Atomic number and isotopy before nuclear structure: multiple standards and evolving collaboration of chemistry and physics

We provide a detailed history of the concepts of atomic number and isotopy before the discovery of protons and neutrons that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing on research by Frederick Soddy and Ernest Rutherford, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role of the periodic table led to a relatively coherent notion of atomic number. Subsequent attention to valency, still neglected in the secondary literature, and to nuclear charge led to a decoupling of the concepts of elemental identity and weight and allowed for a coherent concept of isotopy. This concept received motivation from empirical investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards. After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly accepted explanatory relations. It is an episode of scientific collaboration and partial integration without simple, wholesale gestalt switches or chemical revolutions.


Introduction
We provide a detailed history of the concepts of atomic number and isotopy, from 1896 to 1914 (before the discovery of protons and neutrons), that draws attention to the role of evolving interplays of multiple aims and criteria in chemical and physical research. Focusing primarily on research by Frederick Soddy (1877Soddy ( -1956 and Ernest Rutherford (1871Rutherford ( -1937, we show that, in the context of differentiating disciplinary projects, the adoption of a complex and shifting concept of elemental identity and the ordering role and rule of the periodic table led to a relatively coherent notion of atomic number. Then, in the second decade of the twentieth century, developments in structural theories of the atom and the observation of regularities in radiation-scattering experiments and X-ray spectra led to this concept being mapped onto nuclear charge (and, later, the structure of the nucleus). This decoupling of elemental identity from weight allowed for a coherent concept of isotopy, which arose from investigations on the decomposition series of radioelements and their unstable chemical identity. A new model of chemical order was the result of an ongoing collaboration between chemical and physical research projects with evolving aims and standards.
Physicists and chemists sought a fixed relation between atomic weight and charge that integrated in the same model the new electrical dimension of the atom with its mechanical nature. From a chemical perspective, this gave the relation taxonomic significance (alongside the use of valency). However, the phenomenon of isotopy would upset the taxonomic use of the regularity and would ultimately be used to give atomic number a taxonomic value superior to that of weight or valency. For the physicists, nuclear charge would gain explanatory value.
The notion of atomic number has been given prominence by studies of changes in the concept of a chemical element in the twentieth century; some have made the advent of atomic number a turning point (Kragh 2000) while others have focused on understanding how competing concepts arose afterwards (Scerri and Ghibaudi 2020). Nevertheless, the role of valency in decoupling the concept of chemical identity from weight has been neglected, which we remedy in this paper.
While we do not offer an historiographical interpretation of our own, this detailed evidence will make clear the implausibility of any account relying on incommensurable paradigms or gestalt switches (Wray 2018(Wray , 2022Vogt 2021). We inform this discussion by considering the way chemistry and physics formed a hybrid field for a time and showing that the concept of atomic number arose gradually within this milieu via a series of definitional changes (some purely theoretical speculation, others in response to new empirical evidence). After key concepts were considered resolved and their territories were clarified, chemistry and physics resumed autonomous projects, yet remained bound by newly suggested and accepted explanatory relations. This is an episode of scientific collaboration and partial integration (Boyer-Kassem et al. 2018;Mäki and MacLeod 2016).

Atomic weight and charge, a physico-chemical story
The groundwork for understanding charge, matter and the structure of the atom was being developed at the Cavendish laboratory through the 1890s. J.J. Thomson (1856Thomson ( -1940 identified electrons on the experimental grounds that the cathode rays that produce ionisation phenomena have a constant mass-to-charge ratio (Thomson 1897). Electron theory, a theory of moving charges and electromagnetic radiation, was placed at the foundation of the electromagnetic worldview that rendered mechanics and mechanical mass derivative from charge and electromagnetic forces. The debate over the nature of electricity revolved around two interlocking taxonomic distinctions, between the mechanical and the electromagnetic and between radiation, or waves, and particles.
At Cambridge, Thomson invited the newly arrived Rutherford to join his investigation of the ionization of gases by the recently discovered Röntgen radiation (Thomson and Rutherford 1896). 1 The new electron physics had also chemical sources. New developments in electricity research were in progress out of ion physics, connecting two developments: theoretical (electric) physics would become electron-theory (electrodynamics) based on research in experimental physics that was effectively electrochemistry. The synthesis would lead to Thomson's discovery of the electron in cathode rays and its subsequent use in his atomic model. In the meantime, electrons had been proposed on the Continent as the cornerstone of the electromagnetic worldview, as the alternative to the mechanical worldview struggling to reconcile mechanics and optics. 2 Meanwhile in Paris, Henri Becquerel (1852Becquerel ( -1908 announced the spontaneous emission of "uranium radiation", to be investigated after the research on the penetrating and ionizing powers of X-rays. By the turn of the twentieth century, experimental research on radioactivity was guided by experimental practices and standards that included representing and classifying different kinds of radioactivity in terms of powers such as penetration (or absorption) and ionization. 3 Becquerel adopted the standard of penetrating power to distinguish his radiation from cathode rays, X-rays and light (Becquerel 1896). He investigated the penetration of radiation on different metals and then inferred something significant about the nature of the radiation. First, he tracked rough differences in strength of exposure of photographic plates, in the X-ray tradition. Next, he measured the more precise differences in the speed at which a charged electroscope was discharged by exposing it to radiation from the same amount of uranium salt and found that different metals blocked the radiation to different degrees, proportional to the thickness of the screen. But when two different metals were used together, their absorption power was more than the sum of each. From this he concluded that the radiation emitted by uranium salts must not be homogeneous in kind (Becquerel 1896, 765).
How did Becquerel reach this conclusion, and shift from applying a chemical/mineralogical taxonomy of blocking metals to applying a physical taxonomy of kinds of radiation? He assumed that thicker plates are more opaque, that is, less penetrable; but did not have enough data to assume that the correlation was (even approximately) linear. Becquerel reasoned as follows: A linear relation will obtain if you simply increase the thickness of a 1 Having studied physics and chemistry at Canterbury College in New Zealand (specializing in electrical research with a focus on the emission and detection of electromagnetic waves), Rutherford joined the Cavendish Laboratory on a three-year research fellowship from 1895 (Trenn 1977, 20). Despite their collaboration, Thomson's approach to physics remained very conservative and theoretical, due to his Tripos-based mathematical training, whereas the success of Rutherford's experimental approach would lead to two distinct cultures of British physics (Hughes 1998). 2 For a discussion of the role of ion chemistry, see Hughes (1998) and especially Darrigol (2000, ch. 7). 3 Radioactivity was also considered, from a chemical standpoint, a universal atomic phenomenon, independently of any physical model of atoms. Physicists carefully considered the various possible sources of energy that this new radiation embodied before concluding that it must come from within the atom (Curie and Skłodowska Curie 1902). single substance, but not if you add a different one. The best explanation was that different kinds of radiation are blocked differently by different substances.
Marie Curie's (1867Curie's ( -1934 investigation of radiation emitted by various uranium and thorium minerals showed quantitative differences in their activity. She knew from Becquerel's experiments that the amount of radiation was proportional to the amount of the uranium element present, no matter what the compound, and she also knew that uranium and thorium produced different amounts of radiation. When she found that samples of pitchblende and chalcolite were more active than any sum of uranium and thorium could produce, she inferred the presence of another, more active, radioelement in her samples (Skłodowska Curie 1898, 1102. In July of that year, she and Pierre Curie (1859Curie ( -1906 coined the term "radio-active" to describe this variable property of the phenomenon of radiation and to apply it in a comparative analysis . Consequently, attention to the atomic level led to modelling and measuring scattering phenomena of penetration and ionization. By 1898, Rutherford had inverted the terms of his research and, instead of investigating ionization by means of radiation, he turned to investigating radiation by means of ionization. Adopting Becquerel's standard, Rutherford (1899) distinguished between a less penetrating alpha radiation and a more penetrating beta; he would then investigate the absorption of alpha radiation as a measure of its penetrative power and confirm in 1902 its particulate nature. 4 Atomic weight first entered the picture in a paper by William Henry Bragg (1862-1942) and Richard Kleeman (1875-1932 of Adelaide who measured the range of penetrating alpha particles: 'the loss in traversing any atom is nearly proportional to the square root of the weight of that atom ' (1905, 328). After Rutherford discovered alpha particle scattering in 1906, his postdoctoral assistant at Manchester, Hans Geiger (1882Geiger ( -1945, pursued the physical modelling and looked to Bragg and Kleeman's paper. Assuming that the number of atoms per unit thickness of the stopping/scattering material is inversely proportional to the square root of the atomic weight, he concluded that 'The probable angle through which an α-particle is turned in passing through an atom is proportional to its atomic weight' (Geiger 1910, 504). Bragg's model for establishing the stopping power integrated the older experimental consideration of absorption, or penetration, power in the classification of radioactivity and the atomic perspective. The phenomenon of scattering was modelled precisely as a part of the process of penetration in those atomic terms. Geiger drew an analogy between his probabilistic approach to scattering angles and James Clerk Maxwell's model of distribution of molecular velocities in conditions of mechanical, not electrical, scattering (Geiger 1910, 495). Here we find the model-laden entrenchment of considerations of atomic weight in atomic experimental research. Geiger claimed the result was borne out by experimental data to sufficient approximation.
Thomson proposed a version of his famous plum-pudding model that could explain scattering, 'The atom is supposed to consist of a number N of negatively charged corpuscles, accompanied by an equal quantity of positive electricity uniformly distributed throughout a sphere. The deflexion of a negatively electrified particle in passing through the atom is ascribed to two causes (1) the repulsion of the corpuscles distributed through the atom, and (2) the attraction of the positive electricity in the atom' (as described in Rutherford 1911, 670-71). Thomson's student, Crowther (1883-1950, confirmed his model as consistent with scattering phenomena for β particles. Since the deflection due to attraction of the positive charge would 'depend upon whether the positive electricity is uniformly distributed through the atom, or whether it is divided up into small units' (Crowther 1910, 229), he was able to confirm experimentally, 'That the positive electricity within the atom is not in an electronic condition, but is distributed fairly uniformly through the atom ' (1910, 247). 5 Hence, penetration or absorption was modelled in Thomson's laboratory as atomic stopping power. 6 Rutherford described Thomson's model in such a way as to not be seen to explicitly disagree-'The theory of Sir J.J. Thomson is based on the assumption that the scattering due to a single atomic encounter is small, and the particular structure assumed for the atom does not admit of a very large deflexion of an a particle in traversing a single atom, unless it be supposed that the diameter of the sphere of positive electricity is minute compared with the diameter or the sphere of influence of the atom' (Rutherford 1911, 670). But "stopping power" is based on fictitious theoretical atoms; atomic weight entered the picture through the physical model of the phenomenon and not the experimental design.
For Rutherford, scattering data suggested larger angles for single scatterings than Thomson's model allowed. In order to explain them, in 1911 he introduced an alternative structural model of the atom consisting of orbiting external electrons and a positively charged nucleus. The mathematical theory developed around the model was correspondingly grounded on the magnitude of the nuclear charge. In addition to deriving from the model an expression of the scattering angle in terms of nuclear charge (Rutherford 1911, 674), he derived the empirical law expressing the scattering number 7 also as a function of the nuclear charge (Rutherford 1911, 675). As part of this project, Rutherford had tasked his Manchester collaborators Geiger andErnest Marsden (1889-1970) with the experimental test of the mathematical theory, which Rutherford had broken down into four testable relations, each between the scattering number and a different quantity-angle, thickness of scattering material (gold foil), nuclear charge and initial velocity.
Using Geiger's model-laden experimental result associating scattering angle and atomic weight, Rutherford further claimed that scattering data suggested that their nuclear charge was 'approximately proportional to their atomic weight ' (1911, 686). 8 As an expression of a universal law, he pointed to the fact that the ratio would be a constant for at least metals heavier than aluminium, citing experimental results from Geiger and Marsden for aluminium, iron, copper, silver, tin, platinum, gold and lead.
The same year, Charles Barkla (1877Barkla ( -1944 independently investigated the scattering of X-rays by light elements and the number of scattering electrons per quantity of matter, 5 "Electronic" here meaning embodied in discrete electrons. 6 The model was based on energy loss, as inversely proportional to a negative power of the velocity of the alpha particle; measurement results established the square root. 7 Number of alpha particles hitting a screen, or, experimentally, number of observed resulting scintillations, by unit area deflected at a given angle. 8 Introducing this relation in his expression of the scattering number, Rutherford derived the proportionality between the scattering number for any thickness and the square of the atomic weight (1911,681). Geiger had used Bragg's estimation that the stopping power of an atom for an alpha particle is proportional to the square root of the atomic weight and the stopping thickness is inversely proportional (Geiger 1910, 501). Rutherford concluded that the scattering coefficient is proportional to the 3 2 -power of the weight (1911,681). that is, atomic charge. 9 Barkla used the most recent values for the electron's charge/mass ratio and the density of molecules in a gas to calculate that the number of scattering electrons was half the atomic weight of the element; he estimated the diminution of energy or intensity of beams through a layer of air or a substance of low atomic weight due to scattering and due to absorption (Barkla 1911, 651). (The corresponding rates are the scattering and absorption coefficients, respectively.) The estimate, Barkla noted, relied on Thomson's model of scattering but conflicted with Crowther's estimate in his 1910 tests of Thomson's scattering model as three times the atomic weight. 10 Experimentally, the investigation extended the earlier focus, introduced in France and Germany, on penetration and ionization powers of radioactivity. Like Pierre Curie and Rutherford, Barkla measured the energy as the latter power with an electroscope. In 1914, Rutherford cited Barkla's results, based on a different physical model and experimenting with a different kind of radiation, as independent evidence that the relation of nuclear charge to weight was ½. 11 In 1913 Geiger and Marsden published the results of the tests of Rutherford's 1911 nuclear structure of the atom. They listed the empirical conclusions of the theory: the specific variations of the number of scattered particles with angle, thickness of scattering material, nuclear charge and velocity of incident alpha particles (Geiger and Marsden 1913, 606). However where they listed the corresponding variables to be investigated, they substituted for variation with nuclear charge the 'variation with atomic weight of scattering material ' (1913, 606). To justify the substitution, they mentioned Rutherford's assumption that 'the central charge of the atom is proportional to the atomic weight ' (1913, 616). They next followed Rutherford in the derivation of proportionality between the number of scattered alpha particles and the square of the atomic weight and, for the number per centimetre of air equivalent, to the 3 2 power. Rutherford's claim was that the ratio was constant at least for metals. Geiger and Marsden tested the relation for metals, from aluminium to gold, and added carbon as the lightest element.
Their assessment of the results is notable in two respects, experimental and theoretical. They appealed to experimental error to conclude that the range of values for the ratiobetween 0.85 and 1.37-showed the essential correctness of Rutherford's claim (Geiger and Marsden 1913, 619). They also pointed to the theoretical limits of the validity of the claim over elements lighter than carbon, as 'the laws of scattering will require some modification to take into account the relative motion of the atom itself when a collision occurs' (1913,619). Expecting deviations in those cases, their explanation would require a revised atomic model of single scattering. The question, however, still remains about their preference for testing the theory in terms of atomic weight, a derivation offered by Rutherford himself, although in relation to Geiger and Marsden's ongoing tests of the theory (1911,688). The most likely explanation might be the entrenchment of the weight-based taxonomy in experimental practice and, in this particular context, introduced by Geiger's earlier result of the relation between scattering angle and atomic weight.
The same year, his Manchester student John Mitchell Nuttall (1890-1958) extended the claim of validity of the charge/weight relation to light atoms or gases to the general claim that 'the atom consists of a positively charged nucleus of minute dimensions surrounded by a compensating distribution of negative electrons. The charge on the nucleus for heavy atoms is approximately ½Ae where A is the atomic weight and e the electronic charge' (Rutherford and Nuttall 1913, 712). The theory, then, would imply that 'hydrogen has a nucleus of one charge, helium of two, and carbon of about six ' (1913, 702). No mention is made, however, of the significance of the result for chemical ordering. Instead, they place emphasis on the evidence for the structural physical model of the atom: 'this deduction is of great importance in connexion with the constitution of the simpler atoms ' (1913, 702). 12 From the beginning, the research strand we have just identified was consistently informed by theoretical, as well as experimental, physical standards. Far from turn-ofthe century French chemical and experimental radioactivity research, both experimental and theoretical contributions relied particularly on the role of physical models, structural atomic and subatomic models, which emerged in the context of electron physics (even tied to electrochemistry) and radioactivity research. Recall that charge entered Rutherford's theory through the explanatory physical model and not through correlation between experimental data about scattering angles and charge. In the experimental context, the modelling helped entrench considerations of atomic weight.
The perspective extended to Rutherford's earlier model of (physical) disintegration as a model of radioactivity, even as part of his sustained collaboration with Soddy. While in the French context, any physics, such as Pierre Curie's electric measurements, was introduced at the service of the chemical, experimental project, in the British context, it provides the phenomenon that helps extend and develop physical theory (see our longer paper for details). The collaboration and development of physical and chemical projects exposes a complex dynamic of evolving, differentiated and integrated taxonomic standards and purposes.

The periodic table, chemical classification and identity: from atomic weight and valency to Pb isotopy
The collaboration between the Oxford-trained chemist Frederick Soddy and the physicist Rutherford began at McGill University in 1901. Their main result by 1903 was identifying and investigating two separate aspects of radioactivity-radioactive emissions and chemical transformation-and proposing a theory of transformation (Rutherford and Soddy 1902a, b) and disintegration (1903) for their unified understanding.
Soddy's interest in physics manifested itself early in different ways. In a prize essay of 1895, Soddy praised Wilhelm Ostwald's theory of dissociation of electrolytes into ions in a programmatic tone, as a new physical approach for addressing chemical problems and a new area of research between the disciplines: It seems certain that by physical methods we shall be able to investigate the absolute structure of matter by methods so clear and definite as has hardly been anticipated hitherto. (...) The vast field of research (...) between chemistry and physics is almost virgin soil, holding out a bountiful harvest to those who (...) are enterprising enough to attack the problems, and patient enough to overcome the difficulties, which pioneers of scientific research always have to encounter. (Quoted in Trenn 1977, 22) The object of Soddy's methodological concern was the structure of matter, namely, the relation between atoms in a molecule and the place of electricity in the structure. His own research in organic chemistry investigated the effect of light weakening the bonds between atoms in chlorine molecules (Trenn 1977, 23). In addition, in his first year, he attended Rutherford's course on X-rays, ionization, radioactivity and electrometry.
Chemistry was becoming, as was the mechanical worldview in physics, increasingly subservient to the study of electricity and the understanding of the electron. What was at stake was the chemist's point of view, namely, the understanding of matter and the nature of the chemical atom, its elementarity, stability and indivisibility. 13 Rutherford's acceptance of the electron challenged the conception of the indivisibility and stability of the atom. Was the electron material and what properties were thereby entailed? For Soddy, the burden of proof fell on Rutherford. Otherwise, what he considered the chemical atomic theory would not need revising and the chemist 'will retain a belief and reverence for atoms as concrete and permanent identities, if not immutable, certainly not yet transmuted' (quoted in Trenn 1977, 26).
On the physical nature of the electron, Rutherford distinguished opposing views-German and English-and presented the most recent evidence of the corpuscular, material nature of the electron and the radioactive emissions of uranium and radium. But he acknowledged the unsettled question of the irreducibly electric nature of the electron's mass, derivative from its charge. Their collaboration on radioactivity research would lead to Soddy having both to uphold and to revise a distinctive chemical project and viewpoint.
Turning to the radioactivity of different chemical elements, Rutherford and Soddy explored first what they called thorium emanation, or thorium-X. Using electrometric techniques perfected by Rutherford (1900;1901), they traced ionization effects that helped in turn track radioactivity. The particulate nature of the thorium emanation, identified first by Rutherford, was understood relative to the taxonomic distinction between matter and radiation, in which radiation was considered a form of energy or wave, after electromagnetic radiation. Despite the recent evidence that beta radiation was particulate, consisting of the same electrons Thomson had identified in cathode rays (Becquerel 1900), they applied the chemical mereological taxonomy that distinguished between a pure element and a compound and decided thorium was a composite that included the radioactive thorium-X.
In 1902, Soddy and Rutherford introduced their transformation theory. It relied on a new chemical taxonomy, the distinction between composition and production, as chemical change or transformation. Because they began with the assumption that uranium radiation was a spontaneous event, Rutherford focused on the starting material without speculating on intermediate products and described the process with little regard for the identity of the final product; the only products he was concerned with were the alpha and beta particles released along the way.
Both types of transformations (alpha and beta) constitute a fundamental change in the concept of substance, since the permanence of elements is undermined. The final product was seen as spent waste, not a new element. As their attention remained on the source, Rutherford and Soddy came to identify its chemical change and conceptualise the process of spontaneous radioactivity as a "radioactive change" and "spontaneous transformation". 14 To explain the observed phenomena, they concluded that they were witnessing a spontaneous change in chemical identity. Hardly a trivial choice for Soddy, by the standard of chemical atom he had defended against Rutherford. Relative to the different classifications, the particular nature of the emanation suggested the spontaneous emission was a case of a spontaneous breakup. According to the initial version of the theory, emission followed change; in a subsequent, modified version, Rutherford and Soddy connected emission and change. 15 In 1903 they introduced the disintegration theory. After evidence mounted that alpha radiation was also particulate, transformation was associated with the general notion of radioactivity as material expulsion and hence material disintegration. Rutherford and Soddy distinguished between two different kinds of processes in radioactivity: radioactive change and chemical change (1903, 586f). Radioactive change is radioactive emission subject to the law of change, which tracks decay in activity (this being the original meaning of "decay"). Chemical change is the change in chemical identity that results from the process of production they also called disintegration. This involves the loss of a part of the atom by emission in radioactive change but, without a specific structural model of the atom, this was accounted for only in terms of mass.
Along the way, Rutherford and Soddy introduced a physico-chemical decay law that provided a general mathematical representation of the behavior of radioelements in a series. Initially, in the French tradition of measuring powers, the law represented decay of activity but by 1904 it was reformulated from the exponential decay of activity to the exponential reduction of sample mass. 16 Rutherford and Soddy's talk of disintegration in terms of mass and energy introduced, then, merely an abstractly structural, or at least mereological, conception of the process of chemical change underlying the decay of activity. The new conception was both serial and quantitative (mass): "The disintegration of the atom and the expulsion of heavy charged particles of the same order of mass as the hydrogen atom leaves behind a new system lighter than before, and possessing chemical and physical properties quite different from those of the original element" (1903,586). Extensive observations of regularities in mass change during alpha particle emissions, coupled with observation of the chemical valencies 14 '[R]adioactive elements must be undergoing spontaneous transformation… It is apparent that we are dealing with phenomena outside the sphere of known atomic forces. Radioactivity may therefore be considered as a manifestation of subatomic chemical change' (Rutherford & Soddy 1902a, 395). 15 'Hence it is not possible to regard radioactivity as a consequence of changes that have already taken place. The rays emitted must be an accompaniment of the change of the radiating system into the one next produced' (Rutherford and Soddy 1903, 578). 16 Following the molecular statistical theories of thermodynamics by Ludwig Boltzmann in Vienna, Egon von Schweidler (1873Schweidler ( -1948 turned the statistical notion into the probabilistic atomic notion of the phenomenon (Schweidler 1906). of the decay products, would lead Soddy, Kasimir Fajans (1887-1975) and Alexander Fleck (1889-1968 to develop of a set of "displacement laws", tracking the "movement" of the decaying atom through groups of the periodic table. At work were dual disciplinary standards for the acceptance of disintegration theory: In physics, disintegration was compatible with the mechanical conception of the atom and had explanatory power, especially for electrical phenomena such as ionization. In chemistry, while incompatible with the entrenched conception of the chemical atom as elementary and stable, it had ordering power for radioelements. Thus, it served the general chemistry project of classification. Since the 1860s, classification in the periodic table included two main criteria: classification by position according to atomic weight and by row or column according to similar chemical properties such as valency (Van Spronsen 1986, 95-96).
Soddy and others faced a proliferation of disintegration products that needed identification and placing. The methodological challenge was that new elements would share occupied positions in the flat two-dimensional table. The solution to this problem took two comprehensive forms: proposals of three-dimensional arrangements and the notion of isotopy (Van Spronsen 1986, 99). Soddy, Anton van den Broek (1870-1926) and Fajans, for instance, contributed to the first; Soddy, to the second. From disintegration research Soddy would introduce first a displacement rule in 1911 and next the concept of isotopy, so named in late 1913.
On top of the established taxonomy of physical powers: penetration (absorption) and ionization, Soddy introduced two, more important, connected features: range of emitted particles and average life. 17 The operative taxonomic standard was classification by valency or, approximately, group number-at that time extending from 0 (noble gases) to VIII (transition metals)-not atomic weight or individual properties such as half-life. 18 Why? Valency carried chemical experimental and theoretical significance.
British chemists analysed the elements in terms of their valency as a commensurable measure of their tendency to combine with the various anions, by precipitating metal cations from solution through the sequential addition of various non-metal anions that render them insoluble and studying their insoluble precipitates. According to Soddy, two Swedish chemists, Daniel Strömholm and The Svedberg, were the first to combine the characterisation of radioelements by valency and 'were probably the first to attempt to fit a part of the disintegration series into the Periodic Table' ( 1966,381). 19 According to Soddy's assessment of 1911, Strömholm and Svedberg's attempt to classify the disintegration series on the periodic table and their conjecture that non-separability might extend beyond radioelements were chemically significant by virtue of the combined values of classification and generalization (Soddy 1966, 381). From the chemical taxonomical perspective, Soddy pitted non-separability, or isotopy, against both elementarity, or "general complexity of matter", and the fundamentality of weight. 20 Evidence of chemical non-separability between radio-elements in decay series mounted between 1907 and 1911 (Kauffman 1986, 68-69). 21 Soddy (1910) declared that nonseparability is chemical identity, not chemical analogy. In 1912, Aston (1877-1945) identified isotopes of neon. This is significant, according to Soddy (1912), because it grants general taxonomic applicability to the notion of non-separability as a standard of chemical identity. The research relied on recently established chemical techniques employed in Soddy's laboratory-by Fleck, his demonstrator at Glasgow, where Soddy took up a position in 1904-in order to prove that many purportedly new elements were chemically identical. Worth noting is the limited role of spectroscopic analysis.
New chemistry standards included experimental isolation and identification of the products of radioactive change. The chemical point of view is characterized by the identification of chemical properties and classification of chemical elements (Soddy 1914a, 24). Chemical identity, and atomism, is the combination of the two. Through 1913, the chemical point of view relied on distinctive epistemic standards, chemical classification and generality of rules and concepts. The key concept in taxonomic order is chemical identity, which Soddy analyses into considerations of constancy, fundamentality and homogeneity.
In 1911, Soddy introduced a group displacement rule for alpha emissions in terms of valency or group classification: 'The loss of a helium atom or α-particle appears to cause the change of the element, not into the next family but into the next but one ' (1911b, 29-30). Not understanding the zig-zag nature or having a law governing beta-decay, Soddy noticed but could not explain why the disintegration series passes through the same valencies multiple times. 22 This recurrence was the first hint at isotopy.
Working with Rutherford at Manchester, Alexander S. Russell (1888Russell ( -1972 introduced a displacement rule for beta emissions, which he communicated privately to Soddy in October 1912. Like Soddy, Russell adopted the group taxonomy. According to Russell's 19 Soddy cited their 1909Soddy cited their paper in (1914a. 20 'The question naturally arises whether some of the common elements may not, in reality, be mixtures of chemically non-separable elements in constant proportion, differing stepwise by whole units in atomic weight. This would certainly account for the lack of regular relationships between the numerical values of the atomic weights' (Soddy 1911a, 80). 21 Soddy's (1913a) paper in Chemical News refers to precipitation/solubility results from McCoy and Ross (1907) showing radiothorium to be inseparable from thorium, which would help separate elements but not fully identify them without additional indicators that Soddy was familiar with as part of the identity/taxonomical standard, e.g., a set of different experimental methods of separation associated with an element. The method applied by McCoy and Ross to radioelements was part of a tradition going back to the nineteenth century but their results marked an inversion of the trend of discovering new elements; the method of separation by precipitation was perfected by A.C. Neish (1904) at a time when "didymium" was still believed to be an element (i.e. not yet resolved into praseodymium and neodymium). rule: when a beta-ray or rayless change occurs, 'the group in the periodic system to which the resultant product belongs is one unit greater, or one unit less, than that to which the parent product belongs' (Russell 1913, 52). With these two rules in hand, in January 1913 Russell published a diagram summarising the series of changes that uranium, thorium and actinium undergo, in terms of the valencies of each product (Fig. 1). In February, Soddy (1913a, after p. 98) would publish a geometrically re-orientated version of this diagram, also in terms of group number, but would by September of that year have incorporated physical modelling, such that his next diagram (Fig. 2) would add a physical interpretation to the valency axis in terms of the number of electrons (which in December he would identify as nuclear electrons).
Also in Rutherford's Manchester laboratory but German-trained, Georg von Hevesy (1885-1966) measured and tracked valency through radioactive decay changes, 23 hinting at valency rules for both alpha and beta emissions in disintegration series (Hevesy 1912(Hevesy , 1913. Hevesy is ambiguous about the direction of the shift in alpha decay-'the valency of the resultant atom is two units different from that of the parent atom after the latter has expelled an α-particle.' He does not give a clear rule for the direction of this shift but says, 'expulsion of a β-particle seems to affect the valency in a direction opposite to that affected by the α-ray change ' ( 1913, 413).
Hevesy also introduced qualifications to tracking valency and pointed to differences between valency and atomic weight: atomic weight is a constant property of the element, whereas valency, the genuine chemical property, is secondary and contextual, a tendency to combine with other elements -'The first is that the valency of an element is not an invariable quantity like its atomic weight, but depends on various factors such as, for instance, the nature of the element with which the element is combined ' (1913, 411).
Back in Germany, Fajans tracked the change in electronegativity of radioelements, giving a more reliable measure of the direction of the change than tracking change in valency, which enabled him to confirm Hevesy's observation that alpha and beta transmutations go in opposite directions. 24 Building on Soddy's rule that alpha decay meant a change of two places in the periodic table and Russell's rule that beta decay was a change of one place, Fajans established a complete set of better established displacement laws.
Soddy, Fajans and others set out to test and confirm predictions of the displacement rules. The main two were the origin of actinium and the anomalous atomic weights of lead of radioactive origin (Kauffman 1986, 74). 25 The determination of atomic weight was facilitated by the stability of the samples. Soddy and Fajans predicted that the stable lead products of uranium and thorium differed in atomic weight from each other and from ordinary lead. Between 1913 and mid-1914, the lead produced by uranium-and thorium-based minerals was studied closely by the chemist Max E. Lembert working in Theodore W. Richards's (1868Richards's ( -1928 laboratory at Harvard, at the behest of Fajans. They found great variance in the atomic masses of samples of ordinary lead and the lighter product of radioactive decay. George Kauffman (1986) and Lawrence Badash (1979) have argued that the younger radio-chemists around Soddy and Fajans took this discrepancy to be evidence of isotopy. They emphasised how Richards, an older chemist and the recognized authority on atomic weights, was reluctant to embrace a concept as disruptive as isotopy and tried to explain away the products of radioactive disintegration as "admixtures" of different elements, but, by the same token, was forced to concede that even ordinary pure lead might be a "medley" of different substances in some sense, despite being a single substance chemically (Badash 1979, 251-52). Conversely, Gareth Eaton emphasises Richards' confidence in the accuracy of his atomic weight determinations and glosses over Richards' reluctance to align himself with Soddy's hypothesis (2020, p. 91). 26  Russell 1913, 51) Eventually, in 1914, lead obtained from non-radioactive sources was shown to be a mixture of different isotopes, with the ratio varying depending on the mineral source (Soddy and Hyman 1914). Soddy had speculated, as early as February 1913, 'that "lead" is actually such a mixture ' (1913a, 99). But the connection to radioactivity would remain uncertain for a few more years-as late as 1917 he conceded, 'The actual production of lead has not yet been proved directly in the same way as the production of helium has… But even without the actual direct proof of this kind there is practically no room for doubt on the point' (Soddy 1920, 101). It would seem, then, that Soddy held stricter standards, which, in this case, allowed him nevertheless to accept a weaker, promising and provisional closure of the controversy. The lead controversy established both the displacement rules and a widespread acceptance of the empirical reality of isotopy.
The periodic system was established on a firmer general theoretical basis in 1913: a set of new chemical concepts-isotopy and atomic number-and generalizations-displacement laws for radioelements and ordering standards for the entire periodic table-as well as new physical subatomic models-Rutherford's and Bohr's quantum solar system model of a charged nucleus surrounded by electrons. 27 It was newly observed regularities in this Footnote 26 (continued) its general explanation and reconceptualization. Thus, only retrospectively (i.e. anachronistically) could the data be tied to supporting the rising consensus around the notion of isotopy and its general applicability. 27 Kragh (2020, 7) has suggested that Rutherford's nuclear hypothesis does not even rise to the level of an "atomic model" because it only explains scattering phenomena and that it was not until Bohr's 1913 quantum-theoretical account of electron shells that detailed explanation of chemical phenomena was possible. extended and reinterpreted periodic table that drove chemists to seek further theoretical explanations in Rutherford and Bohr's physical models (recall Soddy's own early interest in physical aspects of chemical phenomena).
During that year Soddy published several papers drawing general lessons from the recent experimental research on the radioactive decay products in the disintegration series. The papers express a chemical standpoint centered on the general problem of chemical classification and identity, especially in terms of chemical non-separability, or isotopy. The papers also point to implications for assumptions of chemical elementarity/complexity of matter linked to taxonomic differences in atomic weight. Also, as part of the chemical perspective, Soddy valued especially general chemical results, beyond the case of radioelements.
In 'Radio-elements and the Periodic Law', Soddy took stock of the research on displacement rules spawned by his 1911 proposal for the case of alpha emission and concluding in Fajans's comprehensive proposal for alpha and beta emission. The broader significance of the displacement rules lay, according to Soddy, in the dynamical dimension of identity and classification exhibited by disintegration series relative to the static ordering criteria: individual and group identity associated with individual position-and with atomic number-of the chemical element and with group (or "family") number-approximately valency. The particular new kind of general order is marked by the chemical recurrence of group number across the series of decay elements so that 'the Periodic Law [Table] is the expression of the periodic character of the radio-active changes' (Soddy 1913a, 97). 28 This is the new, experimental, chemical identity: 'when similar groups recur the elements are not merely similar, but non-separable ' (1913a, 97). 29 Finally, Soddy emphasized two connected negative general implications for the taxonomic concept of chemical identity: (1) common elements might be 'mixtures of non-separable elements of different atomic weights in constant proportions', or the notion that later in the year he would call "isotopy" expressed in terms of the chemical complexity of matter; and (2) atomic mass is not 'a real constant fixing all the chemical and physical properties of the elements ' (1913a, 97-99).
In 'The Periodic Law from the Standpoint of Radioactivity', Soddy touted the displacement rules as 'the general law (…) governing the evolution of the elements through the Periodic Table'. 30 Besides generality, the central notion in the chemical project of classification remains chemical identity and its increasingly looser dependence on physical characteristics. In this paper Soddy added new evidence of isotopy in terms of differences Certainly, Rutherford was not proposing a model of the chemical atom but what he provided was certainly a physical model that explained the physical phenomena, also pointing to its potential relevance to chemistry by serving its taxonomical aim and identifying elements with a particular nuclear charge (Rutherford 1911, 685-88).
Footnote 27 (continued) 28 For Soddy and especially Fajans, the "periodic law", with a more general and abstract connotation than "table", could express 'the periodic character of radioactive changes ' (1913a, 97). 29 Soddy sought to tie his conclusions to the newly accepted structure of the atom. He distinguished between chemical and physical properties and between the inner and external constitution of the atom -the inner identified with the more permanent material, or physical atom (Soddy 1913a, 99). Chemical and spectral non-separability concern only the "electronic satellites", which determine both spectra and valency, and not so-called "constitutional electrons". 30 Soddy (1913c, 363). This paper is a translation of an earlier version published in German (Soddy 1913b). in the ranges of travel in air for alpha particles emitted in uranium decay. 31 The ranges he associated with not only differing atomic weights of the different chemically non-separable forms of uranium, also with different periods of average life.
In September of that year, Soddy outlined the significance of the previous results at the meeting of the British Association for the Advancement of Science. Soddy proclaimed that, during 1913, 'the general law governing the passage through the periodic table of the elements in process of radioactive change has been discovered ' (1914c, 445). This was in line with the value of general laws, now in dynamical form, within the chemical perspective.
Unlike Fajans, and holding it against him, Soddy saw the significance of the general displacement law in its relevance to the general taxonomic project expressed in the periodic table, namely, the general criterion of chemical identity of elements setting what he called the ultimate level of chemical analysis of matter. He insisted that research leading to the displacement law not only showed different elements occupying the same position, it also suggested a new taxonomic criterion of identity at that level (and not the group level). Henceforth, chemical identity was determined by chemical non-separability and, tentatively, also by spectroscopic indistinguishability. 32 Notably, Soddy presented two different stories with corresponding diagrams, which appeared first in the German paper (1913b, 193): one story, told through a set of small single-series diagrams, is about the displacement laws tracking changes in mass and group number (the old, even if approximate, working taxonomic criteria); the other story is exemplified in a larger diagram (Fig. 2), juxtaposing the three decay series and accounting for these changes in both 'units of atomic mass' and 'relative N° of negative electrons'.
According to Soddy, the phenomenon of non-separability that challenges the taxonomic standards is significant also to the extent that it meets the epistemic standard of generality at work in the chemical viewpoint that defines his project of chemical research. The new experimental criterion of identity is fundamental since evidence suggested it applies beyond the domain of radioelements.
Soddy speaks to further aims and standards of chemical research and perspective: chemical complexity of matter and atomic constitution. 'Matter,' he declared, 'is even more complex than chemical analysis alone has been able to reveal ' (1914c, 447). What is the chemical problem of the complexity of matter? The negative lesson for the project of taxonomy concerned the role of atomic weight. Soddy could declare now that it is not a real constant that tracks chemical difference systematically, as a general criterion, and therefore holds less 'fundamental interest ' (1914c, 447). Simultaneously, he also declared that rejecting the taxonomic role of tracking and ordering chemical differences for atomic weights may have made the problem of atomic constitution simpler, since the lack of simple numerical relations between atomic weights was no longer an obstacle. The developing taxonomic standards are, then, interlocked with evolving aims and problems of chemical, and physical, research. 31 Soddy (1913c, 363-64). As first described in Geiger and Nuttall (1911). 32 Spectroscopic analysis had for Soddy a hybrid physical-chemical status (1914c, 447).

From atomic weight to atomic number in classification and ordering: From displacement laws to electronic number
Soddy's was not the only project informed by new standards, problems and aims in the different contexts of evolving and connected research activities. To Soddy's and Rutherford's, projects we have to add Anton Van den Broek's in this section and, in the next, Henry Moseley's. The differences appear more visibly precisely in different situations of public collaboration or debate. In the aftermath of the collaboration between Soddy and Rutherford, Soddy pursued the chemical implications of the theory of physical disintegration for chemical classification, while Rutherford used chemical classification to pursue the physical implications for atomic constitution. While acknowledging that radium, like other radioactive substances in the decay series, was a chemical element, Rutherford only ever used chemical identities as a proxy for their physical properties of mass and charge. Van den Broek (1907) combined both projects with a focus on chemical classification in the periodic table, while engaging with Rutherford's work on the physical nature of radioactivity. Rutherford had sought to understand alpha radiation after having established its particulate nature by analogy with Thomson's identification of the electron by its e/m ratio. He turned to the experimental value of chemical classification and knowledge linked to his and Soddy's physical-chemical theory of disintegration and offered three different possible chemical identities for the particle emitted by radium: a hydrogen molecule, a helium atom or half of a helium atom-ruling out the first option but remaining agnostic between the latter two (Rutherford 1906a, 184).
Rutherford had already established a connection between alpha radiation and helium (1905,211). 33 The empirically determined charge-to-mass ratio for alpha particles could be explained as two charges on a whole helium atom or as a single positive charge spread either over two hydrogen atoms or over half a helium atom. 34 Rutherford himself rejected the idea of a double charged hydrogen molecule as implausible and was left with the underdetermined options of a whole helium atom or half of one, which Van den Broek preferred to name an "alphon". Van den Broek (1907) briefly considered both Rutherford's hypotheses for the mass and charge of the alpha particle as a way of building a periodic table inspired by Prout's hypothesis-that every atom is composed of multiples of a fundamental unit-venturing well beyond Rutherford's physical goals, into the realm of chemical classification. Choosing Rutherford's least preferred option-twice the mass and electric charge of a hydrogen ion-Van den Broek postulated a theoretical entity, the "alphon", as the fundamental building block of atoms-its chemical identity being half the helium atom. He suggested 33 After establishing that the charge-to-mass ratio is the same for alpha particles emitted by a range of different radioactive materials, Rutherford set about pinning down their absolute qualities by comparing them to the known properties of hydrogen and helium. Helium atoms were known to be approximately 4 times heavier than individual hydrogen atoms (based on the relative density of the two gasses, understanding that helium is monatomic and hydrogen diatomic and assuming equal volumes of different gasses contain equal numbers of molecules). Since alpha particles were known to form helium gas, their mass could not plausibly be any greater than the mass of a helium atom but could be less. The ratio of density of helium gas to hydrogen gas for the same number of molecules was found to be almost two (Rutherford 1906b, 365). The ratio of atomic weights, Rutherford inferred, is almost four. For the same charge, a unit charge or hydrogen ion, the value of the charge-to-mass ratio for helium is then half the value of the one for alpha particles. 34 Any smaller mass would imply a charge smaller than the elementary charge, although Robert Millikan would not perform his famous experiment to determine this value till 1909. that the double-unit-weight alphon system could provide a more suitable taxonomic unit than Prout's single-unit-weight hydrogen to organize the periodic table. 35 The choice of the ordering generalization would be adequate from the standpoint of the taxonomic goal of chemical research. 36 The reasoning integrates a number of classifications and aims. Besides the chemical classification of elements, he assumed the classifications of physical properties into mechanical and electrical, and into particles and rays, and the classification of radiation into different types, alpha, beta and gamma. He also assumed and generalized the applicability of the relation between atomic weight and charge in the model of the atom. He pursued the aim of chemical classification, where, from a chemical perspective, ordering is an epistemic value.
But this cannot be all. Rutherford's chemical hypothesis about alpha particles was the beginnings of a physical model of the chemical atom, radioactivity and disintegration. Van den Broek inferred and adopted from Rutherford's disintegration theory a structural, compositional assumption-both physical and chemical-that would explain radioactivity, disintegration, and chemical change, as well as, thereby, justify chemical order: radioactivity and disintegration are based on a particular physical composition into parts such as alpha particles. Those parts, whether alphons or, later, beta particles can track and organize chemical classification. The classification project becomes more central in two communications of 1911. In the first, Van den Broek addressed the classification scheme independently of any reference to the grounding role of the alphon. Instead, he focused on the ordering principle the alphon had introduced, separating elements uniformly by two units of weight. 37 Meanwhile, Van den Broek kept up with Rutherford's radioactivity research. Rutherford and Barkla had independently announced the relation between atomic weight and atomic charge as one result of their scattering experiments-with alpha particles and X-rays, respectively (Barkla 1911;Rutherford 1911). In a one-paragraph-long letter to Nature later that year, Van den Broek cited Rutherford and Barkla's related conclusions, while proving 35 Up to uranium, predicting a total of 120 elements each made up of an integral number of alphons -only at the exclusion of the awkward case of hydrogen's "half" atom ( Van den Broek 1907, 199). Eric Scerri points to the physical relation between atomic charge and weight that Rutherford and Barkla had defendednuclear charge as half the atomic weight -and whose application Van den Broek generalized to all elements, the only reason cited in Scerri (2016, 45). But this is chronologically and conceptually wrong. As physicists, Rutherford and Barkla (whom Van den Broek never cited) were certainly focussed on this fixed relation between the two variables but all Van den Broek wanted to learn from them (and all he used to further his own chemical project) was the mass of the fundamental particle. By stating that Van den Broek was concerned with e/m, Scerri mischaracterizes what he actually takes from Rutherford. The only role e/m played is helping determine the ratio of atomic weights, on the assumption that it varies for hydrogen, alpha particles and helium. And this is not the general fixed relation between atomic weight and charge, one half, that Rutherford and Barkla conjecture much later, after 1910. 36 He explained that a table whose cells increase by a mass of four units (a "Heliad" system) would not allow enough places for all the known elements whereas cells increasing by two mass units (an "Alphad" system) would leave some gaps. Since gaps in the periodic table were not a problem-famously, Mendeleev himself left gaps in his original table, which were subsequently filled through the discovery of new elements, although he did not consider this necessary (Kragh 2019, 8)-Van den Broek developed his new table based on the alphon as the fundamental particle ( Van den Broek 1907, 200). 37 In addition, he followed up on an earlier suggestion by Mendeleev to organize the spatial representation of the elements in a three-dimensional, cubic arrangement, one of the several such solutions to the problem of accommodating the newly identified radioelements (Van den Broek 1911a). Contrary to Scerri's remarks, this proposal can hardly be understood as a new step in the direction of introducing the notion of atomic number (Scerri 2016, 46). Barkla's formulation: 'the number of electrons per atom is half the atomic weight' (1911b). Unlike Rutherford and Barkla, his purpose was not to serve the project of atomic modeling with physical generalizations. Instead, in the spirit of his 1907 paper, it was to serve the chemical project of classification by means of chemical generalization in the form of the simplest ordering pattern of periodicity of general validity.
In addition, Van den Broek inferred from the validity of the Rutherford-Barkla relation over all known elements, one could associate with each possible element 'each possible permanent charge (of both signs) per atom' (Van den Broek 1911b). 38 In Van den Broek's final conclusion-that to each amount of permanent charge 'belongs a possible element'-the quantity of charge (not yet called the atomic number) is measured indirectly by the number of electrons removed and acts effectively as an ordering number serving the taxonomic purpose. Notice that Van den Broek is considering both the Rutherford-Barkla experimental relation and his taxonomic hypothesis empirically adequate, in spite of the inaccuracies in atomic charge measurements.
Van den Broek did not claim this charge-based system was superior to the one based on atomic weight but it arguably was. The superior value of the new ordering system cannot be just validity or correctness, 39 since the Rutherford-Barkla relation between atomic weight and charge makes both quantities, in that regard, stand or fall together. The primary goal remains ordering, not predictive or explanatory value. Thus, the superiority of charge number lies specifically in its suitability as an ordering system (just as the alphon was superior to Prout's hydrogen). And this might stem from at least two separate, yet connected, values. The first is its higher generality of application, since, unlike the alphon system, charge number would extend to hydrogen. The second consideration is its higher simplicity, in a specific sense: the charge number is identical to the position of the element in the table; that is, the number of charges tracks the element's ordinal place, beginning with the lowest ranking number, one. Van den Broek's evolving appreciation of atomic charge number appears, then, informed by a chemical perspective with multiple considerations of descriptive, taxonomic standards and methodological values.
In a new paper composed in November 1912, Van den Broek again equated an element's order in the periodic table with the charge that was now, after Rutherford's model, located in the nucleus as intra-atomic charge-not number of electrons (Van den Broek 1913a). He assumed the unitarity of electric charges and associated with the number of intra-atomic charges what he called a series number (Folgenummer), soon to be known as atomic number (1913a, 39). It is in this early 1913 paper, not in the subsequent letter to Nature, that Van den Broek effectively introduced the concept of atomic number, independently of the measure of charge. 40 Although aware of deviations in atomic weights, he argued that the general trend of intra-atomic charge equalling half an atom's weight (Rutherford's relation) has sufficient predictive power to be considered a law. Rather than landing on Soddy's 38 In 1907 he had defended, as more suitable than Prout's hydrogen, one-unit system, the alphon, 2 weightunit system, that is, one based on 'a constant mean difference between consecutive atomic weights' equal to 2 (Van den Broek 1907). In 1911, he adopted a generalized version of the Rutherford-Barkla relation between atomic weight and effective charge, extended to all predicted 120 possible elements between hydrogen and uranium, and used it to conclude that the number of possible elements corresponds to the number of possible charges. 39 As suggested, for instance, by Abraham Pais (1986, 227). 40 Scerri places it in the letter to Nature of 1911, where all Van den Broek claims is that the charge tracks position in the table; although he is correct that in the 1913 paper Van den Broek introduced what he translates as the "serial" number. wholly mass-based concept of isotope, Van den Broek speculated that any deviations in the ratio could be due to the existence of unknown positively charged components of the atom.
A letter submitted a year later (Van den Broek 1913b) contains a significant development in his taxonomic project in relation to the recent physical models of the constitution of the atom. After introducing the taxonomic hypothesis now in terms of the series number and intra-atomic charge, Van den Broek examines Geiger and Marsden's experimental test of Rutherford's scattering law from his physical model of the constitution of the atom. Just as Soddy had been using physical information to develop and support chemical theory (including taxonomy) and serve chemical goals-while Rutherford had been using chemical information, instead, to pursue and support physical modelling-now it was Van den Broek who was also using physical modelling to pursue his general taxonomic chemical project.
In their experiment, Geiger and Marsden adopted as an auxiliary hypothesis the Rutherford-Barkla empirical relation between nuclear charge and atomic weight to transform one of Rutherford's testable relations, namely, between scattering number and nuclear charge, into a relation between scattering number and atomic weight. 41 Despite a margin of experimental error of approximately 8% in their results, they judged the results favourably, in accordance with Rutherford's general physical regularity.
By contrast, Van den Broek challenged their standard of precision and their assessment of the results in support of Rutherford's empirical hypothesis. However, Van den Broek did not conclude that Rutherford's hypothesis and nuclear model of the atom were at fault. Instead, he noted that current measurements of atomic charge were largely inaccurate (up to 20% error) and that Rutherford's hypothesis was better supported, from a chemical standpoint, by using his own taxonomic hypothesis as an alternative auxiliary hypothesis. Rather than atomic weight or even Rutherford's original variable, charge, Van den Broek correlated the scattering data against his own proxy, the series number. 42 As in his 1911 letter, Van den Broek was committed to the empirical adequacy of this taxonomic hypothesis correlating atomic charge and element number, despite the error in charge measurements.
From the more accurate regularity that resulted from applying his own taxonomic hypothesis, Van den Broek drew three conclusions. First, implicit in his statement quoted above is that the match supported Rutherford's physical hypothesis in its original form (in terms of charge). Second, indirectly, the accuracy of Rutherford's physical hypothesis lent support to his general empirical taxonomic hypothesis. Third, he concluded that Geiger and Marsden's empirical auxiliary hypothesis, the Rutherford-Barkla relation, was mistaken. Given the inaccuracy and also uncertainty in atomic charge measurement, in addition to the inaccuracy and imprecision in Geiger and Marsden's weight data, Van den Broek would have assumed that the empirical relation between atomic charge and weight was itself beset by the problem of insufficient precision. Van den Broek's assessment did not rely on an explicit particular standard of acceptable error; instead, he made a comparative judgment with the more accurate application of his taxonomic hypothesis whose adequacy depended on the sufficient accuracy of the relative value of atomic charge, that is, charge differences. In a subsequent communication he noted that the uncertainty concerned the absolute values (Van den Broek 1913c, 476).

The significance of this publication, the second of 1913, does not reside in Van den
Broek's introduction of the concept of atomic number, which he did in the first publication (1913a). Here Van den Broek was committing to both key features of Rutherford's general physical model and relying on the analysis of results of its experimental test in order to support the general validity of his chemical taxonomic hypothesis about the series number of chemical elements. 43 In doing so, Van den Broek was pursuing a chemical project and applying its epistemic standards and purposes such as generality, experimental precision and descriptive order.

The December 1913 debate over intra-atomic charge: physical explanation and constitution of the atom vs chemical classification and identity
The shifting diversity of aims and standards continued to appear and play a contributive role within chemical projects. Public references are made to earlier results put to new uses only to become problematized in public debate. In a reply to Van den Broek in Nature, Soddy (1913d) purported to point to recent results in support of Van den Broek's claims. However, he altered the relation at the heart of Van den Broek's chemical taxonomic hypothesis in two connected ways. First, he presented the relation as, more specifically, one of determination. In what sense? Did he intend it to carry the same taxonomic value Van den Broek seemed committed to in the pursuit of the chemical project? That cannot be, since the numerical determination is of the nuclear charge. Descriptive or predictive, then? Likely both. Either way, it concerns the physical model of the constitution of the atom.
Second, he reversed the order of the relation from Van den Broek's claim that 'the number of each element in that series must be equal to its intra-atomic charge' to the transposed claim that an element's place in the periodic table determines an element's intra-atomic charge (Soddy 1913d, 399), thereby making the project of physical modelling the only point of discussion in his letter. No doubt, Soddy's focus is on Van den Broek's physical hypothesis about nuclear charge as an alternative to the view he attributed to Rutherford: 'Van den Broek's view that the intra-atomic charge of a nucleus is not a purely positive charge, as on Rutherford's tentative theory, but is the difference between a positive and a smaller negative charge.' 44 In a reversal of perspective, Soddy was now putting chemistry at the service of physical modeling.
Soddy believed the proof was provided by his and Fajans' recent general displacement rules for radioactive decay. The proof is indirect, because Soddy used the general rules to first test Fajans' own inference of a hypothesis about the physical constitution of the atom-'radio-active changes must occur in the same region of atomic structure as ordinary chemical changes, rather than with a distinct inner region of structure, or "nucleus"' (Soddy 1913d, 399). Soddy had appealed to the same distinction within the electronic 43 Van den Broek observed that the mass to charge ratio of many elements is higher than that of an alpha particle so, if the atom consists primarily of alpha particles, the nucleus (which Rutherford assumed to be positive) must also contain some negative charge carriers-nuclear electrons-to reduce the positive charge without changing the mass. Hence, a relation between the "permanent" positive charge on a nucleus (cf. Van den Broek 1911b) and its scattering pattern might be preserved, while allowing for deviations from the Rutherford-Barkla relation. 44 Soddy (1913d, 399), which Rutherford promptly denied; see below.
structure of the atom in a note appended to the paper on the displacement law and isotopy published in February. In that note, Soddy sought to add spectroscopy to chemical separability as an additional criterion for chemical identity and ordering. He observed that a mixture of two purported elements of distinct weights-thorium and ionium-gives a spectrum indistinguishable from a pure sample of thorium. Having discussed numerous radio-elements that are chemically inseparable from various known elements, Soddy did not offer the bald conclusion that they should be considered the same element; rather, he discussed the physical modelling necessary to motivate the taxonomic significance of spectral indistinguishability-'the spectrum does not reveal the inner constitution of the atom, as previously assumed, but only its external characteristics ' (1913a, 99).
In the main conclusion of his article, Soddy addressed a general issue of the general epistemic physico-chemical value of atomic weight. He extended the negative conclusion about its ordering value to the claim that atomic weight fails to determine, or "fix", 'all the physical and chemical properties of the elements ' (1913a, 99). As a result, he was at pains to attribute the determination of these properties-and the spectrum-to the outer electrons and distance them from the nucleus, which determines the atomic weight. Regarding spectral inseparability tracking chemical identity, next to the taxonomic value of valency, Soddy noted that 'The electrons giving rise to spectra are probably those which condition valency and chemical properties and are not what have been termed "constitutional electrons." Such "constitutional electrons" are, of course, merely a name for the material atom itself, considered apart from its electronic satellites ' (1913a, 99). Nevertheless, his attention to the structure of the atom is now explanatory; the "fixing" of chemical properties of elements he attributed, for chemical spectra and valency, to orbiting electrons has the meaning of "giving rise" to them. It is in this sense, relative to the explanatory role of atomic constitution, that the structural distinction between the nucleus and the "electronic satellites" mirrors the disciplinary distinction between physics and chemistry; although this would soon break down in December when Soddy came to see, with Van den Broek, intraatomic charge as the numerical determinant of chemical identity and general taxonomic order.
In the February article, Soddy had already considered the model of the constitution of the atom in relation to its chemical properties. It is not surprising that, in his response to Van den Broek, he directed his attention to Van den Broek's hypothesis about nuclear charge and the chemical evidence from radioactive decay and isotopy. Relative to his chemical criteria of identity, isotopy drew a line between chemical properties and physical models. According to Soddy, atomic weight, no longer a reliable tracker of chemical identity, would be instead the source of the few physical differences between isotopes. 45 It is in this late-1913 communication that Soddy introduced the term 'isotopes', however he also admits the term 'isotopic elements', indicating that he does not take the intra-atomic charge to be the sole determinant of the chemical identity of an element. 46 45 Earlier that year the fact that he was in the early stages of modifying the taxonomic criteria of chemical identity and elementarity, and hence lacking suitable terminology, forced Soddy to make statements that appear contradictory-'each known element may be a group of non-separable elements.' Likewise, he hesitated to equate chemical separability with chemical identity, employing locutions that would seem tautologies in another context, such as-'the impossibility of distinguishing between elements which are chemically identical and non-separable' (Soddy 1914c, 447). 46 Soddy (1913d, 400). There is some disagreement about when the concept of isotope came to be accepted by the chemical community. Kauffman (1986, 66-67) takes the first sign of acceptance to be Soddy and Hyman's paper to the Chemical Society of London of 7 May 1914 and notes that this report and other reports to learned societies were announced in popular newspapers soon after; he sees Richards and Lem-Meanwhile in December, Rutherford's demonstrator at Manchester, Henry Moseley (1887Moseley ( -1915, published an article with results of work from previous months, testing Van den Broek's taxonomic hypothesis of early the same year. 47 Just as Van den Broek had done in that paper, Moseley assumed the correctness of the Rutherford-Barkla hypothesis about the relation between atomic weight and charge. 48 Following Barkla in testing the interaction of X-rays with metals, his quantitative study examined the frequencies of X-rays emitted by different metal cathodes from cathode-ray tubes, finding that their energy corresponded to the atomic number of the elements in a remarkably regular way.
Unlike Van den Broek, who was using the hypothesis to meet the chemical aim of arriving at a general taxonomic order, Moseley was following Rutherford and Bohr in using chemical differences to test a general physical model of the constitution of the atom: 'We have here a proof that there is in the atom a fundamental quantity, which increases by regular steps as we pass from one element to the next. This quantity can only be the charge on the central positive nucleus, of the existence of which we already have definite proof' (Moseley 1913(Moseley , 1031.
In particular, Moseley valued in Van den Broek's hypothesis not the power for general chemical ordering of the nuclear charge, but its predictive chemical power and its physical explanatory power: 'We can confidently predict that in the few cases in which the order of the atomic weights A clashes with the chemical order of the periodic system, the chemical properties are governed by N.' 49 For N, Moseley introduced the English term "atomic number." Moseley's conclusion echoed Soddy's distinction between the electronic satellites that determine the chemical and spectral properties of an atom and its nucleus-'The very close similarity between the X-ray spectra of the different elements shows that these radiations originate inside the atom, and have no direct connexion with the complicated light-spectra and chemical properties which are governed by the structure of its surface' (Moseley 1913(Moseley , 1031. In a response of the same month to Soddy's communication and Moseley's paper, Van den Broek further pursued the discussion of the structure of the atom, distinguishing between the nuclear charge and rings of orbiting electrons and postulated the existence of both positive and negative nuclear charges (Van den Broek 1913c).
bert's paper published 14 May 1914 in the Journal of the American Chemical Society as the conclusion of this debate (1985,82). It is worth noting, however, that both Norman Lockyer, the editor of Nature, and Alexander Findlay, editor of Soddy's Chemistry of the Radio-Elements, did not hesitate to publish Soddy's claim and terminology as early as late-1913.
Footnote 46 (continued) 47 Van den Broek (1913a). Wray (2018, 214) suggests that Moseley's research was separate from Van den Broek's speculation, yet Moseley stated that his work, 'was undertaken for the express purpose of testing Broek's hypothesis, which Bohr has incorporated as a fundamental part of his theory of atomic structure' (Moseley 1914, 554). 48 Moseley's interest in the hypothesis stemmed from its place in Bohr's new quantum theory of the atom. He cites Van den Broek's article in Physikalische Zeitschrift (1913a). Bohr's opening paragraph states, 'The number of electrons in an atom is deduced to be approximately equal to half the atomic weight' but gives all credit for preceding modelling to Rutherford. Later, in response to criticism from Oxford physicist F.A. Lindemann, Moseley states that not only did he prove that Bohr's theory is correct with respect to its reliance on Van den Broek's hypothesis but that he had also proved other aspects of Bohr's work (Moseley 1914, 554). 49 Moseley (1913Moseley ( , 1031. Here Moseley is coining his version of atomic number. He defines N as tracking the place of the element in the periodic table, equal to the positive nucleus's regular increase in charge, corresponding to an integral number of fundamental charge units, not electrons.
In the context of the different chemical and physical aims of inquiry such as classification, prediction and explanation, the significance of Moseley's papers, immediately appreciated by Rutherford, rests on his attention to lighter, non-radioactive metals. His series of elements contributed evidence for generalizing the applicability of Van den Broek's hypothesis beyond the scope set by Rutherford's physical model of radioactivity and Soddy's chemical periodic law of displacement. It thus served both Rutherford's pursuit of general physical explanation and Soddy and Van den Broek's pursuit of general chemical classification.
Rutherford promptly responded to Soddy's December letter to Nature. He clarified that his commitment to the positive charge of the nucleus was to the net positive charge, compatible with different models of the composition of the nucleus. 50 Rutherford also accepted Van den Broek's rejection of the Rutherford-Barkla hypothesis as promising and pointed to Moseley's article as providing the most convincing evidence in support of Van den Broek's taxonomic hypothesis in terms of atomic number. Reversing Soddy's negative claim about atomic weight, Rutherford formulated the positive general explanatory claim that Soddy would immediately incorporate in the second edition of his book, released the following year: the atomic weight tracks the nuclear charge only approximately and is 'probably a complicated function' of it. 51 More generally, Rutherford concluded in explanatory terms, it 'would appear that the charge on the nucleus is the fundamental constant which determines the physical and chemical properties of the atom' (1913,423).
Four days later, Soddy published a response. While agreeing that Moseley's work provided independent confirmation for Van den Broek's hypothesis (at least for non-radioactive metals), he asserted that his own publication in German eight months earlier already included a diagram visualizing the taxonomic hypothesis tracking radioactive decay and displacement in terms of changes in electric charge (Fig. 2). Recall that neither in the German article nor in the British Association lecture with the same diagram, had he remarked on its significance. He added that the article also provided sufficient proof that his student, Fleck (Moseley's chemist counterpart in the developments) had provided more direct proof of the phenomenon, particularly as concerns the radio-elements (Soddy 1913e).
Van den Broek's hypothesis about the series number of elements had the form of a relation of numerical identity between the place number and the magnitude of intra-atomic charge. The relation, or correlation, makes the physical model of the atom subservient to the chemical ordering project. Likewise, Soddy, with very direct language, asserted the priority of chemists over physicists in the race to understand chemical classification and the periodic table. What Soddy did not point to was the priority of the taxonomic goal pursued by chemists such as himself, Fleck and Van den Broek nor the interest in a general explanatory model of the atom shared by physicists such as Rutherford, Moseley and Bohr. 50 Rutherford (1913). Rutherford's original model of the atom based on scattering could not say whether the nucleus was positively or negatively charged-'The deductions from the theory so far considered are independent of the sign of the central charge, and it has not so far been found possible to obtain definite evidence to determine whether it be positive or negative' (Rutherford 1911, 688). As late as April 1913, Geiger and Marsden, of the Rutherford research group, were uncertain as to whether the nucleus was a small dense mass of positive or negative charge (Geiger and Marsden 1913, 605). 51 Rutherford (1913, 423). Recall that Soddy admitted that a few physical properties depend on mass, namely those that differ between isotopes.

The larger picture: shifting chemical criteria of identity and classification and physico-chemical collaboration
In the second edition of his book, finished by the end of 1913, Soddy (1914a) surveyed radioactivity research and the general significance of the results for the project of chemistry defined around classification, or chemical identity, and generalization (beyond series of radioelements). He now offered a picture of change that enshrined the new application of his taxonomic aims and standards in chemistry.
The change must be related to his earlier statement of the old standard of chemical identity, first challenged by radioactivity research and disintegration theory. He claimed that the underlying concept of an element was and remains, 'the possession of a unique chemical character, distinguishing it and sufficing for its separation from all other elements.' 52 By the early twentieth century, this meant a standard set of reactions that amounted to testing the relative solubility of metal cations and this is what Rutherford and Soddy meant when they used the term "chemical analysis" in their early papers. 53 Hence, Soddy declared that, 'The chemical analysis of matter is thus not an ultimate one. It has appeared ultimate hitherto, on account of the impossibility of distinguishing between elements which are chemically identical and non-separable ' (1914c, 447).
The atomic number hypothesis introduces the new general standard of identity in relation to place, which is now tracked by 'successive unit increments in the nett positive charge of the atomic nucleus, from 1 to 92' (Soddy 1914a, 10). In the new second volume of his textbook, Soddy republished the diagram with the reference to negative electrons tracking decay transformations and displacement laws (1914b, 3).
Atomic number tracks the new explanatory standard, nuclear charge, which unifies chemical and physical properties. Soddy (1913a) echoed Rutherford's general statement in the December letter to Nature in explanatory terms of "determination", stronger than his own accounting term "fixing", with a taxonomic function. Here he expressed the new general claim, now also about the explanatory role of nuclear charge, in terms of "control": The atomic number-that is, the magnitude of the central positive charge on the nucleus-rather than the mass controls the chemical and physical properties of the atom, so that atoms of different masses but of identical atomic number are identical in chemical properties. (Soddy 2014a, 11) He also suggested the explanatory relation of conditioning: 'It is probable that it is the nett internal positive charge of the nucleus of the atom, and not its mass, which conditions its chemical properties' (Soddy 2014a, 51).
But the disciplinary dichotomy between chemical and physical properties cannot be mapped on to the new structural atomic dichotomy between nucleus (or nuclear charge and mass) and orbiting electrons, at least not as neatly as he declared in the letters to Nature of late 1913. The classification in the structure of the atom requires a distinction between the nucleus and the outer electronic shells or rings: Whereas all the older phenomena encountered in the study of matter are concerned solely with the negative electronic outer system, and usually only with the outermost ring or shell of it, the newer phenomena of X-rays and radioactivity are concerned with the innermost region and the positive nucleus respectively. (Soddy 2014a, 10-11) That Soddy was interested in presenting the generalizations as significant for chemistry beyond radioactivity is clear also from a section titled 'The Relation between Radio-Chemistry and Chemistry'. The chemical perspective is expressed there in relation to the project of classification: Uppermost in the mind of anyone approaching the subject from the point of view of chemistry is the question as to how far such knowledge as can be acquired of the chemical properties of these short-lived radio-elements can be accepted literally, and used as a basis of classification of the radio-elements in the same way as the common elements have been classified in the Periodic Law, for example. (Soddy 2014a, 43) Throughout 1913, in the different articles establishing isotopy and displacement rules, Soddy pointed to the generalizability of the shifting taxonomic standards and relations, as suggested further by Moseley's results on lighter, non-radioactive metals. Generality and classification-order and identity-constitute the epistemic chemical perspective. The possibility of a new taxonomic generalization in the form of invariant order rather than invariant substances was suggested by the displacement rules (first hinted at in the first edition of Soddy's book in 1911) tracking change rather than general order, although in the partial form of an ordered (disintegration) series: Since then, the increase in our knowledge of the successive products in the disintegration series, of their order of sequence, and of their chemical character, has resulted in a complete generalisation being established connecting the position of the radio-element in the Periodic Table, and the nature of the change in which it is produced. (Soddy 2014a, 48) The new standard of chemical identity distinguishes identity from element, and Soddy straddled the conceptual gap between the older and new conception of element by making the term element the narrowest-referring to type of elements-and allowing chemical identity-as seen through position in the periodic table-to be a superset: 'The separate places in the Periodic Table thus do not correspond with single elements, necessarily, but with single chemical types of elements' (Soddy 2014a, 50). By 1919 Soddy had reversed the definition of element, making it synonymous with atomic number and position in the periodic table and instead describing individual isotopes as "types of matter"-'In the ten occupied places are forty-three distinct types of matter, but only ten chemical elements' (1919,17).
The new standard of chemical identity was tracked by place and explained by electronic properties of the atomic structure rather than weight. Notice that atomic number carries taxonomic value, but no explanatory value. Place is operationalized in terms of experimental procedures as chemical separability, and secondarily in terms of spectral separability. The new identity, unlike the older, invariant notion, is linked to change and complexity. The link with change was the lesson for chemistry that Soddy derived in 1903 from disintegration theory. 54 Identity was linked to place, and no longer atomic weight, and place included shared chemical properties: 'All the elements in the same place exhibit identical chemical properties. For this reason these are called "isotopes"' (Soddy 1914a, 50-51). Identity, then, also included differences. Complexity is the lack of homogeneity in chemical matter associated with identity and place. In his paper of February that year, Soddy (1913a) phrased it in terms of a 'mixture of non-separable elements'; in his presentation to the British Association in September he spoke of complexity: 'matter is even more complex than chemical analysis alone has been able to reveal ' (1914c, 447). As he put it in his most recent statement, in the second edition of his book: 'Chemical analysis may not be an analysis of matter into atoms homogeneous as regards mass, but rather homogeneous as regards the nett nuclear positive charge ' (1914a, 11).
In 1919 Soddy introduced a more nuanced and inclusive characterization of identity, or character: The non-separable elements, with identical chemical character, on this scheme were found to occupy the same place in the periodic table, and on this account I named them isotopes. Conversely, the different elements recognized by chemical analysis should be termed "heterotopes," that is, substances occupying separate places in the periodic table, but themselves mixtures, actually proved or potential, of different isotopes, not necessarily homogeneous as regards atomic weight and radioactive character, but homogeneous as regards chemical and spectroscopic character, and also physical character, so far as that is not directly dependent on atomic mass. 55 The result of the new representation of chemical change and identity is the new general classificatory order tracked by the atomic number: 'The successive "places" in the Periodic Table correspond with unit differences in the nett charge of the atomic nucleus, and the identity of this charge is all that is implied by chemical proof of homogeneity. This charge changing unit by unit gives us the periodic table of elements' (Soddy 1914a, 51).
Soddy's disciplinary chemical perspective relies on a number of aims and standards linked to atomic number: identity (homogeneity, stability) linked to classification order, predictive and explanatory values of atomic number and isotopy. Atomic number and isotopy sustained the fixed notion of chemical identity in the faces of the radioactive break between chemical identity and physical individuality of chemical atoms. The history we have been tracking also shows they are attached in complex methodological ways to evolving physical models of the atom -especially the nuclear charge, which atomic number tracked. Chemical distinctions are inseparable from chemical practices and physical atomic modeling. However, for Soddy, the physical model was relevant as a model of the chemical type and not of the individual atom, which radioactive disintegration showed to have mutable chemical identity. In this sense, chemical identity and taxonomy were not merely 54 This link between atomic number and identity change would evaporate in 1920 when Aston demonstrated the isotopy of non-radioactive elements. Using his newly invented technique of mass spectrometry, he confirmed the existence of two distinct isotopes of neon and four of chlorine. Moreover, he declared that, although they could be averaged to give the accepted value, none of his isotopes matched the chemically determined mass exactly (Aston 1920). He would be credited with the "whole number rule", which described the striking empirical regularity of atomic masses, in an era before the Rutherford atom's mass came to be the mere sum of protons and neutrons. 55 Soddy (1919, 15). In a further qualification, he noted that isotopes need not have different atomic weights (at 22). conventional, or purely experimental. But they were not fully reducible to physical structure either.
For Soddy, the nucleus carried taxonomic and explanatory value, but subject to structural distinctions in the model of the atom (1913a, 99). The nucleus determines chemical identity through atomic number, tracking net nuclear charge, while the outer electrons determine chemical properties and inner electrons determine the X-ray spectra; but he did not provide a detailed connection between them. 56 In a series of papers on the structure of the atom published in 1914, Rutherford readily accepted the notions of atomic number and isotopy and drew general lessons. For Bohr and Rutherford there is a chain of mechanisms determining both physical and chemical properties at various levels: the atomic number determines the total number of electrons; Bohr, applying Max Planck's notion of quantum of energy, describes the configuration of these electrons in shells, which determines the chemical and spectroscopic properties. 57 These spectroscopic properties and molecular structures that Bohr's more comprehensive atomic model could explain added taxonomic value and contributed to the domain of chemistry in a qualitatively different way from merely defining the identity of each element -quantum physics could now underwrite the chemical field of spectroscopy. Thus for the physicists, there is a structural and explanatory unity in the way the atomic model determines the known properties of matter. 58 By 1914, Rutherford and Soddy had concluded that physical atomic structure has explanatory value in chemistry. The explanation depends on connecting the role of the nucleus with the role of electronic configuration. The latter was provided by Bohr, who explained the mechanism by which electrons produce the spectral properties of elements. The former was claimed by Van den Broek, Soddy and Rutherford, who appealed to nuclear charge to explain chemical difference-or identity-for the purpose of classification. Bohr's quantum explanation supported the promise of a wider physical explanatory role for electronic configuration, but neither Van den Broek, Soddy nor Rutherford pointed to a specific example of electronic explanation in chemistry beyond Bohr's case of spectral properties. 59 Either way, their black-boxed commitment to the explanatory value of nuclear charge supported by its role in determining chemical identity, and thereby 56 N.B. Rutherford's model of the atom at this time necessitated that some electrons reside in the nucleus in order to cancel out some of the positive charge of the alpha particles and hydrogen ions. Even after the concept of the proton was introduced, "nuclear electrons" were required to balance the charges and mass. 57 'It is clear on the nucleus theory that the physical and chemical properties of the ordinary elements are for the most part dependent entirely on the charge of the nucleus, for the latter determines the number and distribution of the external electrons on which the chemical and physical properties must mainly depend' (Rutherford 1914, 497). 58 Bohr's determination to use his structural model in the context of his quantum theory to explain chemical features reached beyond Rutherford's project and the limits of his simpler model (Kragh 2020, 8). The nuclear model served the purpose of explaining physical scattering data and, by correlation, explaining chemical classification and identity in terms of nuclear charge (Kragh unduly underplays this aspect of Rutherford's model). By 1913, Rutherford was pointing to Bohr's new model to pursue stronger explanatory connections to chemistry. Both had also successfully placed chemistry at the service of physics and valued that connection (Kragh 2020, 8). Kragh calls Rutherford's attitude to chemistry ambiguous, noting the ironic tension between his rating of chemistry below physics and his collaborations, contributions and awards (2020,13). 59 The first glimmer of an explanation of chemical bonding came from Irving Langmuir in 1919-'The properties of the atoms are determined primarily by the number and arrangement of electrons in the outside shell and by the ease with which the atom is able to revert to more stable forms by giving up or taking up electrons' (Langmuir 1919, 933). chemical properties, would have relied on the mediating explanatory role for electronic structure. The explanatory and the taxonomical successes of physical atomic structure were inseparable.
For Rutherford, the value of chemical and radioactive phenomena rests on contributing to the general descriptive and explanatory power of evolving atomic theory. By contrast, for Soddy, the epistemic and methodological value of generality he sought to serve was embedded in the chemical perspective, it took the form of general validity of chemical rules and standards and was tied to a chemical classificatory aim. Yet, for their respective successes, both aims and both disciplines relied on each other.

Epilogue: the element concept
Readers will no doubt be aware that the Rutherford model of the atom presented here was further streamlined with the discovery of the neutron in 1932-nuclear charge was thus reduced to the number of protons and isotopic mass, rather than being 'a complicated function' of nuclear charge, could now be calculated as a simple sum of the parts. Nevertheless, neither the elegance of this model nor the now clear and distinct notion of atomic number was enough to convince all chemists that the concept of a chemical element-with all its historical baggage-had been resolved once and for all. 60 In his attempt to address Fajans' concerns that isotopes may not be the same element for all intents and purposes, Whereas 61 Austrian chemist Friedrich Paneth stumbled upon duelling definitions of the term "element", which he argued were both true meanings (Paneth 1962(Paneth [1931). This has come to be regarded as one of the key problems in the philosophy of chemistry (Scerri and Ghibaudi 2020). We acknowledge that the concept of a chemical element was reproblematised by Paneth soon after, but our account of chemists working in the field of radioactivity from 1900 to 1915 stands on its own.
Few others motivate their discussion of the Paneth problem with an account of atomic number beyond a simple statement that Moseley replaced atomic mass with atomic number; this includes but is not limited to Kuhnian approaches. 62 We have avoided collapsing these discoveries in a way that suggests a gestalt switch, leading immediately to a mid-twentieth-century model of the atom -as glossed over by Kuhnian accounts such as Brad Wray's. 63 The question of the connection between atomic number and elemental identity has even become another battle-ground between revolutionary and continualist 60 'The second phase in the development of radioactive change has now negatived each and every one of the conceptions of last century that associated the chemical element with the atom. The atoms of the same chemical element are only chemically alike' (Soddy 1919, 26). 61 Whereas Hevesy was content to connect atomic number to chemical properties via interchangeability-'two atoms can replace each other chemically without having all properties in common' (Hevesy & Paneth 1914, quoted in Kragh 2000, Fajans criticised this stance for ignoring the fact that the different physical properties of isotopes affect their thermodynamic behaviours. 62 Moseley was the first to use the term "atomic number" in English but some more popular histories have confused the term with the concept. Joseph Earley's paper in Scerri and Ghibaudi (2020) condenses the decay series, isotopes of lead and the discovery of isotopes through X-ray spectra to a mere paragraph. Kragh (2020) gives a history of the change that is insightful but lacks details. 63 '[The discovery of atomic number] required some significant reconceptualizations, including the realization that the atomic weight of an element is determined, not only by the number of protons in an atom, but also by the number of neutrons' (Wray 2018, 214). historiography (Vogt 2017(Vogt , 2018Scerri 2018Scerri , 2021Wray 2022). Approaches to the history of science featuring significant lacunae can easily bias the philosophical lessons drawn from them. To treat atomic number as a concept that appeared fully-formed favours a particular view but this cherry-picking and neglect does not do justice to the actual processes of science. 64 By identifying and examining neglected changes we are contributing efforts towards remedying the situation.
Both the present paper and our forthcoming article show how the fields of physics and chemistry converged on radioactive phenomena and developed a theory of disintegration to understand it. Researchers in this new field had been trained in different disciplines and retained those identities while collaborating to produce joint understandings. The discovery and understanding of various phenomena shook and transformed chemistry and physics differently (the disintegration of the atom and isotopy violated some long-held assumptions within chemistry, while the energy produced by radioactive decay was a significant puzzle for physics until solved by relativity theory). This is anathema to a strict Kuhnian view of revolution, wherein anomalies appear in a discrete and comprehensive paradigm and each paradigm is incommensurable both with the ones that precede or succeeded it and with parallel disciplines. 65 Chemistry and physics formed a hybrid field with distinct projects for a time but, after certain key concepts were considered resolved and their territories were clarified, they proceeded separately once again, while retaining and further exploiting the newly accepted explanatory relation between them.
An alternative historiographical approach is Scerri's attempt to provide a story of lesserknown scientists who made discoveries that proved crucial for the overall progress of science is an attempt to replace elitist "great man" history by a more inclusive history of science. 66 His efforts here are misdirected: the present article demonstrates how speculative and uninformed by physics Van den Broek was when compared to Soddy and his team. If anyone gets more credit than they deserve, it is Moseley, whose contribution was to experimentally confirm Van den Broek's hypothesis; yet Scerri (2007Scerri ( , 2014 gives him almost as much credit as Van den Broek at the expense of figures who have rarely been given the prominence they deserve by historians of science, such as Soddy (who did receive the recognition of his peers in his lifetime in the form of a Nobel prize).
Our version of Soddy's collaboration with Rutherford and his rivalry with Fajans and Hevesy, is a more faithful account of how chemistry developed its own concept of atomic number, informed by but not beholden to physics. Along the way, different and competing aims and standards of taxonomy appeared distinguishing different disciplines and enabling their productive interaction.
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