60 Bull. Hist. Chem. 4 (1992-93)
PERSPECTIVES LECTURE
Precursors and Cocursors of the Mendeleev Table: The Pythagorean Spirit in Element Classification
0. Theodor Benfey, Chemical Heritage Foundation
The ancient Pythagorean faith in simple numerical patterns as guides to the structure of the natural world constantly reap- pears in science. The Pythagoreans worshipped numbers and l t r n l l t S r by numbers they meant whole numbers - integers. Since two points can define a line, three a plane and four a three- l t b ld n bl f r th l t r l tr n l nd th r dimensional body, they believed all reality could be subsumed by whole numbers and geometry. The Cubist movement in art four elements, the fifth element was relegated to the heavens. hints at the Pythagorean vision. That vision, that religious It was a logical assignment since the behavior of celestial movement, was shattered by the discovery of irrationals, bodies differed from that of objects on earth. Since the natural unreasonable quantities that were incapable of being expressed motions of earth, air, fire and water when displaced from their as ratios or other combinations of whole numbers. The square normal abode were rectilinear, returning to their "proper" root of 2, the reciprocal of 7 and the ratio of the circumference place, celestial motions, which were circular rather than linear, to the diameter of a circle are examples. must be due to a different kind of stuff, of which the heavens The simplest Pythagorean principle is the search for iden- were made. Behavior was seen as integral to an object, not tity. The identity of the velocity of light and of electromagnetic something imposed upon it. waves united optics and electromagnetic theory. The next Plato in the Timaeus spells out the identification of regular simplest is the identity in the number of members of two sets. solids with the elements of antiquity. The atoms of fire are the The four elements of Empedocles - earth, air, fire and water - sharpest, hence tetrahedra; the next sharpest are octahedra found a counterpart in the discovery of four regular solids - the which are assigned to air since it too can slip through very small tetrahedron, octahedron, icosahedron and cube. The belief interstices. Earth is the most stable, hence corresponds to the grew that there must be a connection between them. When the cube. The dodecahedron is the closest to the sphere, thus fifth (and last) regular solid, the dodecahedron, was discov- fittingly belonging to the heavens, leaving the icosahedron as ered, a fifth element was postulated that corresponded to it. It the form of the atom of water. became the quintessence, the fifth essence, the ether of antiq- We need to recognize the genius of Plato's view. First it uity. Since terrestrial events were sufficiently described by the accounted for transmutation. Since tetrahedra, octahedra and icosahedra were all made from equilateral triangles, they could be taken apart into their constituent triangles and reassembled into new forms. These transformations were quantitative. The eight faces of two tetrahedra can be taken apart and reas- sembled into those of one octahedron. One water particle (20- sided icosahedron) can be changed into two air particles and one fire particle. We have here a universe made up of a small number of particles which, by rearrangement, make up the phenomena we observe. It is the form of the descriptive pattern we now use in describing nuclear transformations. The more commonly accepted precursor of modern atomic theory, the atomism of Democritus and Leucippus, had neither of these two key characteristics. Those thinkers postulated an unlim- ited number of different atoms and had no quantitative predic- tive theory for explaining change. The second of Plato's contributions to element theory is more speculative. Karl Popper has suggested that Plato's choice of atoms was designed to overcome the Pythagorean scandal. Plato's atoms were actually the half-equilateral tri- angle (for tetrahedron, octahedron and icosahedron) and the h f v r l r p l h dr r l t n l d half-square for the cube. These two triangles have sides in the
Bull. Hist. Chem. 4 (1992-93) 61 ratios of 1, 2, I3 and 1, 1, q2 respectively, thus incorporating two of the Pythagorean irrationals into the fundamental build- ing blocks of nature. Popper further suggests that the hope existed that all irrationals could be derived from 42 and '43. Their sum, for instance, to four significant figures is 3.146, a figure within the limits of accuracy of the calculation of it of that era (1). Thus irrationals, though not exactly banned from the universe, were at least tamed. They were incorporated into the building blocks of nature. The dream of finding a numerical pattern to the phenomena of nature lay in abeyance for centuries. Although the was the only dialogue of Plato translated into Latin during the ancient period, the sections of the dealing with the regular solids were not included in the early Latin versions (2). The prevailing description of terrestrial nature throughout the medieval period was the qualitative Aristotelian world-view. Mathematical perfection could only be found in the heavens. Only as we enter the period of the Renaissance do we again find significant attempts to correlate what we would call chemical events with numbers. The most famous Pythagorean or Neoplatonist of the Ren- aissance was no doubt Johannes Kepler (1571-1630). His most celebrated attempt to apply the Pythagorean vision was his rationalization of the sizes of the planetary orbits by inscribing and circumscribing the orbits with the Platonic solids. But Kepler did not confine his interest to the heavens. In his work,
h S x C rn r dSn fl , he proposed an essentially modem explanation for the snowflake's shape in terms of the packing of spheres. L. L. Whyte, in the preface to the new edition of Kepler's booklet, describes it as "the first recorded step to-
K pl r f ph r p n t xpl n r t l f r wards a mathematical theory of the genesis of inorganic or organic forms (3)." The iatrochemist William Davisson (1593-1669) was equally convinced that number and geometry were the key to under- standing nature. One of two engraved plates in his élé n d l ph l ph d f rt d f h of 1651 shows the Platonic solids followed by 15 other geometric forms. The opposite page shows natural forms - crystals, flowers, leaves and the beehive hexagon, to illustrate the Biblical phrase writ- ten in Latin across the center of the page: "all is disposed in measure, number and weight." The Pythagorean fascination with integers makes a perma- nent reentry into chemistry with John Dalton's (1766-1844) l n t r rb t nd th r l r l d chemical atomic theory. Antoine Lavoisier's (1743-1794) (fr K pl r M t r r ph f 159 emphasis on weight relations led logically to the determination ll t Ch 4 (199 -93
of percentage compositions. But what assurance of being on the right path of theory is contained in the fact that the lower oxide of carbon contains 57.1% oxygen while carbonic acid gas contains 72.7% oxygen? Dalton's atomic theory gave a visualizable model for the Pythagorean law of multiple propor- tions: For two compounds of elements A and B, the weights of A combined with a fixed weight of B are in the ratio of small whole numbers. Thus, recalculating the composition data, 1 g carbon combines either with 1.33 grams of oxygen or 2.66 grams of oxygen, an integral ratio of 1 to 2. Another Pythagorean pattern was proposed within six years of the completion of Dalton's book S t f Ch l h l ph . In 1816, the physician William Prout (1785- 1850), whose quantitative analysis of natural urea was used by Friedrich Wöhler (1800-1882) to compare it with the urea he had accidentally made synthetically, pointed to the remarkable fact that most atomic weights used at that time were close to integral multiples of the atomic weight of hydrogen. That particular Pythagorean venture has, of course, had a checkered history, being espoused by some, such as Thomas Thomson (1773-1852), as true, by others, such as Jean-Servais Stas (1813-1891), as pure illusion, while Jean-Charles Marignac (1817-1894) accepted it as an ideal law analogous to the ideal gas laws and Dmitri Mendeleev (1834-1907) hinted at a mass- energy interconversion to account for the deviations. There can be little doubt that Prout's proposal acted as a most powerful stimulus to accurate atomic weight studies and en- couraged others to look for additional numerical patterns in the atomic weights slowly being accumulated. Even if Prout's simple proposal had been right, if all atoms were in fact aggregates of hydrogen atoms, such a conclusion would have done little to illuminate the richness and diversity of chemical behavior. It certainly was not the final clue, because the elements then would only differ quantitatively and progressively as their atomic masses increased. Johann Wolfgang Döbereiner (1780-1849) from 1816 to 1829 searched for numerical relations between similar elements in the same l t fr W ll v n Les élémens de la philosophie de l'art way that the Pythagoreans sought number patterns relating the du feu ou chimie h n n t r l f r th h p l r t th lengths of strings producing harmonious chords. Döbereiner's f r l r l d triads not only demonstrated such arithmetic relations but thereby suggested unit building blocks converting atoms of (of 14) in these weights suggested that perhaps organic radicals lithium to those of sodium and hence to potassium, or calcium held the clue to the internal structure of inorganic atoms. Jean- to strontium and then to barium. Döbereiner was influenced by Baptiste André Dumas (1800-1884) and Justus Liebig (1803- the Romantic movement and t rph l ph which had 1873) had already proposed in 1837 that organic radicals play been flourishing in Jena around 1800, a decade before Döbere- in organic chemistry the role played by atoms in mineral (or iner' s arrival. "His predilection" according to Alan Rocke, inorganic) chemistry (6): "was toward a Pythagorean synthesis, the mathematization of nature" (4). In n r l h tr th r d l r pl ; n r n h tr th The idea of unit building blocks gained support from Max r d l r p nd; th t ll th d ff r n h l f Pettenkofer (1818-1901) who pointed to the analogy between b n t n nd f r t n r th r th n th t an atomic weight series of similar elements and the pattern of br n h f h tr molecular weights in organic homologous series (5). Thus CH = 16, C2H6 = 30, C 3H = 44, etc. The common increment What Pettenkofer was now proposing was that the radicals or ll t Ch 13-14 (199 -93 3 atoms of mineral chemistry were not simple - they were as bl 1 n l b t n f l f h l l nt compound as were organic radicals because the same mathe- nd h l r f r n r d l matical patterns occurred in the unit masses of both. Dumas developed these ideas about the composite nature of atoms independently in 1851 in a speech before the British Association for the Advancement of Science but only pub- lished them six years later (7). His parallel tabulations of organic radicals and families of elements (Table 1) show that he had freed himself from Döbereiner's preoccupation with sets of three elements, and that he was developing the families of elements as they would later be incorporated in the periodic table. John Alexander Reina Newlands (1837-1898) broke away from searching for numerical patterns in the atomic weights of similar elements and proclaimed instead a pattern for all elements, similar or dissimilar. He did not need the actual values of atomic weights; all that was needed for his law of (1826-1910) speech and pamphlet. Meyer later wrote how, on octaves was a rank order, the ranking of elements in order of reading the booklet, "the scales fell from my eyes and my increasing atomic weight. In some of his earlier tables New- doubts disappeared and were replaced by a feeling of quiet lands left gaps for missing elements - Mendeleev certainly was certainty." His Moderne Theorien was a direct outcome of that not the first to do this - but by 1864 he had found an arrange- experience. Calculating all atomic weights according to ment not requiring gaps and obeying his now famous law of Cannizzaro's principles, he arranged them by increasing atomic octaves, though he did not give it this name until 1865 (8). On weight and in families, and calculated the increments of weight presenting it at a meeting of the London Chemical Society, the from each atom to the next similar one. So far nothing was British chemist George Carey Foster posed the immortal ques- new. But when we look at the table he published of 27 elements tion of whether a similar pattern might exist if elements are arranged in this way, three remarkable facts stand out: arranged alphabetically. Carey Foster clearly did not compre- 1. He leaves a gap between silicon and tin and estimates the hend the essence of the Pythagorean discovery - that numerical atomic weight of the missing element to be 28.5 + 44.55 order lies in the essence of things while alphabetical order is 73.05. Germanium's atomic weight was later found to be man-made and arbitrary. What Newlands discovered was an 72.59. Newlands had also done this in 1864. orchestration of the elements, a periodicity, a repetition com- 2. He places tellurium before iodine in spite of the fact that bined with novelty, the essence of all musical composition. It its atomic weight, 128.3 is greater than that of iodine (126.8). would have delighted Pythagoras (9). Newlands also did this. And yet something was missing. Except for the atomic 3. Most impressive of all, he places at the heads of the weight order, why do the alkaline earths follow the alkali families the notations 4-werthig, 3-werthig, 2-werthig, l-wer- metals rather than the halogen family? Was there any intrinsic thig, l-werthig, 2-werthig, that is successive valences of 4, 3, pattern that linked elements of different families, that would 2, 1, 1, and 2. These are the valences toward hydrogen, the show an essential order to the relation among families? The number of hydrogen atoms that attach themselves to an atom year 1864, the same year as Newlands' law of octaves, saw the of the element. publication of the first edition of Julius Lothar Meyer's (1830- The fact that water was 14 O and not HO, and that oxygen 1895) Die Modernen Theorien der Chemie (10). Meyer was therefore was divalent, was not universally accepted until after fascinated by Prout's hypothesis, by Döbereiner's triads and the Karlsruhe Congress. Within organic chemistry, Avogadro's by Pettenkofer and hypothesis (based on Dumas' analogies be- that other Pythagorean tween chemical ele- law - Gay-Lussac's law ment families and or- of combining volumes) ganic homologous se- had been widely ac- ries. He had attended cepted particularly by the Karlsruhe Congress Auguste Laurent (1807 in 1860 as had Men- -1853) and Charles- deleev. Both had been Frederic Gerhardt deeply influenced by (1816-1856) in their Stanislao Cannizzaro 's l nd bl f O t v f 1 5 thorough reexamina- ll t Ch 13 14 (199 -93 tion and reorganization of organic theory. Alexander William- property. The only places where sets of new elements could be son's (1824-1904) studies of ethers had established the water located would be at the beginnings and ends of each horizontal type and divalent oxygen, August Wilhelm Hofmann's (1818- series, or at the beginning of the whole list or beyond the 1892) amine work did the same for the ammonia type and the heaviest element. Meyer organized 21 other elements in seven trivalence of nitrogen. Friedrich August Kekulé (1829-1896) further families which can be appended to the earlier table but in 1857 rescued organic radicals from being looked at merely do not show the stepwise change in valence. They are all as good substituents in inorganic type formulas, and estab- transition metals. lished methane as the parent type of all carbon compounds and No one, it seems, suspected that from a purely numerical hence gave carbon a valence of 4. Laurent and Gerhardt point of v there was in fact one other place for new elements accepted and universalized Avogadro's conclusion beyond the - between the two univalent families, a family of valence zero. ready applica- The absence bility of Avo- of any expec- gadro's hy- tation of such pothesis. a family re- They tended minds us of to assume that the centuries all elements, that it took not only the before the common zero symbol gaseous ones, was intro- were com- duced into the posed of dia- Hindu-Ara- tomic mole- bic numeral cules. With notation - be- that assump- fore zero was tion formulas recognized as of numerous a number. inorganic Mendel- compounds eev's periodic looked most table of 1869 unlike the for- was charac- mulas of to- terized by his day. Canniz- successfully zaro's reform arranging ll introduced th elements two other ma- into one table jor criteria for th r M r t bl f 1 and in demon- atomic weight stratin g that determinations, particularly useful for elements that do not periodicity holds throughout. His 1871 table clearly indicates readily form gaseous compounds. Besides Avogadro's hy- that valence periodicity, by integer-unit steps, applies to all pothesis, he used as guides the law of Pierre-Louis Dulong elements. (1785-1838) and Alexis-Thérèse Petit (1791-1820) and Eil- It appears that Mendeleev was extremely skeptical of any hard Mitscherlich's (1794-1863) law of isomorphism. Pythagorean or Proutian implications of his work, considering Meyer's book in its first edition was in large measure a them mere utopias. Yet he did much to suggest their signifi- detailed exposition of the application of these three methods. cance (11). With them formulas could now be confidently established, and There seems to be no question now that Meyer and Men- when they were examined a new pattern emerged. The deleev independently discovered the periodic law. For a elements from carbon to magnesium change by one valence number of years a somewhat bitter debate raged between Men- unit, decreasing first to unity and then increasing again. The deleev and Meyer regarding the original contributions of each same pattern recurs from silicon to calcium, from arsenic to to the chemical literature. Meyer's paper was submitted in De- strontium, from tin to barium. No element is expected to be cember 1869 and published in March 1870 (12) and refers to found between any pair of successive elements, for valence can the brief German notice of Mendeleev's longer paper in Rus- only change by integral steps. It was a true Pythagorean sian (13). Meyer, in that paper, published the atomic volume Bull. Hist. Chem. 4 (1992-93) 65
C
6C
C
4
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th r M r t v l v r t ht rv r dr n b h l t r th Philosophical Magazine in 1 curve for which he is most generally remembered. However, ing almost all known elements, arranged by increasing atomic we need to recognize that Mendeleev as well as Meyer in their weights and in periods, with the A and B subgroups separated, classic papers discuss both atomic volume and other properties and with a gap left between silicon and tin suggesting the fu- which vary periodically as atomic weight rises. ture discovery of germanium. Meyer's table places lead Meyer begins his paper with the assertion that it is most im- correctly below tin (column 8) while Mendeleev had put it probable that the chemical elements are absolutely undecom- with calcium, strontium and barium. On the other hand, hy- posable and mentions Prout, Pettenkofer and Dumas as precur- drogen, boron and indium are not on the table, presumably sors of this idea. because Meyer did not know where to locate them. The 1868 In 1893, two years before Meyer's death, his successor, table was published posthumously by Karl Seubert, Meyer's Adolf Remelt, at the School of Forestry in Neustadt-Ebers- successor in Tubingen (14). Mendeleev and Meyer were walde, showed him a handwritten draft of a periodic table which recognized as independent developers of the periodic table of Meyer had given to him in July 1868 and which was intended the elements by the Royal Society of London when they were for a new edi- both award- tion of the ed the Davy Mod erne medal in Theorien. 1882. Meyer had to- The Peri- tally forgotten odic Table the existence was not by of this draft any means since, after the final tri- Mendeleev's umph of the 1869 paper, it Pythagorean had to be dream in ele- redone. It de- ment classi- monstrated fication. clearly Mey- Prout's hy- er's independ- pothesis was ent arrival at a shown to be table contain- essentially ll t Ch 13-14 (199 -93 correct as far as the weights of individual nucleides were con- S t f Ch l El nt : A t r f th r t ndr d Y r , cerned. Non-integral atomic weights are mainly due to the El v r A t rd 19 9 presence of isotopic mixtures in the usual samples of elements. 1 M r M d rn n h r n d r Ch , M r h The ordinal number of Newlands' "rank order" of elements nd r ndt r l 1 became identified in 1913 by Henry Gwyn-Jeffries Moseley 11 M Kn ht h r n nd nt l rt fCh tr , n (1887-1915) with the number of increments that the square l t n K nt 197 p 5 root of the frequency of X-rays must be shifted to predict the 1 M r " t r d r h h n El nt l n t n correct X-ray frequency for a given element (15). The ordinal hr r At ht " Ann S ppl., 1870, 7 35 -3 number became the atomic number, the integral positive charge 13 I M nd l v " h l t n t n th r p rt nd th and number of protons of an atom's nucleus and the number of At W ht f th El nt " h rn l f z h h electrons surrounding it. But these Pythagorean identifica- b h tv , 1869, , -77 ( n n ; br f G r n tions once again did not account for the diversity of chemical b tr t f th p p r pp r d "U b r d z h n n d r properties. That was achieved by arranging the electrons in E n h ft n z d n At ht n d r El nt " Ch ., superbly simple Pythagorean patterns, by recognizing that 1869, 2, 5- similar chemical properties imply similar arrangements of 1 K S b rt " r G h ht d p r d h n S t " electrons. We are the true inheritors of an idea 2500 years old n r . Ch ., 1895, , 33 -33 - that the properties of the elements are the properties of 15 G- M l " h h r n Sp tr f th numbers (16). El nt " h l. M ., 1913, [6 26, 1 -1 3 1 S n r t n th r n l dr ft f th l t r v r l dd t n l References and Notes r f r n h v t tt nt n W n n "Cl f t n S tr nd th r d bl " C p. & M th . th Appl ., A n l d nt : An rl v r n f th p p r pr nt d t th 19 1 (// 7-51 h x n d th tr t r nd d v l p nt M nd l v S p b r 19 9 Ann l M t n f th f th p r d t bl n th l ht f d r n f nt p r r A r n A t n f r th Adv n nt f S n It th t l n pt h b rv t n h v b n f rth r x- r n ll pr p r d f r p bl t n t h n r th h t nd h l p nd d th n n h t r l nt xt n h r r d t A fb : d t r n ld G ll p n h 5th b rthd b t n d r d lv t r n th t r nd t r f th r d , b d t h t r l f r th p l ( v b r 19 9 f th C n d n n l t r v n t th 1991 n C nt r W r h p n th rn l f Ch tr p bl h d n h h n r t r f Ch tr nd t th 199 W dr W l n In t t t t 1 K pp r " h t r f h l ph l r bl nd th r r n t n nd d t b p bl h d n xt r Al f r t nt r t t n S n " r t. . h l. S ., 1952, , 1 -15 t d n S th p p r b E Strö r " Ordn n d r El nt Ent t h n nd l n nd G df ld h Ar h t t r f M tt r, rp r nd d t n d r d n t " n W S dn Opf r h nd Y r 19 p A S h n d Ch Sp l d r hrh nd rt , Un v r- G S rt n Intr d t n t th t r f S n , l 1 tät v rl Ul 199 pp 7-79 C rn In t t t n W h n t n C 19 7 p 113 3 K pl r h S x rn r d Sn fl (1 11 d t d nd tr n l t d b C rd Oxf rd Un v r t r 19 p v Theodor Benfey is editor for the Chemical Heritage Founda- A 1 " h pt n f Ch l At n tion, 3401 Walnut Street, P hiladelphia, P A 19104 , and Adjunct G r n " I , 1979, 0, 519-53 Professor at the University of Pennsylvania. Author, editor 5 M tt n f r "U b r d r l ä n Ab tänd d r A - and translator of several books on the history of chemistry, v l ntz hl n d r n nnt n nf h n d l " G l hrt former editor of the ACS magazine "Chemistry," a past-chair Anz n A d. W n h ft. M n h n, 1850, 0, 1- 7 ; r - of the Division and a current member of the editorial board of pr nt d th n Intr d t n b th r n Ann 1858,105, 1 7- the Bulletin, he is particularly interested in the history of A nd 3 b " t r ét t t l d l organic chemistry, the history of Japanese and Chinese sci- h r n " C pt r nd , 1837, , 5 7-57 ence, and the development of the dye industry. 7 A "Mé r r l v l nt d rp pl " C pt r nd , 1857, 4 , 7 9-731 r A l nd ll t d p p r h h v r f th r d nd n l t n A n th At W ht , BOOK NOTES Sp n nd n 1 9 th r rl nd v r th r n p n r f l nt Curiosity Perfectly Satisfyed: Faraday's Travels in Europe
l f t n r th r n h l t Al x ndr E l é r 1813 1815, Edited by Brian Bowers and Lenore Symons, d Ch n rt nd th n h-A r n h t G t v tl f Peregrinus, London, 1991. xvi + 168 pp. Cloth (Typeset), nr h r f rth r d t l W v n Spr n n h r d $33.00. Michael Faraday's 'Chemical Notes, Hints, Sugges-