Thomson stepped forward repeatedly in a very unjustcause, which could never do him credit, as the advocate of Mr. Dalton, while the latter stood silenttrembling as the bar of justice. It could easily be part of a play.46 A list of several tens of articles dealing with Higgins’ claim can be found in Wheeler, T.S.,Studies, An Irish Quarterly Review 43, 327 (1954).47 Wollaston, W.H., Phil. Trans. Roy. Soc. London 104, 1 (1814).

1.10 If You Dislike a Theory, Reinvent it Under Another Name 15

Table 1.3 Wollaston’ssynoptic scale compared withaccurate values of the atomicweights relative to oxygen =10, as assumed by Wollastonin 1814

Element Synoptic scale Accurate

Hydrogen 1.32 0.625Oxygen 10.00 10.00Water 11.32 11.25Carbon 7.54 7.51Sulphur 20.00 20.0406Phosphorous 17.40 20.609Nitrogen 17.54 8.75Chlorine 44.1 22.158Magnesium 24.6 15.191Strontium 69 54.763Barium 97 85.829Iron 34.5 34.903Copper 40 39.719Zinc 41 40.869Mercury 125.5 125.369Lead 129.5 129.5Silver 135 67.418

It it is requisite [. . .] to determine the proportions in which the different known chemicalbodies unite with each other, and to express these proportions in such terms that the samesubstance shall always be represented by the same number.

Wollaston stated that the original idea was due to Richter.48 Wollaston sorted out theresults by his predecessors and came up with Table 1.3. The table gives the elementand the synoptic scale of the element and the compound. As can be seen, Wollastonsuggested taking oxygen as reference, and attributed a scale of 10 to it. A columnhas been added to show the correct atomic weight, assuming the atomic weight ofoxygen to be 10. The comparison shows once again how poorly the atomic weightswere known.

A simple glance at the table shows that:

• The synoptic scale49 is nothing but the atomic weight.• Many numbers in the table are in error.

The newly invented name was very promising, but as soon became clear it containednothing but the atomic weights that Dalton had been talking about. Inventing a newname is not necessarily a discovery.

It is interesting to ask why the atomic weight of oxygen was used as a referencefor the atomic weight. The reason Berzelius chose to relate all atomic weights to

48 But I could find no reference for it in Wollaston’s paper.49 Wollaston did not explain in the paper why he chose this name for his scale. It is implied inthe paper that this number should provide a good explanation for the chemical properties of theelements and compounds.


oxygen was the fact that oxygen was capable of combining chemically with everyother element. In fact, oxygen compounds were almost the only ones made use of atthat time for the derivation of atomic weights. In Berzelius’ own words: Oxygen isthe central point around which the whole of chemistry revolves.

1.11 Avogadro: A Superb Insight, Perfect Timing,but Rejected

Shortly after Dalton suggested the atomic hypothesis, in 1811, the hitherto unknownItalian chemist Amedeo Avogadro (1776–1856m)50 came up with a sensational hy-pothesis:

The first hypothesis to present itself in this connection, and apparently even the only admis-sible one, is the supposition that the number of integral molecules in any gas is always thesame for equal volumes, or always proportional to the volumes. Indeed, if we were to supposethat the number of molecules contained in a given volume were different for different gases,it would scarcely be possible to conceive that the law regulating the distance of moleculescould give in all cases relations as simple as those which the facts just detailed compel us toacknowledge between the volume and the number of molecules.

Avogadro based his hypothesis on Gay-Lussac’s demonstration that gases alwaysunite in a very simple proportion by volume. Avogadro also reasoned that the distancebetween molecules is so large that their mutual attraction cannot be effective. Heessentially found what we call today an ideal gas, i.e., a gas in which the interactionbetween the molecules of the gas is negligible. Avogadro needed this assumptionabout the mean distance between the molecules in order to safely assume that theimaginary caloric plays no role in the problem. Avogadro assumed that caloric isimportant only when the gases condense. So, to be on the safe side, Avogadro claimedthat:

[. . .] in our present ignorance of the manner in which this attraction of the molecules forcaloric is exerted, there is nothing to decide us a priori in favor of the one of these hypothesesrather than the other, and we should rather be inclined to adopt a neutral hypothesis, whichwould make the distance between the molecules and the quantities of caloric vary accordingto unknown laws, were it not that the hypothesis we have just proposed is based on thatsimplicity of relation between the volumes of gases on combination, which would appear tobe otherwise inexplicable.

As for Dalton, Avogadro claimed that:

Dalton, it is true, has proposed a hypothesis directly opposed to this, namely that the quantityof caloric is always the same for the molecules of all bodies whatsoever in the gaseous state,and that the greater or lesser attraction for caloric only results in producing a greater or lesscondensation of this quantity around the molecules, and thus varying the distance betweenthe molecules themselves.

The caloric was of course a red herring, but Avogadro did not know it, so to be on thesafe side he considered those cases in which he thought that it could not be important.

50 Avogadro, A., J. de Physique 73, 58 (1811). Alembik Club Reprint no 4.

1.11 Avogadro: A Superb Insight, Perfect Timing, but Rejected 17

Avogadro’s logic was very simple:

M. Gay-Lussac has shown in an interesting Mémoir [. . .] that gases always unite in a verysimple proportion by volume, and that when the result of the union is a gas, its volume also isvery simply related to those of its components. But the quantitative proportions of substancesin compounds seem only to depend on the relative number of molecules which combine,and on the number of composite molecules which result. It must then be admitted that verysimple relations also exist between the volumes of gaseous substances and the numbers ofsimple or compound molecules which form them. The first hypothesis to present itself inthis connection, and apparently even the only admissible one, is the supposition that thenumber of integral molecules in any gas is always the same for equal volumes, or alwaysproportional to the volumes. [. . .] For example, since the numbers 1.10359 and 0.07321express the densities of the two gases oxygen and hydrogen compared to that of atmosphericair as unity, and the ratio of the two numbers consequently represents the ratio between themasses of equal volumes of these two gases, it will also represent on our hypothesis the ratioof the masses of their molecules. Thus the mass of the molecule of oxygen will be about 15times that of the molecule of hydrogen, or, more exactly as 15.074 to 1. In the same way themass of the molecule of nitrogen will be to that of hydrogen as 0.96913 to 0.07321, that is,as 13, or more exactly 13.238, to 1. On the other hand, since we know that the ratio of thevolumes of hydrogen and oxygen in the formation of water is 2 to 1, it follows that waterresults from the union of each molecule of oxygen with two molecules of hydrogen.

Avogadro extended his theorem to gaseous molecules containing atoms from morethan one element. But Avogadro made a grave mistake when, in his enthusiasm, heerroneously extended his theorem to non-gaseous bodies and consequently causedmany to distrust the hypothesis and flatly reject it. It should also be pointed out thatAvogadro had no reputation as a leading scientist, and nor did he have a prestigiousaffiliation—and in those days such things mattered. How about today?51

Three years later, in 1814,52 André Marie Ampère (1775–1836m) rediscoveredthe hypothesis. Ampère was careful to distinguish between particles and the atomswhich compose them, but it did not help to gain acceptance for the Avogadrohypothesis. It was just ignored. Progress was delayed for about half a century untilCannizzaro came along and rescued Avogadro’s hypothesis from oblivion.

1.12 Prout and the Name of the Game: Numerology

As early as 1815, William Prout (1785–1850)53 proposed that the atomic weightof any substance could be represented by an integer multiple of the atomic weightof hydrogen, as if hydrogen were the basic building block of all atoms. Prout was

51 Avogadro was born into a well-known family of lawyers and as such, studied law and even startedpractising. But his soul was in the natural sciences, and in 1800, he began to study physics. In 1809he started teaching in a high school and it was while serving as a teacher that he announced hisdiscoveries.52 Ampère, A-M., Ann. de Chim., 1ère serie xc, 43 (1814). There is a mountain ridge called MonsAmpère on the moon.53 Anonymous, On the relation between the specific gravities of bodies in their gaseous stateand the weight of their atoms, Annals of Phil. 6, 321 (1815). The paper was published anonymously.


not sure whether his hypothesis was right, and wrote in a paper published withanonymous authorship:

The author of the following essay submits it to the public with the greatest diffidence; forthough he has taken the utmost pains to arrive at the truth, yet he has not that confidence inhis abilities as an experimentalist as to induce him to dictate to others far superior that itsimportance will be seen, and that some one will undertake to examine it, and thus verify orrefute its conclusions. If these should be proved erroneous, still new facts may be broughtto light, or old ones better established, by the investigation; but if they should be verified, anew and interesting light will be thrown upon the whole science of chemistry.

Strange as it may be in science, the editor of the journal, Thomas Thomson,54

a chemist and mineralogist, who through his chemistry textbooks did much to spreadthe atomic theory of Dalton, agreed to publish such a paper. This may have been be-cause the idea appealed to him, as he was an ardent supporter55 of the atomic idea.56

Mind you, Thomson charmingly changed his mind about the claim that no suchdivisor could be found!

A year later, a second unsigned paper appeared in the Annals of Philosophy,57

in which the anonymous author corrected some errors made in the first paper andimproved the hypothesis. A year later, Thomson wrote a paper on the atomichypothesis and exposed Prout as the anonymous author of the papers. Prout’s originaltable is given in Table 1.4. As attested by the table, the atomic weights are extremelyclose to being integer products of the atomic weight of hydrogen. In the secondpaper Prout admitted that if the view we have ventured to advance be correct, wemay almost consider the πρωτηvλη58 of the ancients to be realized in hydrogen; anopinion, by the by, not altogether new (Fig. 1.2).

Although Dalton had already shown in 1805 that the gases in the atmosphere are amixture and not a compound,59 and even discussed the amount of water vapor in theatmosphere, Prout considered the atmosphere to be a compound made of one atomof oxygen and two atoms of nitrogen, whence it constituted a proof of the atomictheory.

(Footnote 53 continued)This is a rare phenomenon. Most frequently you find cases were no citation to a previous discovery ismade and the author wants to credit himself for it. Such behavior is a testimony to Prout’s standards,i.e., if you are not sure, you publish anonymously.54 In 1813 Thomson founded and subsequently edited the Annals of Philosophy.55 Thomson, T., Annal. Phil. 2, 32 (1813). Thomson announced Dalton’s theory in his 1807 book,a year before Dalton himself published it.56 How times have changed! Can we imagine an anonymous publication today, motivated by theauthor’s uncertainty regarding an idea?57 Anonymous, Annals of Philosophy 6, 321 (1815).58 πρωτηvλη means ‘raw material’, from which the term protyle was coined for a hypotheticalprimitive substance.59 Dalton, J., Memoirs of the Literary and Phil. Soc. Manchester 1, 244 (1805). Read before thesociety 12 November 1802.

1.12 Prout and the Name of the Game: Numerology 19

Table 1.4 Prout’s table of relative atomic weights of elements. Prout was courageous in ignoringthe round-off errors in the inaccurate experimental results

Name Sp. weight Relative to Prout’s Commentatmos. hydrogen number(air = 1) (accurate) rel. to H

Hydrogen 0.06944 1 Based on ammoniaCarbon 0.4166 6.003 6 Assumed weightNitrogen 0.9722 14.009 14 Based on air being a compound

of O and N in 1:5 ratioPhosphorus 0.9722 14.009 14 See comment in textOxygen 1.1111 16.010 16 Based on air being a compound

of O and N in 1:5 ratioSulphur 1.1111 16.010 16 Weight assumed to be 20Calcium 1.3888 20.012 20 Value 20.08 from Prout’s numbersSodium 1.6666 24.014 24Iron 1.9444 28.017 28 Value 28.08 from Prout’s numbersZinc 2.222 32.020 32 Value 31.85 from Prout’s numbersChlorine 2.5 36.023 36 Assume that sp. gr. does not differ

much from 2.5Potassium 2.7777 40.025 40Barytium 4.8611 70.045 70Iodine 8.6111 124.079 124 Based on an iodine solution

The idea of error analysis did not exist at that time, and the difficulty in measuringthe specific weight of a light gas like hydrogen was not expressed in the final result.60

Checking Prout’s calculations carefully, we find that he rounded his numbers with-out proper justification, sometimes giving numbers to 4 significant figures and thenrounding at the 10% level! However, if it were not for this rounding, the atomic theorymight have had to wait another century before the idea resurfaced again, and onceagain, the accuracy, or rather insufficient accuracy, would only lead to a vindicationof Prout and the conclusions would still be wrong (see Sect. 1.36).

Why did Prout not have a good value for the atomic weight of phosphorus? As heexplained in his paper:

I have made many experiments in order to ascertain the weight of an atom of this substance;but, after all, have not been able to satisfy myself, and want of leisure will not permit me topursue the subject further at present.

60 As the molecular weight of hydrogen is 2, this means that 22.4 l of gas weighs 2 g. The weight ofthe container is then much greater, and manipulations were needed to determine the weight of thegas accurately. Comparison between the results of different researchers gives a good indication ofthe degree of accuracy in the weights obtained in those days. The fact that hydrogen gas is made upof molecules containing two hydrogen atoms confused the issue, since only one atom of hydrogenparticipates in some of the molecules, leading to ‘half molecules’.


Fig. 1.2 Prout’s first of twoanonymous papers publishedin 1815 and 1816

It appears that in those days scientists appreciated rest more than the perpetual pursuitof new results.

Prout found that nitrogen and phosphorus should contain 14 hydrogen atoms, andlikewise that oxygen and sulphur should contain 16 hydrogen atoms. So why wasnitrogen different from phosphorus and oxygen from sulphur? No answer was givento this question, and nor did Prout comment on it. For Prout the issue was to getan integer number. Moreover, the fact that all numbers came out even, meaning thatonly an even number of hydrogen atoms was possible, did not cause any concern.It was not an oversight because, when he found that ammonia had been claimed tobe composed of one atom of nitrogen and only 1.5 of hydrogen, he declared thatthis must be an error. A glance at the specific weights reveals that many of themwere obtained by divisions of rounded, guessed numbers, in which the result wasmotivated by the hypothesis.

Worse than that, it is clear from Prout’s own comments in the paper that hearbitrarily changed the atomic weights to make them fit his hypothesis. Prout himselfwas a physician, and his own investigations in chemistry were few in number andanything but conclusive, accurate, or methodical.

1.13 Berzelius and the End of Prout’s Atomic Hypothesis 21

Table 1.5 The stableisotopes of chlorine. Atomicnumber 17

Atomic weight Relative abundance

34.968 852 68 0.757 636.965 902 59 0.242 4

1.13 Berzelius and the End of Prout’s Atomic Hypothesis

A few years after Prout put forward his hypothesis, Berzelius,61 one of the mostinfluential chemists of the 19th century,62 changed his mind about Prout’s atomictheory, although he continued to support Dalton’s theory, i.e., that the atoms ofdifferent elements are different. Berzelius carefully examined63 the measured atomicweights. The most damaging evidence against Prout’s simple assumption was theatomic weight of chlorine, which was measured to be 35.47 times that of hydrogen.64

The fact that an atomic weight was close to half an integer led some, in an attempt tosalvage Prout’s theory, to come up with the ad hoc suggestion that the basic unit wasone half of a hydrogen atom. But to no avail. Further discrepancies surfaced whichresulted in the hypothesis that 1/4 of a hydrogen atom was the basic unit. Berzelius’crusade against Prout’s theory succeeded in driving Prout’s hypothesis into oblivion.

Berzelius’ liquidation of Prout’s atomic theory brought a consensus amongchemists. Spectroscopy, which was used as the exclusive method for identifyingelements as of 1860, was not sufficiently accurate to distinguish the isotopic effect.

The solution of the chlorine conundrum was found in 1919–1920, when Astondiscovered the existence of isotopes and it was clear that chlorine has just two stableisotopes (see Table 1.5) with atomic weights close to 35 and 37, respectively, and anabundance ratio of 3:1, yielding a chemical atomic weight close to 35.5, and therebymisleading all chemists into suspecting Prout’s hypothesis. But as nickel and cobalthad the same atomic weight and were two distinct elements, it is strange that theopposite idea did not emerge, i.e., that chlorine has two types of atoms and that thechemist just observes a mixture of the two. Somehow it was simpler to believe inthe existence of a fictitious fluid like caloric. The atomic weight of chlorine was thestumbling block upon which Prout’s theory fell.

61 Berzelius, J.J., Pogg. Ann. vii, 397 (1821).62 Berzelius discovered the elements cerium in 1803, selenium in 1817, silicon in 1824, and thoriumin 1828. Lithium salt was discovered by Berzelius’s student Johan August Arfwedson (1792–1841) in his laboratory in 1817 (pure lithium was isolated by Davy). Another student of Berzelius,Nils Gabriel Sefström (1787–1845), discovered vanadium. Berzelius also suggested the way wewrite chemical reactions today. Dalton for example, used geometrical symbols, while Berzeliussuggested using the first letter of the element, for example, C + O2 → CO2. Later the superscriptbecame a subscript.63 Berzelius, J.J., Essay upon the Theory of Chemical Proportions, Ann. of Phil. 2, 443 (1813).64 Berzelius actually got 17.735 times the weight of hydrogen for the atomic weight of chlorine.


1.14 Petit and Dulong’s Law and Fading Hopes

The year 1819 brought a very important discovery in the atomic weight saga whenDulong (1785–1838) and Petit (1771–1820m)65 demonstrated that the specific heatat constant volume of an element multiplied by its atomic weight is approximatelyconstant. The number of atoms per unit volume is inversely proportional to the atomicweight. If the heat is expressed as vibrations of the atoms and does not depend onthe mass of the vibrating atom, then the product of atomic weight times the specificheat at constant volume must be constant. However, the motivation for Dulong andPetit was formulated according to Dalton in the following way:

The quantities of heat united to the elementary particles of the elastic fluid are the same foreach. Hence we may, setting out from our knowledge of the number of particles containedin the same weight or the same volume of the different gases, calculate the specific heatsof these gases. This M. Dalton has done, but the numbers which he obtained, and thoselikewise deduced from several other better founded hypothesis on the constitution of gases,are so inconsistent with experiment that it is impossible for us not to reject the principleupon which such determinations are founded.

Owing to these problems, Dulong and Petit decided to measure the cooling rates ofsolids and thereby deduce their heat capacity.

The most important conclusion reached by Dulong and Petit was this: The atomsof all simple bodies have exactly the same capacity for heat. They meant heat capacityat constant volume.66

Indeed, the first expectations were fulfilled and gave rise to the hope that a newand accurate method for measuring atomic weights, in particular for solids, mighthave been discovered. Dulong and Petit even applied their new discovery to correctsome reported results of atomic weights. For example, while Berzelius obtained theatomic weight of lead as 2589 on the basis of O = 10, Dulong and Petit claimed thatthe value should be 1295, or half the value given by Berzelius. Hence, factors of twoand four floating around in Berzelius’s table were spotted very quickly. In short, theymodified eleven out of the thirteen atomic weights given by Berzelius!

While Dulong and Petit hoped their discovery would be applied to the determi-nation of atomic weights, the unexplained inaccuracy involved caused their hopesto fade away (see Fig. 1.3). However, the law helped in screening gross errors.In 1831, Franz Neumann (1798–1895)67 discovered a similar relationship between

65 Petit, A.T. and Dulong, P.L., Ann. Chim. Phys. 2, 395 (1819). Dulong succeeded Petit as professorof physics, and his name is among the 72 mostly French names engraved on the Eiffel tower. Petit,on the other hand, has a mountain on the moon named in his honor.66 Almost a century later, in 1912, Debye discovered that every solid has a temperature, the Debyetemperature, above which, and only above which, the Dulong and Petit law is valid. In their paper,Dulong and Petit did not provide any information about the temperature range of their measurements.But the Debye temperature, which they were unaware of, is very close in many cases to their supposedrange of measurement. For example, TDebye = 470 K for iron, whence the value they got for ironwas doubtful. In other cases like gold, TDebye = 165 K and Petit and Dulong could easily get anaccurate measurement.67 Neumann, F., Poggendorff’s Ann. Phys. 23, 1 (1831).

1.14 Petit and Dulong’s Law and Fading Hopes 23

Fig. 1.3 The results of Petitand Dulong 1819. The atomicweight multiplied by thespecific heat is plotted foreach element

The Specific heat times the Atomic Weight

Atomic Weight

0.44

0.42

0.40

0.38

0.36

0.34

0.32

0.300 2 4 6 8 10 12 14

the specific heat and molecular weight of compounds, but again of limited use forthe same reason: insufficient accuracy.

In 1828, Dumas made an attempt to advocate the use of the Petit and Dulonglaw to measure atomic weights, in particular after he cited experiments which hepointed out were made with the greatest care by La Rive (1801–1872) and Marcet(1803–1883)68 and which confirmed the law, but he was not successful.

1.15 Thomson 1821: Prout Is Nevertheless Right

In 1821, Thomas Thomson (1773–1852)69 published an attempt to confirm Prout’shypothesis. Thomson claimed to have shown that Berzelius’ method to determinethe atomic weights was not precise enough for the determination of the weights ofthe atoms of bodies. Since this was quite a blunt accusation, Thomson felt the needto add:

I ought to observe, however, that Berzelius is undoubtedly a very great master of the analyticalart; that his analysis approach upon the whole exceedingly near the truth; and exhibit aconsistency which is highly satisfactory, and does a great deal of credit to the industry andsagacity of their authors. But unfortunately his mode of experimenting admits of no criterionby which the experimenter can determine whether the results be accurate or not; so he hasnot means of checking himself.

A compliment it was not. A glance at Tables 1.6 and 1.7 will explain the sourceof Thomson’s comment. The comparison given in Table 1.6 shows how different

68 La Rive, A.A. and Marcet, F., Ann. de Chim. et de Phys. 75, 113, 119, 242 (1840). But theirwork was criticized by Weber, H.F., Phil. Mag. 49, 161 (1875) as not being sufficiently accurate.69 Thomson, T., Annals of Phil. I, 1 (1821). This was the last volume of the journal edited byThomson. In the editorial he explained that he was beginning a laborious course of ChemicalLectures with scarcely any previous preparation, and hence had to relinquish the position of editor.


Table 1.6 Typical results obtained by different chemists. After Thomson, 1821. While some ofthe results of each chemist are given to 4 or even 6 significant figures, the discrepancy between thevarious results is sometimes in the second significant figure

Dalton Wollaston Berzelius Prout Thomson

Strontian 6.571 6.9 12.9460 6.5Lime 3.428 3.536 7.1206 3.5 3.625Magnesia 2.428 2.46 5.1272 2.5Phosphoric acid 3.285 3.74 8.9230 3.75 3.5Arsenic acid 14.4077 7.25

Table 1.7 Thomson’s 1813table of atomic weights

Element Atomic weight Atomic weight Accuraterelative to oxygen relative to hydrogen

Oxygen 1.000 7.576 8.00Hydrogen 0.132 1.000 1.00Carbon 0.751 5.689 6.01Nitrogen 0.878 6.652 7.03Phosphorus 1.320 10.000 15.47Sulphur 2.000 15.152 16.03

the results obtained by different chemists were. Thomson pointed out that dividingBerzelius’ result by 2 provided a better agreement with the results of other investi-gators.

Berzelius did not remain in debt.70 The report on the exchange between thetwo chemists was not signed. The title of the paper is: Attack of Berzelius onDr. Thomson’s “Attempt to establish the First Principles of Chemistry by Experi-ment”. It is clear from the text that the purpose of the anonymous author was todefend Thomson, saying that his correspondence between his hypothesis and theresults of his experiments was startlingly precise. The author therefore asked im-patience for Berzelius’ opinion, which was expressed in language extremely strongand extremely unusual, to the extent that the author thought it necessary to employhis own words. He accordingly translated a few passages from the Yares-Bericht for1827. And so wrote Berzelius:

Someone had told Thomson that his whole work was of little value, because, in the funda-mental experiment [. . .] Thomson openly replied that he had supposed chemists would havegiven him credit for a knowledge of the mode of separating oxide of zinc from acids, and hadtherefore omitted the details; but as he found this opinion erroneous, it became necessary topublish a full account of his process. [. . .] It appears to me that love for the real progress ofscience makes it imperative to detect quackery, and expose it to the judgement of every oneas it merit.

70 Anonymous, Phil. Mag. 4, 450 (1828).

1.15 Thomson 1821: Prout Is Nevertheless Right 25

The author of this article went on to say that:

We regret to see the dignity of science sacrificed by the intemperance of those who professto be her advocates. It well becomes Berzelius to expose fallacy in argument, or detect errorin analysis; but let him not pass beyond the limits of fair criticism; let him not arraign thecharacter of an individual. [. . .] Intemperate attacks, such as this, reflect back upon theirauthor, and indicate a mind inflamed by pique, jealousy, or some unworthy passion.

The name of the anonymous reporter remained anonymous.Berzelius did not hesitate to express his view in textbooks.71 In complete contrast

to the way standard scientific texts are formulated, Berzelius criticized experimentsfrom which, according to him, incorrect conclusions were drawn. Meyer72 exempli-fies Berzelius’ approach with the following extract from a letter dated 3 April 1838,which Berzelius sent to Justus Leibig73:

In the treatment of scientific subjects a man must have neither friends nor foes. He combatswhat appears to him to be an error without any reference whatever to the personality of thewriter who advances it. Opinions are not individuals, and one can upset an opinion withoutfinding in that a reason to treat its author as an enemy. Only in the case of palpable scientificplagiarism is one entitled to write sharply; and even then it is best to censure without theleast sign of passion, for this awakens in the reader’s mind the thought: audiatur et alterapars.

The meaning is that no person should be condemned unheard.74

In another paper, in the same year, Thomson75 presented Table 1.8, which providesa nice demonstration of Prout’s hypothesis. However, Thomson had problems withseveral metals, as can be seen from Table 1.9. These elements refused to obey Prout’slaw. Thomson got numbers like 3.39215 (relative to oxygen) for the atomic weight ofiron, and similarly non-integer numbers for the other metals. So Thomson discussedeach element separately to find the reason why it would not obey the law. Despite thedisagreements with the metals, which were not resolved, Thomson did not abandonhis faith in Prout’s hypothesis. It was too beautiful and too symmetric to relinquishbecause of a couple of rebellious metal elements.

Thomson was happy with the resulting table. However, there was no questionraised as to how 28 hydrogen atoms could yield both iron and manganese, and

71 Berzelius, J.J., Lehbuch der Chemie, Dresden, 1820. The book first came out in Swedish in1808–1818, and was later translated to German by Wöhler.72 von Meyer, E., A History of Chemistry from Earliest Times to the Present Day, translated fromGerman by McGowan, MacMillan and Co., London, 1906. The original book was published inLeipzig in 1888.73 Leibig (1803–1873) was a well-known chemist, famous for his analysis of many organic com-pounds and his theory of organic radicals. He is generally considered to be one of the founders oforganic chemistry. However, Leibig’s name went before him in his appetite for scientific contro-versies. As of 1837, he held the powerful position of editor at Anleitung zur Analyse organischerKörper. So Berzelius’ letter was sent hardly a year after Leibeig took the position as editor. Themost famous controversies he was involved in were with Mulder, Wöhler, and Pasteur. We may saythat Berzelius certainly sent the letter to the right person.74 The correspondence was published by Carriere, Pub. Lehmann, Munich and Leipzig, 1893.75 Thomson, T., Annals of Phil. I, 81, 241 (1821).


Table 1.8 Thomson’s 1821table of atomic weights

O = 1 H = 1

Nitric acid 6.75 54Sulphuric acid 5.0 40Muriatic acid 4.625 37Chromatic acid 6.5 52Arsenic acid 7.75 62Phosphoric acid 3.5 28Potash 6.0 48Soda 4.0 32Barytes 9.75 78Strontian 6.5 52Lime 3.5 28Magnesia 2.5 20Silver 13.75 110Lead 13.00 104

26 hydrogen atoms both nickel and cobalt. How could this be? It was not a questionof oversight, because Thomson noted that all the numbers of hydrogen atoms wereeven. In retrospect, it is amazing how the atomic theory was ‘proven’ correct in thepresence of such huge measurement errors.

The conflicting results from different chemists triggered comments by Thomsonlike76:

My object in this paper is to show that the present state of our knowledge leaves no doubtwhatever that Gay-Lussac’s proportions are accurate and that Mr. Dalton has misled himself.

Here, Thomas refers to Dalton’s rejection of Gay-Lussac’s results, although theseresults provided more evidence for his theory.

Berzelius then set about determining atomic weights with more sophisticationthan Dalton had been able to do. In this project, Berzelius made use of the findings ofDulong and Petit and of Mitscherlich,77 as well as Gay-Lussac’s law of combiningvolumes. (He did not, however, use Avogadro’s hypothesis.) Berzelius’ first tableof atomic weights, published in 1828, compared favorably for all but two or threeelements, with today’s accepted values.

Berzelius seemed to destroy Prout’s attractive suggestion (attractive, becauseit reduced the growing number of elements to one fundamental substance, after thefashion of the ancient Greeks, and thereby seemed to increase the order and symmetryof the Universe) with more than one example. Thus, on a hydrogen-equals-1 basis,the atomic weight of oxygen is roughly 15.9, and oxygen can scarcely be viewed asbeing made up of fifteen hydrogen atoms plus nine-tenths of a hydrogenatom.

76 Thomas, T., Annals of Phil. I, 322 (1821).77 Eilhard Mitscherlich (1794–1863) was a German chemist, best remembered for his law of iso-morphism, which states that compounds crystallizing together probably have similar structures andcompositions. This relationship was used by Berzelius in early attempts to assign relative massesto the elements.

1.15 Thomson 1821: Prout Is Nevertheless Right 27

Table 1.9 The number ofoxygen and hydrogen atomscalculated by Thomson tocompose metals. The lastcolumn is the accurate atomicweight as known today

O = 1 H = 1 Accurate valuefound in nature

Copper 8.0 64 63.55Zinc 4.25 34 65.39Iron 3.5 28 55.845Manganese 3.5 28 54.938Nickel 3.25 26 58.6934Cobalt 3.25 26 58.9332

The improved published tables of atomic weights and Berzelius’ assertion thatthe atomic weights of the various elements were not integral multiples of the atomicweight of hydrogen was considered fully established and became an accepted dogma.

1.16 Berzelius and the Realisation that Imaginary SubstancesAre Not Chemical Elements

Lavoisier’s table contained such entities as caloric and light which did not of coursehave any atomic weight. Chemists who came after Lavoisier correctly removed heatand light from the list of chemical elements without providing any explanation.It may be that caloric disappeared from the tables of elements precisely becauseit could not be weighed. However, it should be noted that, years later, Mendeleevsuggested that the imaginary substance ether should be classified as an element withvanishing atomic weight.

It was Berzelius78 who argued that light, heat, and magnetism were properties ofbodies and not entities like elements, and hence had no place in the list of elements.But as late as 1827, Gmelin79 still considered heat to be an imponderable substance.And as a matter of fact, heat was considered to be a chemical entity right up until1842 when Julius Robert Mayer (1814–1878)80 formulated the energy conservationprinciple and essentially moved heat away from chemistry and into physics.

1.17 Dumas 1828

In 1826, Jean Baptiste André Dumas (1800–1884)81 developed a method for measur-ing the density of substances that are liquid or even solid at ordinary temperatures.The gaseous elements known at the time were hydrogen, nitrogen, oxygen, and

78 Berzelius, J.J., Lehrbuch der Chemie, Dresden und Leipzig, 1833.79 Gmelin, L., Handbuch der Theoretischem Chemie, 1827.80 von Mayer, J.R., Ann. der Chem. und Pharmacie 43, 233 (1842).81 Unlike Fourier before him, who served the emperor but continued to be creative in science,Dumas largely abandoned his scientific research and in 1848 went to work for the ministry of


chlorine, and only these gases could be used, for example, in the Gay-Lussac type ofexperiments,82 unless one could use compounds that evaporated easily. Dumas’ newmethod thus allowed a significant extension of the list of elements with measuredatomic weights.

In 1826, Dumas83 carried out experiments on Avogadro’s hypothesis, which hecalled the Ampère hypothesis, without even mentioning Avogadro, and concludedat that time that the Ampère hypothesis was correct. Moreover, Dumas explainedthat the molecules that satisfy Ampère’s law can be further divided. In this way, heexplained how one volume of hydrogen combined with one volume of chlorine toproduce two volumes of hydrogen chloride.84

A couple of years later, in 1837, Dumas published his lectures on the philosophyof chemistry in the form of a book.85 One of the questions raised concerned themeaning of Dalton’s hypothesis, and in particular the question: What are the atoms?Dumas thus wrote86:

You may want proofs for the existence of atoms. But Dalton does not suggest any evidence.Dalton assumed the existence of atoms, but he does not prove their existence. The assumptionabout their existence helps to formulate the relations between chemical phenomena.

And so he claimed that the basis for the existence of atoms was never demonstrated:C’était faire un cercle vicieux, et leur argumentation est demeurée sans authorité,i.e., it was a vicious circle, and the argument remained without force. Dumas went onto argue that the atomic hypothesis was not required to explain observed chemicalphenomena. For example, if a minimum mass was needed for a reaction to takeplace, one could do away with the atomic assumption, while the assumption aboutthe indivisibility of the atom was not needed either. At this point, Dumas enteredinto a long, complicated, and farfetched astronomical argument ending with the claimthat, since the atmosphere of the Earth is finite, this proved, à la Dumas, the infinitedivisibility of matter. Strange logic indeed.

In the first volume of his earlier book87 Dumas dealt with these questions in theintroduction. It was in the introduction that he stated Avogadro’s law, but withoutmentioning either him or Ampère. Dumas discussed the Dulong and Petit discovery.Although surprisingly Prout was not mentioned, Dumas wrote that several English

(Footnote 81 continued)education under Napoleon III. Dumas became a member of the National Legislative Assembly, asenator, president of the municipal council of Paris, and master of the French mint. His administrativecareer came to its end with the collapse of the Second Empire.82 Dumas, J.B.A., Ann. Chim. Phys. 33, 337 (1826), ibid. 50, 337 (1832).83 Dumas, J.B., Ann. Chim. Phys. 33, 337 (1826).84 Dumas realized that the reaction is H2 + Cl2 → 2HCl and not H + Cl → HCl. In the firstreaction, one volume of hydrogen and one volume of chlorine yield two volumes of HCl. Thesecond reaction implies that one volume of hydrogen plus one volume of chlorine yields only onevolume of hydrogen chloride.85 Dumas, J.B., Leçons sur la Philosophie Chimique, Bechet Jeune, Paris, 1837.86 This is the author’s free translation of Dumas, p. 231.87 Dumas, J.B.A., Traité de Chimie, appliquée aux arts, Bechet Jeune, Paris, 1828.

1.17 Dumas 1828 29

chemists, among whom it should be noted Thomson, admitted that there exists asimple relation between the atomic weight of hydrogen and that of the other ele-ments. Indeed, wrote Dumas, One remarks that the weights agree in a striking form.On the other hand, Dumas admitted that it was difficult to prove that an oxygenatom was composed of 8 hydrogen atoms. Clearly, there was no way chemists coulddemonstrate this in the laboratory. Dumas pointed out that the small deviations frominteger values were of the order of the error in the measurements, and he thus jus-tified rounding the numbers off to integers. In this way, Dumas vacillated from oneextreme view to the other.

At the end of 1859, Dumas88 published a Memoir on the ‘equivalents of theelements’. As might be expected, this memoir produced a great sensation due toDumas’ leading position in chemistry. The illustrious French chemist, taking as basisM. de Marignac’s researches on silver, found that all well known substances whichhe had had the occasion to examine conformed to Prout’s principle, when certainmodifications were applied to this principle. However, two elements were recalci-trant: chlorine and copper. Repeated experiments yielded 35.5 for the atomic weightof chlorine, while the atomic weight of copper was found to lie somewhere between31 and 32. Thus, these numbers definitely did not agree with Prout’s hypothesis.Normally, one example is sufficient to destroy a theory. However, Dumas concluded,in contrast to Berzelius, that the law must be accepted in the less general form, namelyfor chlorine the unit is 1/2 a hydrogen atom and for other elements the unit may be1/4 of a hydrogen atom or even smaller.

1.18 Gaudin 1833 and the Correct But Ignored Explanation

It was Marc Antoine Gaudin (1804–1880) who realized in 183389 that the mysteriousfactors of two and four in the atomic weights had to do with the assumption thatonly a single atom can form a compound with another atom of another element.Consequently, he suggested that the number of atoms within a molecule might varyfrom element to element. In other words, the molecules of gaseous elements mightcontain two atoms (diatomic), while compounds of two or more elements mightcontain only one atom of each gas. It was not at all clear why the smallest particlein a pure hydrogen gas contains two atoms of hydrogen. Berzelius, for example,hypothesized that the atoms in a molecule were held together by electrical forces,whence two atoms of the same element should repel each other rather then attract.However, by then the entire atomic theory was in a mess, and all was confusion.Despite Gaudin being so right, the mood of the chemists was not appropriate forcorrections to a poor theory.

88 Dumas, J.B.A., Ann. Chim. Phys. 55, 129 (1859).89 Gaudin, M.A.A., Ann. Chim. Phys. 52, 113 (1833). See the strange history of Gaudin’s papersin Cole, T.M., Early Atomic Speculations of Marc Antoine Gaudin: Avogadro’s Hypothesis and thePeriodic System, Isis 66, 334 (1975).


Table 1.10 Marignac’s tableof atomic weights 1840–1850in units of the atomic weightof hydrogen, and comparisonwith Stas and Prout

Stas Marignac Prout

Silver 107.943 107.921 108Chlorine 35.46 35.456 35.5Potassium 39.13 39.115 39Sodium 23.05 23Nitrogen 14.04 14.02 14Sulphur 16.037 16Lead (from sulphate) 103.453 103.5Lead (from nitrate) 103.460 103.5

It is interesting to note that Gaudin recapitulated Avogadro’s hypothesis in thispaper, and since the hypothesis was already out of favor with ‘established opinion’,this only added to the neglect of Gaudin’s paper by the ‘establishment’. With thisreception of his ideas, and in particular Dumas’ book in 1837, Gaudin lost interest inthe problem and went to serve as a mathematician at the Paris Bureau of Longitudes.

1.19 Marignac and the Quest for Accurate Numerical Values

In 1842–1843, Jean Charles Galissard de Marignac (1817–1894) of Geneva, whowas a student of Dumas, undertook a series of investigations, focusing in particularon chlorine, for the purpose of submitting Prout’s law to a new and careful examina-tion.90 Marignac was fully aware of the experimental difficulties involved in furtherimproving measurements of atomic weights and consequently was led to the conclu-sion that chlorine did agree with Prout’s theory, but that the unit had to be redefined,and in particular that it should be halved. Moreover, Marignac concluded that futurehigher accuracy would not improve the agreement with Prout’s law (Table 1.10).

1.20 Stas and Regrets for Earlier Thoughts

Jean Servais Stas (1813–1891) followed his teacher Dumas by developing accuratemethods for measuring atomic weights and confirming the law of definite proportionsto extreme accuracy. In 1860, Stas91 commented cynically that:

Prout had so little faith in the exactness of his hypothesis that he published his paper under theveil of anonymity. Whatever may be the opinion one holds about this hypothesis, whateverfate may be reserved for it in the future, it is impossible not to pay homage to the rarepenetration of its author. Right or wrong, it permitted him to divine the specific weight ofhydrogen forty years before it was determined experimentally with a degree of accuracy.

90 Marignac, J.C., Pr. Ch. 26, 461 (1842), Ibid., Compt. Rend. 14, 570 (1842).91 Stas, J.S., Bull. de l’Acad. Roy. de Belge. 10, 208 (1860).

1.20 Stas and Regrets for Earlier Thoughts 31

And Stas continued to disprove Prout by stating that there does not exist a commondivisor for the weights of the elements which unite to form all definite compounds.Indeed, this last statement by Stas is correct even today, while the wrong conclusion,i.e., that Prout was consequently in error, could be drawn only because too little wasknown, and the numbers were not accurate.

Stas’ explanation as to why he returned to this dead-as-a-dodo hypothesis wentas follows:

In England the hypothesis of Dr Prout was almost universally accepted as absolute truth. Thework executed by Professor Thomas Thomson of Glasgow in order to base it on analyticalexperiments greatly contributed to this result. Nevertheless, the same thing did not hold forGermany or France.92 The immense prestige which surrounded the name of Berzelius, andlegitimate confidence inspired by his work on the weights of the atoms were incontestablythe cause of this. Even in England doubts arose: as early as 1833 Professor Turner, on theinvitation of the British Association for the Advancement of Science, undertook a seriesof analyses, from which he drew the conclusion that the hypothesis of Dr Prout was notexact. In 1839, Professor Penny of Glasgow arrived at the same conclusion, although hisresults differed in some points from those obtained by Turner.93 The determination of theatomic weight of carbon made by M. Dumas and myself in 1839–1840 called the attention ofchemists anew to this subject. The atom of carbon deduced from our syntheses of carbonicacid agrees in fact entirely with Prout’s hypothesis. The new syntheses of water whichM. Dumas published in 1843, and which were confirmed by the work of MM. Erdmann andMarchand, led to the same result.

Consequently, Stas declared that:

I dare affirm without fear of being contradicted that any chemist who has pursued researchon the weights of the atoms, if he has varied his methods, if he has determined the weightof the atom of one substance as a function of the atom of two or three different substances,has encountered the same difficulties, the same contradictions. I accordingly experiencedfor long many a painful perplexity.

Similarly, Stas himself encountered a problem (with nitrogen), where the deviationwas 0.02 out of 4, or 1/200, whence he inferred that the error was in the atomicweight of hydrogen, and consequently that all previous fits were fortuitous. He thusconcluded that the basis on which Dr Prout had erected in his law is itself withoutfoundation. Stas admitted that, when he started his research, he believed in Prout’shypothesis, but said that he changed his view when confronted with the facts.

Soon Stas was attacked by his compatriot Marignac.94 While Stas believed thatthe numbers were sufficiently accurate to disprove Prout, Marignac did not think so.As an example, he claimed that Stas measured the atomic weight of silver by meansof two methods, and got two different results, viz., 107.943 and 103.924, althoughthe numbers should have been identical. Future accuracy, claimed Marignac, shouldbe better. So which of Dumas’ students, Marignac or Stas, would turn out to be right?

92 Note how the English Channel divided the world of chemistry, according to Stas.93 Turner, E., Phil. Trans. Roy. Soc. London 123, 523 (1833).94 de Marignac, J.C., Bull. de l’Acad. Roy. de Belgique, 2nd Séries x, no. 8. Reprinted and translatedin its entirety in Alembic Club Reprint no. 20, Prout’s Hypothesis from Bibliothèque Universelle(Archives) 9, 97 (1860).


1.21 Whewell: Philosophy a Bit Too Early

William Whewell (1794–1866) was one of the most important and influentialfigures in nineteenth century British science. An all round scholar, Whewell wroteextensively on a variety of subjects and was one of the founding members and anearly president of the British Association for the Advancement of Science. Leadingscientists turned to Whewell for advice on philosophical and scientific matters.95

In 1857, Whewell96 argued essentially in the same way as Dumas before him,claiming that one cannot infer the existence of certain smallest possible particles fromthe simple fact that a certain chemical combines to form compounds in simple ratios.Whewell claimed that, strictly speaking, these experiments tell us only that, if therewere such particles, they should be smaller than the smallest observable. In chemicalexperiments, at least, there is not the slightest positive evidence for the existence ofsuch atoms. Both assumptions, that the particles are not divisible or alternatively thatthey are divisible, explain the chemical fact equally well, claimed Whewell. Note thatthis argument due to Whewell is exactly the opposite of the one given by Avogadro.This was written just three years before Kirchhoff and Bunsen demonstrated that thesmallest particle of each element, the atom, has a unique spectrum which can be usedfor its identification.

1.22 How to Classify the Elements?

A crucial development for chemists took place in 1857, although it went largelyunnoticed, when Dumas,97 and soon after Strecker (1822–1871),98 established theconnection between atomic weight and chemical properties, and showed that chem-ically similar elements could be grouped into sets satisfying the following relation:

atomic weight = a + n × 8 ,

where n is an integer and a is the atomic weight of the first element in the sequence.However, most crucial was the finding that the atomic weight is the sole parameterthat controls the properties of each set. Consequently, chemists searching for anykind of arrangement based their search on the atomic weight. Neither Dumas norStrecker called it a period, but that is exactly what itwas.

95 On the request of the poet Coleridge in 1833, Whewell invented the term ‘scientist’. Before thistime, the terms in use were ‘natural philosopher’ and ‘man of science’.96 Whewell, W., History of the Inductive Sciences, in two volumes, New York, Appleton Comp.,1857.97 Dumas, J.B., Compt. Rend. 45, 709 (1857), ibid. 46, 951 (1858), ibid. 47, 1026 (1858).98 Strecker, A., Theorien und Experimente zur Bestimmung der Atomgewichte der Elemente,Braunschweif, F. Vieweg, 1859.

1.23 The 1860 Karlsruhe Conference: The Fog Lifts 33

1.23 The 1860 Karlsruhe Conference: The Fog Lifts

In the late 1850s, the situation with atomic weights of elements was in disarray.Two different scales were used. Dalton introduced hydrogen as the unit, and thiswas adopted by Gmelin and many others. Wollaston and Berzelius adopted oxygen,to which the former attributed the weight 10 and the latter the weight 100. Thomson,on the other hand, gave oxygen the weight 1. With such differences, life was stillpossible. But in Germany, carbon had atomic weight 6 and oxygen 8, while in Francethe corresponding values were 3 and 8, as though crossing the national border couldaffect the atomic weight. All this came on top of differences in results due to differentmethods and inaccuracies.

In 1858, a then relatively unknown chemist, Stanislao Cannizzaro (1826–1910)from the university of Genoa, published a pamphlet99 about chemistry teaching,in which he demonstrated how to determine a consistent set of atomic weights. Thepaper was ignored.

In view of the disarray affecting the understanding of atomic weights, many voiceswere raised, calling upon the chemical community to dispel this confusion. The orig-inal idea was due to August Kekulé (1829–1896m).100 He convinced Karl Weltzien(1813–1870) and Charles-Adolphe Wurz (1817–1884), who inherited Dumas’ chairin Paris, of the need to organise a meeting. Support was secured from all the greatnames in chemistry. The invitation letter called all chemists authorized by their workor position to express an opinion in a scientific discussion. But did one have to haveofficial authorization to express one’s view on the problem? The declared purposeof the meeting was to reach a common agreement [. . .] on some of the followingpoints: the definition of important chemical notions, such as [. . .] atom, molecule,and in general terms, the differences that had arisen between the theoretical views ofchemists and the urgency of putting an end to these differences by a common agree-ment, as explained by Wurz.101 Forty-five leading chemists signed the invitation andabout 140 chemists responded and participated in the meeting.102

One of the central discussions in the meeting took place between Kekulé andCannizzaro. The former claimed that one had to distinguish between a molecule andan atom and that there was a difference between a physical and a chemical molecule.

99 Cannizzaro, S., Il Nuovo Cimento 7, 321 (1858). The origin was a letter Cannizzaro wrote to acolleague in Pisa, Sebastiano de Luca, a professor of chemistry. The paper in the journal is essentiallyCannizzaro’s letter. The title was: Sunto di un corso di filosofia chimica fatto nella R. Universitàde Genova, which means: Sketch of a Course in Chemical Philosophy at the Royal University ofGenoa.100 Friedrich August Kekulé von Stradonitz is known for discovering the structure of the moleculeof benzene, C6H6, in 1865, long before the details of the chemical bond were known. Bull. Soc.Chim. Paris 3, 98 (1865).101 Wurz, C-A. Account of the sessions of the International Congress of Chemists in Karlsruhe,3–5 September 1860.102 The disarray went far beyond the question of atoms and molecules. There were problems inthe structure of organic molecules as well as the naming of these molecules. The mid-nineteenthcentury saw a dramatic growth in the discoveries of organic molecules.


Cannizzaro, on the other hand, claimed that the Ampère–Avogadro law should bethe basis of consideration for chemical molecules. In another session, Cannizzaroclaimed that there was no difference between a physical and a chemical molecule.The situation was so bad that Wurtz had to stress the difference between an atom anda molecule in the summary of the conference.103

An important subject for us here is the session presided by Dumas. The originalproposal was to debate the symbols of the elements and reactions, but the discus-sion went differently. The dominant speakers, usually expressing opposing ideas,were Cannizzaro and Kekulé. But the highlight of the conference was Cannizzaro’senlightening speech raising Avogadro’s hypothesis from abeyance.

The Karlsruhe congress was both a failure and a great success. It was a failurebecause no practical decision was taken. As a matter of fact, Kopp (1817–1892)104

and Erdmann (1804–1869)105 argued that scientific problems could not be decidedupon by a popular vote. It was a success because most participants took homeCannizzaro’s pamphlet, which was essentially his two-year-old letter to Luca, andeventually overcame their bias against physical methods, agreeing to its content, andacting accordingly. This was probably Cannizzaro’s greatest contribution to chem-istry.106

1.24 Early Attempts to Classify the Elements

It is difficult to trace the origin of the idea of ‘analogy between elements’, whichwas never defined. In 1812, Davy107 discussed the ‘analogy’ in properties between,for example, silver, palladium, antimony, and tellurium, or potassium, sodium, andbarium, but did not define what was meant by an ‘analogy’.

103 Some idea of the personal quarrels that went on in the congress and why no agreement couldbe achieved can be obtained from Hartley, H., Notes and Records of the Royal Society of London21, 56 (1966).104 Kopp found that the molecular heat capacity of a solid compound is the sum of the atomic heatcapacities of the elements composing it. The elements with atomic heat capacities lower than thoseinferred from the law of Petit and Dulong keep these lower values when they are in compounds.Kopp, H., Proc. Roy. Soc. London 13, 229 (1863).105 Erdmann and Marchand measured atomic weights, in particular those of copper and silverErdmann, O.L. and Marchand, R.F., Jour. f. Prakt. Chem. xxxi, 389 (1844).106 Italy was not a country of chemists like France, Germany, or England at that time. Thus,Cannizzaro, an unknown Italian chemist (before the meeting) revived the theory of another unknownItalian, Avogadro. In August 2004, Vincenzo Salerno wrote in the journal Best of Sicily Magazine:His niche is a small but important one. Palermo-born Stanislao Cannizzaro is a special footnote tonineteenth-century physical science. He was, according to some, one of the scientists responsiblefor bringing chemistry and physics out of the realm of alchemy and into the modern world. The titleof the article is: Stanislao Cannizzaro. A Political Physicist.107 Davy, H., Elements of Chemical Philosophy 1, 273, London: Printed for J. Johnson and Co.,1812. Apparently the second part never appeared. This is the only book on chemistry I have everseen which discusses gravitation as part of chemistry.

1.24 Early Attempts to Classify the Elements 35

Table 1.11 The triads discovered by Döbereiner, 1829

Element Lithium Beryllium Boron Arithmetic meanAtomic weight 7.0 9.0 11.0 9.0Element Lithium Sodium PotassiumAtomic weight 7.0 23.0 39.0 23.0Element Carbon Nitrogen OxygenAtomic weight 12.0 14.0 16.0 14.0Element Calcium Strontium BariumAtomic weight 40.0 87.5 137 88.1Element Chlorine Bromine IodineAtomic weight 35.0 80.0 127.0 80.6

In the year 1829, Johann Wolfgang Döbereiner (1780–1849),108 a German scien-tist, was the first to classify elements into groups based on John Dalton’s assertions.He grouped the elements with similar chemical properties into clusters of threecalled ‘triads’. The distinctive feature of a triad was the atomic weight of the middleelement. When elements were arranged in order of increasing atomic weight, theatomic weight of the middle element was approximately the arithmetic mean of theother two elements of the triad (see Table 1.11).

The problem with the triads was that a large number of similar elements couldnot be grouped into triads, e.g., iron, manganese, nickel, cobalt, zinc, and copperare similar elements, but could not be organised into triads. On the other hand,some quite dissimilar elements could apparently be grouped into such triads. Inany case, Döbereiner was only able to successfully identify 5 triads, and since hefailed to arrange all the then known elements in this form, his attempt at classifi-cation was not very successful, and consequently not very influential. In retrospect,we realize that lithium, for example, belonged to two triads. Moreover, while Döbere-iner did correctly place lithium, sodium, and potassium (but also incorrectly beryl-lium and boron), he placed carbon, nitrogen, and oxygen in the same triad. Siliconwas discovered by Berzelius in 1824, 5 years before Döbereiner came up with theidea of triads. It is therefore strange that it does not appear in Döbereiner’s table,given that it is so similar to carbon. Further progress with the triad idea is due toGmelin in 1843.109 While manipulating the triads, he managed to arrange the ele-ments, without really noticing, into an increasing order of atomic weight. But forsome reason, Gmelin’s role is hardly recognised.

It appears as if the subject of element classification lost favor with chemists,because it is only 33 years later that we encounter the next attempt. In 1862,the geologist de Chancourtois (1820–1886)110 published a suggested arrangementof the chemical elements. The elements were organised into a quite complicated

108 Döbereiner, J.W., Ann. Phys. 56, 331 (1817), ibid. 57, 435 (1817), ibid. Ann. der Phys. u. Chem.15, 301 (1829).109 Gmelin, L., Hanbuch der Chemie, 4th edn. Heidelberg, Winter, 1843.110 de Chancourtois, B., Compt. Rend. 54, 757, 840, 967 (1862) ibid. 55, 600.


Fig. 1.4 The periodic spiraldue to Chancourtois, 1862

three-dimensional spiral (see Fig. 1.4). De Chancourtois called his idea ‘the telluricspiral’, because the element tellurium came in the middle. The name for this par-ticular arrangement was appropriate, being coined by a geologist, since the elementtellurium is named after the Earth (from the word Tellus in Latin). De Chancourtoisplotted the atomic weights on the surface of a cylinder in such a way that they wouldincrease by 16 for each trip around the circumference of the cylinder. However, someof de Chancourtois correlations and arrangements were accidental, while others werewrong. Moreover, in certain cases he correlated atomic weights with prime numbersin a rather superstitious way. When he encountered a gap in the table, he filled itwith chemical radicals or alloys. Thus about 23 elements were placed correctly inthe table, while the rest, about 26, were all wrongly placed in one way or another.Today de Chancourtois retains to his credit the first usage of the term ‘period’. Thefigure showing the table as arranged by de Chancourtois was so complicated thatchemists did not follow the basic idea and it was ignored, as well as being wrong.

1.25 Newlands Rediscovers the Octave Law 37

1.25 Newlands Rediscovers the Octave Law

The next step in the development of the classification of the elements based onatomic properties was proposed by John Newlands (1837–1898) in a series of paperspublished in 1864–1866.111 This was an extension of the results reported by Dumasin 1857, which presumably were not known to Newlands. Newlands had the advan-tage that several discoveries had since been made: cesium in 1860, rubidium112 andthallium113 in 1861, and indium114 in 1863, thereby filling several ‘gaps’ in the table.

Since Newlands, who had not attended the Karlsruhe congress, arranged theelements according to atomic weight, he discovered a periodicity: the eighth ele-ment was similar to the first, a phenomenon he called the ‘the law of octaves’ (seeTable 1.12). The problems began after calcium, where the periodicity became vague.No less damaging was the fact that there was little room left for unknown elements.In other words, Newlands blindly followed the atomic weight and ignored inconsis-tencies in the chemical properties. And in other places, two elements occupied thesame location. The halogens, F and Cl, are in the same row as Co and Ni (whichoccupy the same location), and so on. The element Gl (the third element, sometimesdenoted by G alone) is known today as beryllium.115 The atomic weight of uranium iscompletely off. Newlands’ greatest blunder was, however, to insist on a fixed lengthfor the period and overlook chemical properties.

Newlands presented the ‘new order’ to the Chemical Society on 1 March 1866, andseveral very interesting comments were made, which reflect the thinking of his col-leagues. For example, John Hall Gladsone (1827–1902) objected on the grounds thatNewlands assumed that no elements remained to be discovered. This comment showshow Newlands adopted the atomic weight as the sole factor determining the locationof the element, while ignoring its chemical properties. It was too much accordingto Dumas’ principle, without any suspicion that something might be wrong. CareyFoster (1835–1919), who was on the publication committee of the Royal Chemi-cal Society, humorously inquired of Mr. Newlands whether he had ever consideredexamining the elements according to the order of their initial letters, because hebelieved that any arrangement would present occasional coincidences in the chem-ical properties. On the other hand, he wondered why Mg was so far away from Cr,or Fe from Ni. Newlands response was that all other schemes he tried had failed, inparticular one based on the specific weight.

111 Newlands, J.A.R., Chemical News 7, 70, (1863); ibid. 10, 59 (1864); ibid. 10, 94 (1864); ibid.On the Law of Octaves 12, 83 (1865); ibid. 13, 113 (1866).112 Bunsen, R.W., Ann. der Chemie und Pharmacie 119, 107 (1861).113 Crookes, W., Chem. News 3, 193 (1861).114 Reich, F. and Richter, H.T., J. fur Praktische Chemie 89, 441 (1863), ibid. 90, 172 (1863).115 Beryllium was discovered in 1789 by Nicolas Louis Vauquelin in the mineral beryl, whence itsname beryllium. For some 160 years, the element was called glucinium (from the Greek glykys,meaning sweet), due to the sweet taste of its salts. But note that the metal and its salts are toxic, soit is not advisable to taste the salts, even though they are sweet.


Table 1.12 Elements arranged in octaves by Newlands, 1864

H 1 F 8 Cl 15 Co and Ni 22 Br 29 Pd 36 I 42 Pt and Ir 50Li 2 Na 9 K 16 Cu 23 Rb 30 Ag 37 Cs 44 Os 51Gl 3 Mg 10 Ca 17 Zn 24 Sr 31 Cd 38 Ba and V 45 Hg 52Bo 4 Al 11 Cr 19 Y 25 Ce and La 33 U 40 Ta 46 Tl 53C 5 Si 12 Ti 18 In 26 Zr 32 Sn 39 W 47 Pb 54N 6 P 13 Mn 20 As 27 Di and Mo 34 Sb 41 Nb 48 Bi 55O 7 S 14 Fe 21 Se 28 Ro and Ru 35 Te 43 Au 49 Th 56

Newlands’ paper was rejected and the distinguished society failed to publishthis seminal paper. The reason given by Odling, then the president of the ChemicalSociety, was that they made a rule not to publish theoretical papers, and this on thequite astonishing grounds that such papers lead to a correspondence of controversialcharacter. So does this mean that chemists do not like to argue? Perhaps we mightsuggest instead that the refusal had more to do with Newlands’ affiliation, with aprivate laboratory rather than a distinguished university.

In 1873, Newlands tried to establish his priority as discoverer of the periodiclaw, but his request to the Chemical Society to publish a note referring to his 1866presentation was flatly rejected by Odling. Newlands, unhappy with the response,published a booklet in 1884,116 in which his results and claims were detailed. Onlyupon his death, in 1898, did the Royal Society of Chemistry concede Newlands’contribution, and a plaque was placed on the wall at his birthplace which states:Newlands, chemist and discoverer of the periodic law for the elements. Better latethen never, but how many people pass by West Square in south London and note thesmall plaque?

1.26 Odling 1864

William Odling (1829–1921) started to investigate the grouping of similar elementsin 1857,117 and was the first to take into consideration the valence concept in additionto the atomic weight.118 In 1864,119 he noticed that the difference in atomic weightbetween the lightest two or three elements of every group is approximately 16. The

116 Newlands, J.A.R., On the Discovery of the Periodic Law and on Relations among the AtomicWeights, London, Spon, 1884.117 Odling, W., Phil. Mag. 13, 423 (1857), ibid. 480.118 Each element has a chemical valence, which is an integer. This number expresses how manyunivalent atoms of each element are needed to form a chemical compound. For example, the valenceof hydrogen is 1 and the valence of oxygen is 2, so two hydrogen atoms are needed for a singleatom of oxygen to form a molecule of water.119 Odling, W., Phil. Mag. 27, 115 (1864); Quarterly J. Sci. 1, 642 (1864).

1.26 Odling 1864 39

Table 1.13 Odling’s suggested table of the elements in 1864. Note that all atomic weights areeither integer or half integer

I II III IV V

Ro 104 Pt 197Pu 104 Ir 197Pd 106.5 Os 199

H 1 Ag 108 Au 196.5Zn 65 Cd 112 Hg 200

L 7 Ti 203G 9 Pb 207B 11 Al 27.5 U 120C 12 Si 28 Sn 118N 14 P 31 As 75 Sb 122 Bi 210O 16 S 32 Se 79.5 Te 129F 19 Cl 35.5 Br 89 I 127Na 23 K 39 Rb 85 Cs 133Mg 24 Ca 40 Sr 87.5 Ba 137

Ti 50 Zr 89.5 Ta 138 Th 235Ce 92

Cr 52.5 Mo 96 V 137Mn 55 W 184Fe 56Co 59Ni 59Ni 59Cu 63.5

next publication120 already included a table which contained (a) missing elementsand (b) unequal lengths of periods. The last point was crucial (Table 1.13).

1.27 Mendeleev 1869 and Meyer 1864–1870

Julius Lothar Meyer (1830–1895),121 who was a student of Bunsen in Heidel-berg, also attempted to arrange the chemical elements. The first publication in 1864included only 28 out of about 80 elements known at that time. Dumas’ and Stecker’sinfluence was obvious, and the latter was actually cited by Meyer. Meyer’s system

120 Odling, A., A Course of Practical Chemistry, 2nd edn., Longmans, Green, London, 1865, ibid.3rd edn., 1868.121 Meyer, L., Die Moderne Theorien der Chemie, Breslau, 1864. English version: Longman Pub.,London, 1888.


evolved in time and the final version was only published in 1870,122 not beforeMendeleev’s publication, and included some improvements.

Soon after the Karlsruhe meeting, which both Mendeleev and Meyer attended,many new atomic arrangements were published, culminating in the works of Meyerand Dmitri Mendeleev (1834–1907m). The influence of Dumas and Stecker is clear inboth works. In the first edition of his book,123 Meyer used atomic weights to arrange28 elements into 6 families that bore similar chemical and physical characteristics,leaving blanks for the as-yet undiscovered elements. His one conceptual advanceover his immediate predecessors was in seeing the valence of the element, namelythe number that represents the combining power of an element (e.g., with atomsof hydrogen), as the link among members of each family of elements, and as thepattern for the order in which the families were organized. In his original schemethe valences of the succeeding families, beginning with the carbon group, were 4, 3,2, 1, 1, and 2. All elements in a given row had the same valence. Meyer identified9 groups bearing similarities with regard to these properties. Note that hydrogen didnot appear in Meyer’s table (see Table 1.14).

The only parameter chemists had at the time was the atomic weight. The atomicweight is a simple, well defined parameter and the idea was to arrange the elementsaccording to increasing atomic weight and then look for periodicities. The problemswere that:

• several elements had not yet been discovered,• the periods appeared to be of variable length.

The valency was also known, but it was definitely not periodic and did not help inthe mission of classification.

Meyer published his classic paper in 1870,124 and described the evolution of hiswork since its beginning in 1864. This paper is particularly famous for its graphicdisplay of the periodicity of atomic volume plotted against atomic weight (seeFig. 1.5). This was a very quantitative expression of the periodicity and the onlyone presented at that time! All other descriptions were entirely qualitative. Whilemany chemists, including Bunsen,125 had their doubts about the periodic law at first,these doubters were gradually converted by the discovery of elements predicted bythe tabular arrangement and the correction of old atomic weights that the table cast in

122 Meyer, L., The Nature of the Chemical Elements as a Function of Their Atomic Weights, JustusLiebig Annalen der Chemie, Suppl. 7, 354 (1870).123 Meyer, L., Die Modernen Theorien der Chemie und ihre Bedeutung für die chemische Statik,Breslau, Verlag von Maruschke and Berebdt (1864).124 Meyer, J.L., Liebig’s Annalen der Chemie, Suppl. 7, 354 (1870).125 Meyer and Mendeleev were Bunsen’s students, with a five year separation. Interestingly,Bunsen did not trust the work of his students. Bunsen, like most members of the German chemicalcommunity, was mainly interested in experimental work and analytical chemistry, as opposed totheoretical work like classification of elements, let alone prediction of the existence of unknownelements. Years later, Meyer commented on the German chemists’ resentment of theoretical papers‘without any new data’. Brauner, who was also a student of Bunsen and an enthusiastic supporterof Mendeleev’s periodic law, argued that the young members of the editorial board of the journalpress for the publication of Mendeleev’s ‘no new data’ paper.

1.27 Mendeleev 1869 and Meyer 1864–1870 41

Tabl

e1.

14T

hepe

riod

icsy

stem

acco

rdin

gto

Lot

har

Mey

er(1

870)

III

III

IVV

VI

VII

VII

IIX

B=

11.0

Al=

27.3

?In

=11

3.4

Tl=

202.

7C

=11

.97

Si=

28Sn

=11

7.8

Pb=

206.

4T

i=48

Zr

=89

.7N

=14

.01

P=

30.9

As

=74

.9Sb

=12

2.1

Bi=

207.

5V

=51

.2N

b=

93.7

Ta=

182.

2O

=15

.96

S=

31.9

8Se

=78

Te=

128?

Cr

=52

.4M

o=

95.6

W=

183.

5F

=19

.1C

l=35

.8B

r=

79.7

5J

=12

6.5

Mn

=54

.8R

u=

103.

5O

s=

198.

6?Fe

=55

.9R

h=

104.

1Ir

=19

6.7

Co

=N

i=58

.6Pd

=10

6.2

Pt=

196.

7L

i=7.

01N

a=

22.9

9K

=39

.04

Rb

=85

.2C

s=

132.

7C

u=

63.3

Ag

=10

7.66

Au

=19

6.2

?Be

=9.

3M

g=

23.9

Ca

=39

.9Sr

=87

.0B

a=

136.

8Z

n=

64.9

Cd

=11

1.6

Hg

=19

9.8


Fig. 1.5 Atomic volume asa function of atomic weight,calculated and plotted byMeyer 1864. This was the firsttime that the periodicity ofthe properties received sucha conspicuous quantitativedemonstration

doubt. Meanwhile, Meyer126 and Mendeleev127 engaged in a long drawn-out prioritydispute.

A glance at Meyer’s table (see Table 1.14) reveals many empty locations. Werethese as-yet undiscovered elements? Meyer did not specify, and refused to commithimself. The table looks more like a Swiss cheese than a complete table with a fewmissing elements. In any case, there were too many ‘holes’ in the table to justifyMeyer’s claim for priority in the discovery of the periodic table. The table essentiallyalready appeared in his book in 1864.

In 1869, Mendeleev published128 a two-page paper which had a profound impacton chemistry and physics. And so wrote Mendeleev:

By ordering the elements according to increasing atomic weight in vertical rows so that thehorizontal rows contain analogous elements, still ordered by increasing atomic weight, oneobtains the following arrangement, from which a few general conclusions may be derived.

Note, however, that Mendeleev deduced the periodic table without any knowledge ofthe existence of electrons. [The electron was discovered by J.J. Thomson129 (1856–1940) in 1897.] It was phenomenology at its best, without explanation or theory.The sole criteria were undefined chemical similarity and atomic weight. The originalMendeleev table is given in Table 1.15. Mendeleev was in the process of writing a

126 Meyer, L., Zur Geschichte des priodischen Atomistik. Ber. Deuts. Chemi. Ges. 13, 259 (1880),ibid. 2043 (1880).127 Mendeleev, D., Zur Geschichte des priodischen Gesetzes. Ber. Deuts. Chemi. Ges. 13, 1796(1880).128 Mendeleev, D.I., J. Russ. Chem. Soc. 1, 35 (1869), ibid. 60; ibid. 3, 25 (1871); Zeit. für Chemie12, 405 (1869).129 Thomson, J.J., Phil. Mag. 44, 293 (1897). The discovery of the electron won him the NobelPrize in 1906.


textbook on chemistry130 when he got the idea about how to arrange the elements.It is puzzling as to why Mendeleev did not rewrite his book in order to make hisbreakthrough discovery the central theme.

Cassebaum and Kauffman131 describe the interesting development of eventsconcerning Mendeleev’s discovery. Odling’s book, in which his results appeared,was translated into Russian in 1867. However, in a footnote to his 1869 paper,132

Mendeleev reported that he was referred by Savchenkov to Odling’s table. Cassebaumand Kauffman show a picture taken during the November 1868 meeting of the RussianChemical Society, in which one can see Mendeleev standing near Savchenkov, andwrote: Yet, Mendeleev emphasized in the footnote in question that he had no previousknowledge of Odling’s table. So why did Mendeleev find it necessary to add his note?On the other hand, Odling had 5 columns, while Mendeleev found that the chemicalproperties require 6 columns. Hence, as a quick look at the two tables reveals, itwould be impossible for the two schemes to relate the elements in the same way.

Mendeleev’s claim was that the elements are arranged according to increasingatomic weight. However, this is not absolutely correct. The two elements nickel andcobalt appear to have the same atomic weight and share the same position. But iftwo elements share a position, there must be another parameter which distinguishesbetween them. The question as to what this extra parameter might be was not asked.Furthermore, rhodium (Rh) was wrongly classified. It belongs between ruthenium(Ru) and palladium (Pd). The element in-between, which years later would be calledtechnetium, does not exist in nature. And the order of the last column is a bit confused.

The element J (atomic weight 127) is iodine. As Mendeleev published his paperin German, he used the German letter J for this element. Iodine is placed correctlyafter tellurium (i.e., with the halogens), despite having a lower atomic weight thantellurium. The idea of isotopes did not exist, and had to wait about five decades forAston.

We note that there is no helium, and indeed no other noble gas in Mendeleev’stable. Helium was discovered by Joseph Lockyer (1836–1920m),133 in 1868, whenhe carried out spectroscopic observations of the Sun during an eclipse and discovereda yellow line never seen before in the laboratory. An independent discovery was madethe same year by Pierre Janssen (1824–1907m).134 Lockyer suggested that this mightbe a new element, unknown on Earth, and this explains the name he gave to it. It wasthe first element to be discovered by spectroscopy.

130 Mendeleev, D., The Principles of Chemistry. The book was written 1868–1870 and translatedinto English in 1891.131 Cassebaum, H. and Kauffman, G.B., Isis 62, 314 (1971).132 Mendeleev, D.I., J. Russian Chemical Soc. 1C, 60 (1869).133 Lockyer is among the very few astronomers who turned stellar spectroscopy into a science. Itled in the end to our understanding the composition of the stars.134 Janssen, M., AReg 7, 107 (1869). The names Janssen and Lockyer appear together becausethey independently devised a method to see the corona in broad daylight without the need for aneclipse. Janssen described the spectra, but the courageous hypothesis about a new element is due toLockyer. Janssen was too enthusiastic about the new instrument to be bothered by an unidentifiednew element.


Table 1.15 The original periodic table due to Mendeleev (1869). Numbers are atomic weights asknown to Mendeleev

I II III IV V VI

Ti = 50 Zr = 90 ? = 180V = 51 Nb = 94 Ta = 182Cr = 52 Mo = 96 W = 186Mn = 55 Rh = 104.4 Pt = 197.4Fe = 56 Ru = 104.1 Ir = 198Ni = Co = 59 Pd = 106.6 Os = 199

H = 1 Cu = 63.4 Ag = 108 Hg = 200Be = 9.4 Mg = 24 Zn = 65.2 Cd = 112B = 11 Al = 27.4 ? = 68 Ur = 116 Au = 197?C = 12 Si = 28 ? = 70 Sn = 118N = 14 P = 31 As = 75 Sb = 122 Bi = 210?O = 16 S = 32 Se = 79.4 Te = 128?F = 19 Cl = 35.5 Br = 80 J = 127

Li = 7 Na = 23 K = 39 Rb = 85.4 Cs = 133 Tl = 204Ca = 40 Sr = 87.6 Ba = 137 Pb = 207? = 45 Ce = 92?Er = 56 La = 94Yt = 60 Di = 95?In = 75.6 Th = 118?

But the idea that the stars might contain elements that do not exist on Earth wastoo revolutionary, and definitely too outlandish to allow them to be included in tablesmade by chemists. Lockyer himself had to wait until 1895, at which point WilliamRamsay (1852–1916m), a Scottish chemist who discovered almost all the noblegases,135 identified helium as the gas released from the mineral cleveite. Radon(the radioactive daughter of radium) was discovered in 1900 by Rutherford andnamed ‘radioactive emanation’ by the Curies. The gas is radioactive and decays intopolonium. The element was isolated in 1908 by Ramsay and Gray, who called it niton.Since 1923, it has been called radon. The chain of events was such that none of thenoble gases were known before Mendeleev’s discovery, but they were all discoveredover rather a short period of time soon after the introduction of the periodic table.Mendeleev succeeded on several counts where Newlands failed:

• He allowed for periods of different lengths for the lanthanides, elements betweenwhich the chemical differences are smaller than usual.

• He ingeniously ignored the small details in order to see the overall picture.• Above all, he had the audacity to predict the existence of unknown elements.

135 Argon in 1894, neon in 1898, krypton in 1898, and xenon in 1898. All were found in liquid air.Ramsay, W., Nature 56, 378 (1897).


This audacity has to be appreciated against a background in which the general ethosamong chemists was not to publish papers ‘without new data’.136 The successfulattempt to arrange the elements, or classify them, or find a general pattern, cameagainst a background of failed attempts to classify the elements according to theirphysical properties. Clearly, he was helped by the fact that none of the noble gaseswas known at the time he published the periodic table, so he escaped further confusionon their count.

Not all scientists hailed Mendeleev’s discovery with the same enthusiasm.Friedrich Beilstein (1838–1906),137 who succeeded Mendeleev at the Technolog-ical Institute in St. Petersburg and may have been driven by personal conflicts withMendeleev, claimed that:

Mendeleev [. . .] has prophesied the existence of all sorts of new elements and believes thathe needs only to conceive of them in order to have them immediately in the bag [. . .]. He isin general an odd chap.

Mendeleev may have been an ‘odd chap’, but imaginative and courageous, unlikesome of his critics.

Mendeleev drew several interesting conclusions:

• The elements, if arranged according to increasing atomic weights, exhibit a peri-odicity of properties.

• Chemically analogous elements have either similar atomic weights (for example,Pt, Ir, Os), or weights which increase by equal amounts, as found already by manybefore him.

• The arrangement according to atomic weight corresponds to the valence of theelements and to a certain extent to the difference in chemical properties, for exam-ple Li, Be, B, C, N, O, F. Here Mendeleev realized that the chemical valence wasa consequence of the trends or location in the table, something like a prediction,and not part of the criterion for classification.

• The most abundant elements in nature have small atomic weights.• One can predict the future discovery of many new elements, for example, analogous

to Si and Al, with atomic weights of 65–75.

So Mendeleev noted one of the important characteristics of element abundance innature, namely, that the abundance decreases with increasing atomic weight. Thiswas the first observation that the atomic weight might somehow be associated withthe abundance of the element or the way it is synthesized. No one suspected in thosedays that the elements might not be primordial, or that they might have been naturallysynthesized. Clearly, when Mendeleev wrote ‘abundances’, he meant abundances in

136 Winkler, who discovered germanium in 1886, the element predicted by Mendeleev aseka-silicon, called Mendeleev’s three predictions ‘bold speculation’ in The Discovery of New Ele-ments During the Last Twenty Five Years, in 1897 [34, p. 136].137 Beilstein is known for compiling the first Handbuch der organischen Chemie 2, 1880–1883, orHandbook of Organic Chemistry, which contained the chemical properties of about 15,000 organiccompounds.


the crust of the Earth, as opposed to cosmic abundance. In any case, this particularconclusion about the abundances went unnoticed.

For Mendeleev138 as a chemist, the ‘chemical element’ was a well defined chemi-cal entity, characterized by its chemical reactions, with no need for a definition. Thediscovery of argon in 1894,139 the first noble gas to be identified, caused havoc asits discovery was totally unexpected, and there was no room for it in Mendeleev’stable. The new gas was found to be monatomic, unlike all the known gases, and tohave an atomic weight of 39.8. Consequently, it did not fit at all into the periodictable. The shock was so great that several chemists suggested abandoning the ideaof a periodic table. Some suggested that the newly discovered ‘element’ was notreally an element, but a more complex molecule comprising several atoms. EvenMendeleev considered the possibility that ‘argon’ might be a compound made upof three nitrogen atoms.140 Adding to the mystery and confusion among chemistswas the fact that it did not react chemically—it was found to be inert, somethingwe call ‘noble’ in today’s parlance, since it refused to react with other elements,as though it had a vanishing valence. The discovery of the rest of the noble gasesrather soon afterwards partially resolved the problem, because then a special group,the inert gases, could be introduced into the periodic table. So the confusion turnedinto a victory of the idea of the periodic table, to the point where Mendeleevsuggested

138 In 1893, Mendeleev was appointed Director of the Bureau of Weights and Measures. In thiscapacity, he was directed to formulate new state standards for the production of vodka. The VodkaMuseum in Moscow claims that, in 1894, Mendeleev determined the new standards for vodka as38% proof. Distilled spirits were taxed according to their alcoholic strength, and consequentlythe percentage was rounded upwards, to 40%, for simplified taxation calculations. See http://www.russianfoods.com/cuisine/article00016/default.asp. Pravda has a slightly different version(see Pravda, 31 October 2009):

In 1860–1870, private production of vodka in Russia became very popular. It was very diffi-cult for the government to control the quality of vodka and fresh raw material. Soon Russiaintroduced the state monopoly for vodka production. Chemists got involved in the develop-ment of the production process to enable product standardization. The brand ‘MoskovskayaOsobaya’ is directly connected to the name of Dmitry Mendeleev, the inventor of the peri-odic table of elements. It took the scientist 18 months to find a perfect ratio for volume ofspirit to water. Mendeleev published his findings in his doctoral thesis ‘Essay on integrationof spirit with water’. This is why Russian vodka is always 40% Alc. by Vol. Mendeleev’sconclusions were appreciated and utilized in alcohol testing and vodka production. His workbecame the basis for the state comparison standard for the original Russian vodka establishedin 1894–1896.

139 The discovery of argon is unique as it collected two Nobel prizes in the same year, 1904. Rayleigh(1842–1919) was awarded the Nobel prize in physics for his investigations of the densities of themost important gases and for his discovery of argon in connection with these studies, while Ramsay(1852–1916) was awarded the Nobel prize in chemistry in recognition of his services in the discoveryof the inert gaseous elements in air, and his determination of their place in the periodic system.140 Mendeleev’s view was reported in Nature 51, 543 (1895) under the title Professor Mendeleevon Argon, and it is a report of what Mendeleev said in the meeting of the Russian chemical Societyon 14 March 1895. The idea of a new set of elements constituting a new column in the periodictable appeared to Mendeleev too absurd.

http://www.russianfoods.com/cuisine/article00016/default.asp

http://www.russianfoods.com/cuisine/article00016/default.asp


in 1903 that the ether,141 the elusive imaginary fluid that physicists invented to helpthem comprehend and ‘explain’ the propagation of light, should be included in theperiodic table with atomic weight zero. But two years later Einstein put paid to theether idea.

1.28 Loschmidt and the Value of the Avogadro Number

So far, the actual value of Avogadro’s number was not known. In 1865, Loschmidt(1821–1895)142 was interested in estimating the size of air molecules. It was duringthis work that he succeeded in deriving the first estimate for the size of a molecule bycomparing the volume occupied by N molecules in the air, where they move freely,with the volume they have when the gas condenses to form a solid and the moleculestouch each other.

The formula Loschmidt got was d = 8Cf l, where l is the mean free path of themolecules in the gas, Cf is the condensation coefficient as defined by Loschmidt(ratio of gaseous to solid volumes), and d is the diameter of the molecule. At thattime liquefaction of air had not yet been achieved, so his gases were water, CO2 andNO, NO2 and NH3.

Loschmidt applied Maxwell’s143 theory to calculate the mean free path of airfrom the value of the viscosity, and found that the mean free path of a moleculeunder standard conditions is 6.2×10−6 cm. The condensation coefficient for air wastaken from the fact that air is 770 times lighter than water. A correction factor of 1.5was assumed by Loschmidt, due to changes in temperature, etc. Consequently, thecondensation coefficient of water is 1/(770 × 1.5). Hence, substituting the numbersin the formula yields d = 9.69×10−8 cm. Once Loschmidt had the size of a moleculeand the mean free path (from Maxwell), he could calculate the number of moleculesin a given volume of the air. Loschmidt’s estimate for the Avogadro number, thenumber of molecules in one gram mol,144 was 4 × 1023.

141 Mendeleev, D., Popytka khimicheskogo ponimaniia mirovogo efira (in Russian). An Englishtranslation appeared as Mendeleff, D. (1904). G. Kamensky (translator): An Attempt Towards aChemical Conception of the Ether, Longman, Green and Co., New York.142 Loschmidt, J., Proc. Acad. Sci. Vienna 52, 395 (1865).143 Maxwell, J.C., Phil. Mag. 19, 28 (1860).144 A gram mol is the molecular weight expressed in grams. In the case of oxygen, for example,it is 16 × 2 = 32 g.


1.29 Meyer 1888: A Historical Perspective

Historians of chemistry toward the end of the nineteenth century, such as Meyer(1847–1916),145 were confident that Prout was utterly wrong and rejected hishypothesis, mainly due to the influence of Berzelius. Here is a typical passage froma history book regarding the advancement of Prout’s hypothesis:

This was one of those factors which materially depreciated the atomic doctrine in the eyes ofmany eminent investigators. On account of its influence upon the further development of theatomic theory, this hypothesis must be discussed here, although it has happened but seldomthat an idea from which important theoretical conceptions sprang originated in so faulty amanner as it did.

In short, the idea was wrong and its consequences should be ignored. An incorrectidea had had too much influence.

Meyer also pointed to wrong chemistry textbooks, for example the one by Gmelin,who:

[. . .] gave the mixture weights as far as possible in whole numbers, which he was assuredlynot justified in doing after Berzelius’ classical researches. Later still in 1840, Dumas andStas [. . .] and Erdmann and Marchand [. . .] and Marignac. The predilection shown by manychemists for this conception, which led to such far-reaching deductions, helped to depreciatethe whole atomic doctrine in the minds of thoughtful investigators.

Gmelin, the author of the most complete handbook of chemistry up to his time,146

and the most influential as it went through many editions, adopted Wollaston’s ideas,which were not so bad. Worse was that fact that he confused compounds and mixtures.

1.30 Certain Elements Are Not Forever

During the last decade of the nineteenth century, the radioactive elements were dis-covered, causing further confusion in chemistry, particularly with regard to the peri-odic table. Could there be such a thing as an unstable element? What could that mean?What were the characteristics of an element? What were its chemical properties, andwhat about the spectra?147 The clarification of these and many other questions cameas a bonus to the discovery of radioactivity.

Since there were now known to be unstable nuclei, the International Union ofPure and Applied Chemistry in conjunction with the International Union of Pure

145 von Meyer, E., A History of Chemistry from Earliest Times to the Present Day, translated fromGerman by McGowan, MacMillan and Co., London, 1906. The original book was published inLeipzig in 1888.146 Gmelin, L., Handbuch der Theoretischen Chemie, Frankfurt am Main, bei Franz Varrwntrapp,1827.147 It became clear very early on that the light emitted by each element was characteristic of thatelement, rather like a ‘finger print’. Thus, by heating the sample in question and carrying outspectroscopic analysis of the light it emitted, it was easy to identify the content of the sample.

1.30 Certain Elements Are Not Forever 49

and Applied Physics148 established criteria that must be satisfied for the discoveryof a new chemical element to be recognized. The first condition was that the nuclideshould exist for at least 10−14 s. Thus, unstable nuclei with shorter lifetimes were notdefined as ‘chemical elements’. The reason for choosing this particular lifetime wasthat this is the timescale for electrons to arrange themselves in the various electronicshells.

1.31 Philosophy of a Discoverer When No TheoryIs Yet Available

Twenty years after the historical paper about the periodic table, on Tuesday, 4 June1889, Mendeleev was invited to deliver the Faraday lecture before the fellows of theChemical Society in the theatre of the Royal Institution,149 and allowed himself towander into philosophy and the deeper meaning of his discoveries.150 Ironically, thelecture was delivered not too long before radioactivity, the nucleus, and quantumtheory were discovered, whence the picture changed completely, along with ourunderstanding and the philosophy.

148 Wapstra, A.H., Pure and Appl. Chem. 63, 879 (1991). In 1991, a committee decided on criteriafor the recognition of new chemical elements.149 Mendeleev, D., J. Chem. Soc. 55, 634 (1889).150 Here are some selected quotes:

The most important point to notice is that periodic functions, used for the purpose of express-ing changes which are dependent on variations of time and space, have been long known.[. . .] This constituted such a novelty in the study of the phenomena of nature that, althoughit did not lift the veil which conceals the true conception of mass, it nevertheless indicatedthat the explanation of that conception must be searched for in the masses of the atoms [. . .].If we mark on an axis of abscissae a series of lengths proportional to angles, and traceordinates which are proportional to sines or other trigonometrical functions, we get periodiccurves of a harmonic character. So it might seem, at first sight, that with the increase ofatomic weights the function of the properties of the elements should also vary in the sameharmonious way. But in this case there is no such continuous change as in the curves justreferred to, because the periods do not contain the infinite number of points constituting acurve, but a finite number only of such points [. . .].While connecting by new bonds the theory of the chemical elements with Dalton’s theoryof multiple proportions, or atomic structure of bodies, the periodic law opened for naturalphilosophy a new and wide field for speculation. Kant said that there are in the world


It is interesting to note that Mendeleev lived for almost 7 years after the first Nobelprize was awarded, but he never received it himself, owing to a personal vendetta.151

1.32 Is the Atomic Weight Variable?

Moreover, the confusion was so great that Paul Schützenberger (1829–1897)152

along with Alexander Butlerow (1828–1886)153 and Vogel suggested that the atomicweight might be variable! Even as late as 1887, Theodore Richards (1868–1928) from

(Footnote 150 continued)‘two things which never cease to call for the admiration and reverence of man: the morallaw within ourselves, and the stellar sky above us’. But when we turn our thoughts towardsthe nature of the elements and the periodic law, we must add a third subject, namely, ‘thenature of the elementary individuals which we discover everywhere around us’. Withoutthem the stellar sky itself is inconceivable; and in the atoms we see at once their peculiarindividualities, the infinite multiplicity of the individuals, and the submission of their seemingfreedom to the general harmony of Nature.

From the foregoing, as well as from the failures of so many attempts at finding in experimentand speculation a proof of the compound character of the elements and of the existence ofprimordial matter, it is evident, in my opinion, that this theory must be classed amongst mereutopias. But utopias can only be combatted by freedom of opinion, by experiment, and bynew utopias. In the republic of scientific theories freedom of opinions is guaranteed [. . .].

Unfortunately, this is not always so.151 Mendeleev’s discovery, and his courageous predictions which were soon vindicated, were sem-inal. But traditional dirty politics was also quick off the mark and mixed itself in liberally with thescience. In 1906, Mendeleev was elected by the Nobel prize committee to win the award, but theRoyal Swedish Academy of Sciences interfered and the prize went to the Frenchman Henri Moissan(1852–1907) in recognition of the great services rendered by him in his investigation and isolationof the element fluorine, and for the adoption in the service of science of the electric furnace calledafter him.

The intervention was prompted by the Swedish chemist Svante Arrhenius (1859–1927m), whowon the prize in 1903 for his theory of electrolytic dissociation. Mendeleev had been an outspokencritic of Arrhenius (correct!) theory, and the unforgiving Arrhenius played it ugly, seizing theopportunity to take revenge. Arrhenius’ disguised argument was that Mendeleev had made hisdiscovery too many years earlier. This illogical argument, which at best implies the failure of thecommittee to recognize Mendeleev’s feat sooner, was nevertheless accepted by the prize committee.The attempt to nominate Mendeleev a year later was thwarted once more by Arrhenius. Animositybetween chemists apparently has an infinite decay time. For more, see Friedman, R.M., The Politicsof Excellence: Behind the Nobel Prize in Science, Times Books, New York (2001). Meyer andMendeleev, who argued over priority, shared the Davy Medal in 1882.152 Schützenberger, P., Chem. News 46, 50 (1882). See also Schützenberger, in a discussion of thevariability of the law of definite proportions before the Chemical Society of Paris in 1883, as quotedin the Proc. Am. Acad. Arts Sci. May, 1888.153 Butlerow, A., Ber. 16, 1559 (1882), ibid. The Inconsistency of the Atomic Weights, Am. Chem.J. 5, 137 (1883).

1.32 Is the Atomic Weight Variable? 51

Harvard154 found it necessary to investigate whether the atomic weight of coppermight depend on its origin. However, he reached a negative conclusion.

In 1906, about a hundred years after Lavoisier’s original study, Hans HeinrichLandolt (1831–1910)155 felt the need to reexamine the law of mass conservation.A special vessel was prepared so that two substances could be accurately weighed,and then a chemical reaction allowed to take place. A large number of experimentswere carried out and the relative differences were less than 10−7, which was consid-ered to be the error in the experiment.156

The fact that the atomic weight of each element does not vary was essentiallyproven by Stas when he measured the atomic weight of silver in different compounds.Stas found 107.921–107.943 for the atomic weight of silver, and the differencewas attributed to the error in the measurement. In 1911, Baxter and Thorvaldson157

compared the atomic weight of meteoritic iron with that of iron of terrestrial originand found them to be identical.

Crookes, Richards’ boss in Harvard, suggested158 that one might assume thepresence of a few of what he called ‘worn atoms’ in the countless numbers of otheratoms, which must come under consideration in any atomic weight determination.This meant the existence of atoms of the same element that had ‘lost some mass’.

Eventually the issue was settled with the discovery of isotopes. The slightlydifferent isotopic composition of various elements found in different natural oreswith different physical and chemical history (like diffusion) gave rise to minutedifferences in the chemical atomic weights.

At the beginning of the twentieth century, Richards159 taking fantastic precautions,produced atomic weight values that may well represent the ultimate possible accuracyusing purely chemical methods.

If Berzelius’s work had left any questions concerning the exact value of the atomicweights, that of Stas and Richards did not. The non-integer values of the atomicweights simply had to be accepted, and Prout’s hypothesis seemed doomed. Yet,even as Richards was producing his remarkably precise results, the whole meaningof atomic weight suddenly had to be reevaluated, and Prout’s hypothesis rose fromits ashes.

154 Richards, T.W., Proc. Am. Acad. Arts and Sci. XXIII, 177 (1887).155 Landolt, H.H., Sitzunsb. d. K. pr. Akad. Wiss. 16, 354 (1908).156 We know today that the chemical binding energy is smaller than 10−8mc2, whence Landolt’scareful experiment was not that accurate, although in 1906, a year after the theory of special relativity,this could have been figured out.157 Baxter, G.P. and Thorvaldson, T., J. Am. Chem. Soc. 33, 337 (1911), Baxter, G.P. and Parsons,L.W., J. Am. Chem. Soc. 43, 507 (1921).158 Crooke, J.P., Memoirs Am. Acad. Arts Sci. 5, 23 (1854), ibid. Nature 34, 423 (1886).159 Theodore William Richards won the Nobel prize in chemistry in 1914, in recognition of hisexact determinations of the atomic weights of a large number of the chemical elements. Generationsof chemists had improved the measurements and, at long last, the one who was most accurate andmade measurements for a sufficiently long time was finally Nobelized.


1.33 Moseley: At Long Last, an Accurate Table

The periodic table remained in the above form until 1913, when Henry Moseley(1887–1915m),160 a student of Rutherford, investigated161 the X-ray spectra of el-ements (see Fig. 1.6). Until that time, only visible light spectra had been used toidentify chemical elements. The spectrum in the visible range was obtained by heat-ing the sample and analyzing the visible light emitted by the element. Moseleyextended the technique to the newly discovered X rays. As it was not possible to heatthe elements to such high temperatures that the elements would emit X rays, othertechniques had to be used, namely, accelerating electrons in cathode-ray tubes andletting the electrons bombard the element under examination. A description of thesetechniques would carry us outside the scope of this book.

Until Moseley’s day, only the atomic weights were known, and the notion ofatomic numbers did not exist. For this reason, Mendeleev and all his predecessorscould only use the atomic weight to classify the elements, a fact that caused problemsfrom time to time, as discussed above. What Moseley did was to arrange the elementsaccording to their X-ray properties. Every element gave two main spectral lines, witha factor of five difference in intensity and about 10% difference in frequency.162

Moseley soon discovered that the frequency of the line was given by

v(X)

R= 3

4(Z − 1)2 ,

where Z is the location of the element in the table and R is the constant Rydbergnumber, obtained from attempts to find a phenomenological formula for spectrallines in the visible range (see Sect. 2.34). For this reason Moseley plotted the Z ofthe element as a function of the square root of the frequency. The meanings to beattributed to the formula and the coefficients were left to various guesses. No suchnumber as Z was measured. The only relevant parameter to describe the element wasits abstract location in a table of X-ray emissions.

However, Moseley quickly realized that he had generated a periodic arrangementof the elements in which the chemical properties of the element were related tothe position in the table. Moseley163 therefore defined the position in his table asa new quantity and called it the ‘atomic number’ of the element.164 So the atomicnumber was an integer by definition, in contrast to the atomic weight, which was not.It soon became clear that the atomic number as defined by Moseley was really the

160 One of the tragedies of science happened when the brilliant scientist Moseley was killed on thebattle field of Gallipoli, Turkey, in 1915.161 Moseley, H., Phil. Mag. 26, 1024 (1913), ibid. 27, 703 (1914).162 Moseley looked for the highest X-ray frequency emitted by the element.163 Moseley, H.G.J., Phil. Mag. XX, 1024 (1913).164 In some textbooks you may find it claimed that, when Moseley arranged the elements accordingto the atomic number, he got a nice periodicity. The truth is, however, the other way round. Moseleyinvented the atomic number.

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1.33 Moseley: At Long Last, an Accurate Table 53

Fig. 1.6 Moseley’s original1913 figure. Note that thehorizontal axis shows thesquare root of the frequency,while the vertical axis shows‘the location in the table’.Marked are Z = 43 and 61,which do not exist in nature,and Z = 75, which wasdiscovered by Noddack in1925. Straight lines indicatethe perfect relation

number of electrons in the atom, as well as the position of the element in the periodictable. Moreover, and most importantly, it was the atomic number that determined thechemical properties of the element, and not the atomic weight.

In retrospect, we can understand the difficulties faced by chemists in the era prior tothe discovery of electrons, neutrons, and so on. They had only the non-integer atomicweight at their disposal. In general, the atomic weight increases faster then the atomicnumber, so Mendeleev did not need to encounter problems arranging the elementsaccording to their atomic weights. But alas, this is not always the case, and the mostabundant isotope, which affects the atomic weight, is dictated by periodicities in thenucleus (see later). In any case, Moseley’s new definition provided a unique integernumber without reference to previous data.

Moseley left spaces for elements he did not know about, whenever the data didnot fit the straight line, as he explained:

The order chosen for the elements is the order of the atomic weights, except in the cases ofA, Co, and Te, where this clashes with the order of the chemical properties. Vacant lines havebeen left for an element between Mo and Ru, an element between Nd and Sa, and an elementbetween W and Os, none of which are yet known, while Tm, which Welscach has separatedinto two constituents, is given two lines. [. . .] This is equivalent to assigning to successive


elements a series of successive characteristic integers. On this principle the integer N 165 forAl, the thirteenth element, has been taken to be 13. [. . .] This procedure is justified by thefact that it introduces perfect regularity into the X-ray spectra.

Moseley did not know that the elements with Z = 43 and 61 do not exist in nature.The location Z = 75 was also empty, because the element rhenium was discoveredonly in 1925.

At that point in time, the periodic table was complete (save for one element withnumber Z = 75, which changed nothing as far as the table was concerned),166

but there were still no explanations for this table. Why should the properties of theelements vary with the atomic number? Why is there a periodicity? Why does thetable come to an end? Why do the lanthanides have similar chemical properties,despite the fact that they have different atomic numbers? The first partial explanationof the periodic table was given in 1921 by Niels Bohr (1885–1962m, Nobel laureate1922), who explained167 the arrangement of the electrons in the quantum levels ofthe atom. He was also able to explain why the noble gases do not react chemically.

Even beautiful, clear, and clean results like the ones obtained by Moseley are notautomatically accepted. Moseley was criticized by the mathematician Lindemann(1852–1939),168 who denied Moseley’s statement that his results strongly supportedBohr’s view. As a matter of fact, Lindemann argued that Mosley’s results yield noinformation about the structure of the atom beyond confirming the views of Rutherfordand van den Broek.169 However, Moseley and Bohr pointed out Lindemann’s error.Lindeman assumed an arbitrary unit of length in the problem of the electric charge.170

On the other hand, Moseley stated that he could not obtain any agreement with theprediction of Nicholson,171 while the agreement with Bohr’s theory was perfect (seeSect. 2.35).

165 Moseley used N to denote the location in the table. Today we use Z to denote the number ofelementary charges in the nucleus, and Z ≡ N .166 The element nipponium was discovered in 1908 by Ogawa. It later became clear that nipponiumis actually rhenium. See Yoshihara, H.K., Proc. Jpn. Acad. Ser. B, Phys. Biol. Sci. 84, 232 (2008).167 Bohr, N., Nature 107, 104 (24 March 1921).168 Lindemann, F.A., Nature 92, 631 (5 February 1914). Lindemann was the one who provedthat you cannot ‘square the circle’ by a ruler and compass construction, since he proved that π

is a transcendental number. This great proof did not prevent him from publishing several incor-rect proofs of Fermat’s last theorem See Bell, E.T., Men of Mathematics, Simon and Schuster,New York 1986.169 Moseley, H., Nature 92, 554 (15 January 1914). Moseley and Bohr replied to Lindemann just aweek later. Bohr’s letter preceded Moseley’s. Lindemann was wrong.170 It was strange to uncover such an error in the article by the scientist who was the first to prove thatπ is transcendental. Lindemann, who was essentially a mathematician, also worked on the theory ofthe electron, and had engaged in controversy over this with Arnold Sommerfeld (1868–1951), oneof his PhD students. Sommerfeld was known as the Prince of German Physics. He was nominated arecord 81 times for the Nobel Prize in Physics, and served as PhD supervisor for more Nobel prizewinners in physics than any other supervisor before or since. However, he never actually got theaward.171 See Shaviv, G., The Life of Stars, Magnes and Springer, 2009.

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1.34 The Theory Behind Moseley’s Discovery 55

1.34 The Theory Behind Moseley’s Discovery

When Moseley looked for a theory to explain his X-ray results, the only availabletheory with any degree of success was Bohr’s. However, the theory was good foratoms with one electron only, i.e., the so-called hydrogen-like atoms. There was asyet no successful theory for atoms with many electrons.

Moseley found that the frequency of the X ray could be described by

v = A(N − b)2 ,

where N is an integer and172 A, which depends on the spectral lines, known as Kα

and Lα lines, is given by

A(Kα) =(

1

12 − 1

22

)v0 , with b = 1 ,

and

A(Lα) =(

1

22 − 1

32

)v0 , with b = 7.4 ,

where v0 and b are constants. The problem was to know how the constant v0 variedfrom one element to the other. The particular form of the formula, with squares inthe denominator, is a consequence of the Rydberg formula (see Sect. 2.34).

1.35 The Last Element to Be Discovered

The last chemical element to be discovered was rhenium, named after the Rhineriver. Rhenium (Re) was discovered by two chemists, Ida (Tacke) Noddack (1896–1979) and Walter Tacke (1893–1960) in 1925. Rhenium, which is the eighty-firstelement to have stable isotopes, was detected in platinum ores. The atomic numberis 75 and the atomic weights of the stable isotopes are 185 and 187. The specificdensity is very high, about 21 g/cm3 at room temperature (only platinum, iridium,and osmium are denser), and at 3 453 K it has the third highest melting point aftertungsten and carbon. With the discovery of Re, the periodic table was complete savefor two unstable elements.

1.36 Aston and the Discovery of Isotopes

As pointed out above, the atomic number is monotonic in the periodic table(by definition), while the atomic weight is not. The solution to this mystery came

172 Moseley, H.G.J., Phil. Mag., Ser. 6, 27, 703 (1914).

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in 1919 when Francis Aston (1877–1945)173 managed to significantly improve hismass spectrometer and published his extensive research on the masses of the chem-ical elements. Aston examined a series of chemical elements and found that theywere all composed of a mix of isotopes, and that each isotope had an integer atomicweight. On the other hand, Aston found that hydrogen has an atomic weight of 1.008(relative to oxygen 16), in agreement with findings by chemical methods. For He,Aston found an atomic weight of 4.007.

Aston reached the conclusion that, apart from the two lightest elements, hydro-gen and helium, all elements have an integer atomic weight, a result he called thewhole-number rule. It became clear that the non-integer atomic weights found bythe chemists were fortuitous and arose from mixtures of isotopes. In particular, thehistorical problem with the non-integer atomic weight of chlorine was solved, aschlorine was found to have two isotopes (with atomic weights of 35 and 37). So the‘evidence’ raised by Berzelius to destroy Prout’s hypothesis finally turned out to bewrong. The implications for atomic structure were enormous. In Aston’s words:

An elementary atom with mass m may be changed to one with mass m + 1 by adding apositive particle and an electron. If both enter the nucleus, an isotope results.

Aston’s major discovery provided experimental evidence for accepting the assump-tion that all atoms were built out of the same standard building blocks.

But Aston faced a problem. The theory of relativity was already known as of1905, although many of its consequences were not yet confirmed experimentally,and many physicists were slow, or even reluctant, to adopt it. So Aston knew aboutE = mc2 (although he wrote that this formula derived from the electromagnetictheory,174 rather than from relativity), which meant that the weights could not beadditive. When two atoms fuse and there is a binding energy, the mass of the newnucleus should be less than the sum of the masses of the individual atoms, but, heargued, it only becomes so when the charges are relatively distant from each other.According to Aston, this appeared to be so in light nuclei. In the case of the heavieratoms, Aston argued that the charges were very close and that the law E = mc2 isnot effective.

But if the weights were indeed an exact product of the same building unit, therewas no room for the formula E = mc2! By pure chance, Aston’s instrument atthat time was not sufficiently advanced to see the effect of E = mc2 on the atomicweight of nuclei, and hence he claimed incorrectly that the formula would not applyto nuclei. It is not clear from his paper why it should not apply. Apparently, Astoncould not imagine that the nuclear binding energy would affect the mass to a degreebelow the accuracy of his measurements! Only 8 years later, and not before theaccuracy was improved, were the effects of the binding energy discovered with themass spectrometer.

173 Aston, F.W., Nature 104, 383 (1919) and Phi. Mag. Ser. 6, 39, 611 (1920), ibid. Nature 104, 393(1919).174 There are several calculations in electrodynamics which yield E = αmc2, where α is of theorder of unity.

1.36 Aston and the Discovery of Isotopes 57

Aston’s discovery of isotopes won him the Nobel prize just three years later.In giving the committee’s arguments for awarding Aston the 1922 Nobel prize inchemistry, professor Henrik Gustaf Söderbaum (1862–1933),175 who was a chemist,stated that:

All the masses so far measured [. . .] can be expressed by means of whole numbers in relationto oxygen 16 [. . .] and must be regarded as the expression of a natural law [. . .] which hasbeen named the ‘whole-number rule’.

In other words, Aston got the Nobel prize for showing the unity of matter by demon-strating that all elements were composed of the same units. In a sense, he provedProut’s hypothesis that the atoms of the elements are all made up of aggregationsof a certain number of atoms of the lightest known element hydrogen. If Prout hadbeen right, so claimed Söderbaum, then all elements should be exact multiples ofhydrogen, but they are not. So Prout’s hypothesis was proven with a twist, the fun-damental unit à la Aston is the sum of a negative and a positive charge. Söderbaumdid not mention that E = mc2!

The impression one gets from reading Söderbaum’s address is that he and thecommittee did not fully comprehend the repercussions of Aston’s results—they leftno room for binding energy and special relativity. After getting the Nobel prize, Astonimproved the mass spectrometer and discovered the behavior of the binding energywith mass. He definitely deserved the prize for this discovery, but doubtfully for theearlier discoveries, which prima facie contradicted relativity and were misunderstoodby the prize committee.

1.37 A Solution to a Long-Standing Problem

It was in 1828 that the botanist Robert Brown (1773–1858)176 observed minuteparticles within vacuoles in pollen grains executing a continual jittery motion. Hethen observed the same motion in particles of dust, enabling him to rule out thehypothesis that the effect was due to pollen being alive. Brown did not provide atheory to explain the perpetual fluctuation. Jan Ingenhousz (1730–1799) had earlierreported a similar effect using charcoal particles in German and French publicationsof 1784 and 1785.177 A year before Brown, another botanist, Adolphe-ThéodoreBrongiart (1801–1876),178 also observed the phenomenon, but his contribution was

175 Söderbaum was a chemist, the secretary of the Swedish Academy of Sciences and a memberof the Nobel committee for chemistry as of 1900. (He must therefore have been involved in theMendeleev case.) In his later years, Söderbaum became interested in the history of chemistry and inparticular the biography of Berzelius, about whom he wrote several books. It is an irony of historythat the Swedish Söderbaum awarded the Nobel prize to the physicists who spoiled Berzelius’arguments against Prout’s hypothesis.176 Brown, R., Miscellaneous Botanical Works 1, London, Royal Society. Ibid. Edinburgh NewPhil. J. 5, 358 (1828). Ibid. Phil. Mag. 4, 161 (1828).177 van der Pas, P.W., The Discovery of Brownian Motion. Scientiarum Historia 13, 17 (1971).178 Brongiart, A-T., Ann. Sci. Naturelles 12, 41 (1827).


apparently completely missed by physicists, and the phenomenon is known today asBrownian motion.

The mystery of Brownian motion prevailed for close to forty years.179 In 1889,Gouy (1854–1926)180 found that Brownian movement was more rapid for smallerparticles, while in 1900, Exner (1849–1926)181 undertook the first quantitativestudies, measuring how the motion depends on temperature and particle size. Themathematical treatment of Brownian motion involved new concepts from stochasticapproaches to problems in physics.182 However, we are interested here in the atomicnature of the disturbing agent and what can be inferred from it.

At long last, in 1905, it was Albert Einstein183 who solved the problem, whenhe showed that the jittery motion is due to collisions of the pollen with molecules.Moreover, Einstein demonstrated that the mean distance squared the particle movesis given by x̄2 = 2Dt , where D is the diffusion coefficient and t the time. This wasthe same diffusion coefficient that Fick was talking about, although Einstein did notmention him.

Only then was Avogadro fully vindicated. In 1916, Perrin184 used the phenomenonto determine the numerical value of the Avogadro number,185 and his result was(6.0–8.9) × 1023.

179 In many writings on Brownian motion, it is claimed that, in 1877, J. Desaulx hypothesizedthat the phenomenon was due to thermal motion of molecules. The texts even supply a quote fromDesaulx. However, I failed to find any article by an author with this name, let alone a hypothesis.See also the footnote on Einstein’s paper.180 Gouy, L.G, Compt. Rend. 109, 102 (1889).181 Exner, F.M., Ann. Phys. 2, 843 (1900). Exner became famous because he was assisted for awhile by Erwin Schrödinger.182 Fick, A., Ann. Phys. 94, 50 (1855). This is a purely phenomenological approach. There is nophysics in it. Smoluchowski, M., Ann. Phys. 21, 756 (1906). This paper was published shortly afterEinstein’s paper.183 Einstein, A., Ann. Phys. 17, 549 (1905), ibid. 19, 289, 371 (1906). This was part of Einstein’sdissertation at Zürich University. Einstein gave no reference in his paper, save one to Kirchhoff’slectures. In Ann. de Physik 19, 371 (1906), there is a paper by Einstein in which he tells the readerthat Seidentopf informed him that he (Seidentopf) and Gouy (J. de Phys. 7, 561, 1888) carried outexperiments on Brownian motion and had data. Einstein remarked that he found agreement betweenhis theory and the experimental data of Gouy. There is no reference to Desaulx, and nor does sucha reference appear in Exner’s paper. Apparently, the heros of Brownian motion did not know aboutDesaulx.184 Perrin, J., The Brownian Motion in Atoms, D. van Nostrand, 1916. Ibid. Compt. Rendu, May1908. Perrin, J. and Donau, J., Fortschritt. über Kolloide u. Polymere 1, no. 6–7, April 1910.185 The accurate value is 6.022 × 1023. Reasonable values were obtained in the late nineteenthcentury using the sedimentation equilibrium of colloidal particles. Millikan’s oil drop experimentin the 1900s gave even better accuracy and was cited in most chemistry text books till about 50years ago.

1.38 Is the Periodicity of the Chemical Elements Really So Obvious? 59

1.38 Is the Periodicity of the Chemical ElementsReally So Obvious?

Is it so obvious that the properties of the chemical elements are periodic? In fact, itis not at all obvious without quantum theory. If we have a potential well with energylevels, then it can be filled with bosons or fermions. In the first case, all bosons willstay in the lowest energy level and all systems will look alike, irrespective of thenumber of bosons. In the second case, the fermions will fill all levels, and every timea level is full we expect to see similar behavior. Thus, when the particles filling thepotential well are fermions, we should expect periodicity, although not necessarilyof equal length, as a function of the number of particles in the system.

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