Gustavus Hinrichs and His Charts of the Elements

Abstract

In this paper, I analyze the efforts of the German-American chemist Gustavus Detlef Hinrichs (1836–1923) to construct a periodic system between 1867 and 1869. Included is a transcription and translation into English of major sections of his Programme der Atomechanik (1867), and a discussion of Hinrichs’s “pantatom” theory of matter. My principal conclusions are: (1) Hinrichs’s chart of 1867 is actually a double spiral that begins in a clockwise fashion but then reverses direction and continues in a counterclockwise direction, (2) the nitrogen and oxygen groups are swapped because Hinrichs felt that that order resulted in more consistent trends in the stoichiometries of the highest oxides, (3) in his chart the trigonoids and tetragonoids each subtend one-third of a circle, and the spokes are arranged so that the maximal valences of the elements increase from right to left, (4) Hinrichs devised an ingenious theory to account for isomorphism, (5) the transition elements in Hinrichs’s 1869 table are listed in reverse order for the same reason that the spiral in his 1867 chart reverses direction, (6) the transition elements in the 1869 system are arranged in a slanted fashion to reflect their relative atomic weights, whereas other elements are not arranged in this way, possibly owing to a printer’s omission, (7) Hinrichs was the first to point out that one advantage of the “long” form periodic tables is that the metals and non-metals can be separated by a single line, and (8) simultaneously with Meyer and Mendeleev, Hinrichs also pointed out the periodic relationship of atomic volume to atomic weight, but only in his oral presentation to the AAAS meeting of August 1869.

1 Introduction

Of the pre-Mendeleev attempts to construct a periodic system, by far the most puzzling and least understood are those of the German-American chemist and polymath Gustavus Hinrichs. Hinrichsʼs first system, published in 1867 [1, 2], is summarized in a two-dimensional graph in which related elements (such as the halogens) are arranged on spokes radiating from a central point, elements with larger atomic weights being located farther from the center. In 1869, Hinrichs published two new charts of his system, in which the elements are arranged in tables rather than a graph [3,4,5].

Over the years [6,7,8,9,10], scholars have discussed Hinrichs’s periodic systems¹ [11] and compared his achievements with those of others who proposed periodic systems in the 1860s, such as Alexandre-Émile Béguyer de Chancourtois (1820–1886), William Odling (1829–1921), John A. R. Newlands (1837–1898), Lothar Meyer (1830–1895), and of course Dmitri Mendeleev (1834–1907).² But many aspects of Hinrichs’s periodic systems have remained puzzling even today.

In this paper, after a short biography of Hinrichs, I will offer some new insights into why Hinrichs constructed his periodic systems the way he did. Specifically, I will address the following questions:

• Are the dotted arcs in the 1867 chart circular or spiral?

• Why are the nitrogen and oxygen groups in the 1867 chart out of order?

• Why are the radial spokes in the 1867 chart located where they are?

• Why are the transition elements in the 1869 chart listed in reverse order and arranged in slanted columns?

• What are Hinrichs’s ideas about how the periodic table gives insights into isomorphism, the relation between metals and non-metals, and atomic volumes?

2 Short Biography of Gustavus Detlef Hinrichs

Several articles [6, 8, 12], books [13, 14], and a thesis [15] give much information about Hinrichs’s life and accomplishments; a list of his publications has also been compiled [16]. Many of Hinrichs’s original publications, and documents about him, can be found today at the University of Iowa [17]. In addition, Hinrichs’s personal papers are located at the University of Illinois, having been deposited there by one of his grandsons between 1959 and 1964 [18]. Here I will briefly summarize some of the details available in these sources.

Gustavus Detlef Hinrichs (Figs. 7.1 and 7.2) was born on 2 December 1836 in the town of Lunden in the Holstein (i.e., southern) portion of the Jutland peninsula. Lunden was then part of Denmark but today is in Germany, about 50 km south of the Denmark-Germany border. He was the third of six sons of Johann Detlef Hinrichs (b. ca. 1802), a musician; Hinrichs’s mother, Carolina Cathrina Elisabeth von Andersen (b. 4 October 1809), was the daughter of an artillery captain. In 1850, at the age of 13, Gustavus ran away from home to participate in the Schleswig-Holstein War, the unsuccessful first rebellion of ethnic Germans to achieve the secession of Holstein (and the adjacent state of Schleswig) from Denmark to the German Confederation. In July of that year, he took part in the battle at Idstedt as a uniformed drummer boy. He returned to Lunden in 1853 after hostilities ended, and shortly thereafter he enrolled in the Polytechnic School of the University of Copenhagen, where he completed the regular course of studies in 1856. He continued at the University for advanced work in mathematics, physics, and chemistry.

Fig. 7.1

Gustavus Hinrichs in his middle years. Left photo courtesy of University of Iowa. Right photo from the Souvenir and Annual, 1881–1882

Fig. 7.2

Gustavus Hinrichs in his later years. Left: photo courtesy of University of Iowa. Right: photo from The Palimpsest, 1930

While at the University, Hinrichs earned money as a private instructor of students. In 1856 he wrote his first book, Die electromagnetische Telegraphie, and in 1860 he passed the exam at the University of Copenhagen for the Candidatus mathematicus degree,³ equivalent to a master’s degree. At Copenhagen, he had been particularly influenced by the Danish biologist Daniel Frederik Eschricht (1798–1863) and the meteorologist and geologist Johan Georg Forchhammer (1795–1865). In April 1861 he married Auguste Margaretha Friederike Springer (1839–1865), and in May–July 1861 he immigrated to the United States with his new wife, most likely to avoid service in the Danish military.

In 1861 Hinrichs settled in Davenport, Iowa,⁴ where initially he taught high school. In 1862 he was appointed Professor of Modern Languages at the University of Iowa in Iowa City (he was fluent in Danish, French, German, Italian, and English, and knew some Greek and Latin), and in the next year he was appointed Professor of Natural Philosophy and Chemistry at that same institution, giving up his former title. Hinrichs’s first wife died in 1865, leaving two children, and in July 1867 Hinrichs married Anna Catharina Springer (1842–1910; Augusteʼs younger sister) in Iowa City; presumably, Anna had come to America to care for Gustavus’s children. With Anna, Hinrichs had two more children.

In 1875 Hinrichs founded the Iowa Weather and Crop Service [19, 20], and in 1886 he was dismissed from the University of Iowa (on trumped-up charges) [13, 15, 21]. In 1889 he was appointed Professor of Chemistry at St. Louis University, and he retired in 1907. He died 14 February 1923 in St. Louis (age 86).

3 Hinrichs and Atomic Weights, 1866

Hinrichs published his first ideas about atomic weights in an 1866 article [22] in the American Journal of Science entitled, “On the Spectra and Composition of the Elements.” Although much of this paper relates to finding regularities in the spectra of the elements (which has been discussed elsewhere [8]), I will instead focus on his ideas about the structure of atoms.

In this paper, Hinrichs states: “We suppose all elementary atoms to be built up of the atoms of one single matter, the urstoff.…” Hinrichs proposes that the atomic weight of hydrogen, referred to this prime element, is 4, but for the rest of the article he gives atomic weights relative to H = 1. He continues,

the laws of mechanics force them [i.e., the particles of the urstoff] to arrange themselves regularly—and the most stable form will be the prism. If quite rectangular, and a, b, c be the number of primary atoms, in the three directions, we shall have [where A = atomic weight] …

A = a·b·c.

If the atom has a quadratic base, a = b, we have

A = a²·c.

If provided with one or several pyramidal additions, we have

A = a·b·c + k.

Thus, Hinrichs clearly believed Prout’s hypothesis [23,24,25,26,27] that all atomic weights are integer multiples of that of hydrogen (or a fraction thereof). As we will discuss below, Hinrichs makes no mention of the 1860 or 1865 publications of Jean-Servais Stas [28, 29] (1813–1891) discrediting Prout’s hypothesis, or of the 1858 publications of Stanislao Cannizzaro [30, 31] (1826–1910) on atomic weights. Hinrichs mentions that he was using the atomic weights given in 1863 by Heinrich Will [32] (1812–1890), which for non-metals, the alkali metals, and the coinage metals mostly resembled the modern values, but for other elements were mostly one-half the modern values.

Examples of how Hinrichs tried to apply a common formula for the atomic weights of elements within groups are shown in Fig. 7.3. In attempting to fit the atomic weights of elements in a group to a common formula, Hinrichs was following efforts made in 1853 by the English chemist John H. Gladstone [33] (1827–1902), in 1854 by the American chemist Josiah Parsons Cooke [34]⁵ (1827–1894), in 1851 and 1858 by the French chemist Jean Baptiste André Dumas [35, 36] (1800–1884), and in 1860 by the American chemist Mathew Carey Lea [37] (1823–1897). All tried to fit the weights to formulas of the type a + md (or to more complicated polynomial formulas), where a and d were numbers that were invariant within a group, and m was an integer that differed from element to element in that group. Only Hinrichs, however, proposed that the polynomial formulas reflected specific geometric (i.e., prismatic) arrangements of the basic building blocks.

Fig. 7.3

Table from Hinrichs’s 1866 attempt to find numerical regularities in atomic weights [22]

Hinrichs mentions two of these predecessors in this 1866 paper [22]:

We cannot here go into any detail as to the relation of these formulae to the numerical relations discovered by Carey Lea, Dumas and others; we hope soon to be enabled to publish our labors on the constitution of the elements. Neither can we here discuss these formulae in the sense of the mechanics of atoms, deducing the physical and chemical properties of the elements from these formula; these interesting relations also we must delay till some future, but I hope not a very distant, time.

Among Hinrichs’s handwritten papers at the University of Illinois are two pages summarizing the polynomial formulas of Cooke and Dumas. We do not know whether Hinrichs had seen any of the classification schemes constructed between 1862 and 1864 by Béguyer de Chancourtois [38], Odling [39], Newlands [40], or Meyer [41].

4 Hinrichs and Atomechanics, 1867

One year later, in 1867, Hinrichs published an expanded version of his ideas about the inner structure of atoms, which he had briefly discussed in his 1866 paper. These new ideas appear in a privately lithographed reproduction of a 44 page handwritten treatise entitled Programme der Atomechanik oder die Chemie eine Mechanik der Panatome (Fig. 7.4; called Programme from here on). It is written entirely in German, except that copies not intended for Germany also include an abstract in French on pages 45–48. At the same time Hinrichs published a four-page English abstract of his Programme in the American periodical Journal of Mining [2]. The English abstract is not a straight translation of the French abstract.

Fig. 7.4

Cover and title page of G. D. Hinrichs, Programme der Atomechanik, oder die Chemie eine Mechanik der Panatome, Iowa City (1867). Images courtesy of the University of Dresden

A total of 112 copies of Programme were printed [42]. Hinrichs sent most of these to societies and universities, with only a few going to individuals. Among the latter were the Irish physicist John Tyndall (1820–1893), the German physicist and editor Johann Christian Poggendorff (1796–1877), the German chemists August Hofmann (1818–1892), Heinrich Will (1812–1890), Justus von Liebig (1803–1873), and Carl Remigius Fresenius (1818–1897), the German dictionary editor Felix Flügel (1820–1904), the London publisher of the Mining Journal Edward David Hearn (1832–1909), and the biologist Charles Darwin (1809–1882). He also sent copies to several geologists and mineralogists in Austria, Germany, and Russia: Hans Bruno Geinitz (1814–1900), Wilhelm Haidinger (1795–1871), Karl Friedrich August Rammelsberg (1813–1899), Carl Friedrich Naumann (1797–1873), Albrecht Schrauf (1837–1897), Aristides Brezina (1848–1909), and Nikolai Koksharov (1818–1893). In all, he sent 37 copies to Germany, 11 to the United States, 10 to France, 10 to England, 8 to Russia, 6 to Austria-Hungary, 6 to Scandinavia, 4 to Switzerland, 3 to Holland, 3 to Italy, 2 to Belgium, and 1 each to Greece, Portugal, and Spain [2]. His personal copy resides among the Hinrichs papers at the University of Illinois along with his hand-annotated list of recipients.

The lithographed text of the Programme is handwritten in English (or Latin) cursive, rather than the now-obsolete Kurrent script that was commonly used by German writers in the nineteenth century. Hinrichs’s handwriting is relatively neat and mostly legible, although letters and words are sometimes sufficiently ill-formed that transcribing them involves guesswork (mit/mir/wir/wie are particularly vexing). In addition to the usual problems associated with distinguishing similarly-fashioned letters, long words at the ends of lines are often compacted and slanted downward to avoid the margin, and are frequently difficult to read as a result.

Hinrichs’s Programme begins with a three-page historical forward (which states that the document was written between November 1866 and June 1867) and a short vocabulary list with definitions. The forward is followed by the main text of the Programme, which Hinrichs organizes into 400 numbered paragraphs. The main text is divided into an Introduction (paragraphs 1–5) and four main sections: Pantogen and the Elements (paragraphs 6–56), Chemical Characteristics of the Elements (paragraphs 57–120), Physical Characteristics (paragraphs 121–228), and Morphological Characteristics or Crystal Forms (paragraphs 229–399). The 400th paragraph contains some brief closing remarks. The text concludes with a colophon, which attests that the monograph was written personally by Gustavus Hinrichs and printed on stone by Augustus von Hageboeck, Lithographer in Davenport, Iowa. August Hageboeck (1836–1907) had immigrated to the United States from Germany in 1857.

In the following text, I will provide English translations of some key excerpts taken from Hinrichs’s Programme (a transcription of original German text up through about paragraph 100, and an English translation thereof, can be found in the Appendix). I will focus on those portions of the Programme that are most relevant to Hinrichs’s ideas on the classification of elements: i.e., the historical forward and the first two sections.

4.1 Historical Forward

The historical forward of the Programme begins with a chronology of the development of atomechanics, which Hinrichs says started with a document he had written in 1855, while still a student at Copenhagen. He states:

I officially certified on the 7th of August a document in characters (“Zeichenschrift”) entitled containing the principles and some of the main conclusions already obtained. This document is also in my possession.

A 1969 article about Hinrichs [6] depicts this sentence in a figure bearing the caption: “The puzzling hieroglyphics in the [historical forward] of Atomechanik, referring to some secret ‘Zeichenschrift’ known only to the author.”

The shortness of the encoded text makes the cryptanalysis more difficult, but after a few blind alleys I solved the puzzle of the “hieroglyphics:” they are a simple substitution cipher in which the plaintext reads HINRICHSSCHE NATUR-PHILOSOPHI (Hinrichs’s Nature Philosophy), the final “E” having been omitted.

There is no document with this title in the archive of Hinrichs’s personal papers at the University of Illinois, but there is a 13-page handwritten document entitled Atom-Mechanik. On the cover of this document is an annotation by Hinrichs written in 1920: “Old document on Atom-Mechanics. June 15, 1868. The main part, in my own shorthand, is not dated, so far as I can see.” Most of the document is unreadable (at least to me): the words are written in a shorthand that resembles one for German writing introduced by Franz Xaver Gabelsberger (1789–1849) in 1834. If Hinrichs’s dating from 50+ years after the fact is wrong, then this document may be the one in “Zeichenschrift” that the Programme says was written in 1855.

This 13-page manuscript, which mentions Pettenkofer, Dumas, and Prout (all of whom had written about atomic weights before 1855), contains some equations, such as O = 32 = 2·4² = 2·□₂, and Mg = 48 = 3·4² = 3·□₂, that suggest that Hinrichs is trying to rationalize (doubled) atomic weights on the basis of points arranged into geometric arrays such as squares. Loosely inserted into the document is a page showing a triangular grid, and calculations of the number of points in regular hexagons based on this grid.

Also in the Hinrichs archive at the University of Illinois (Box 3) are two longer handwritten documents, one entitled Vorläufige Entwurf der Atomechanik (Preliminary Outline of Atomechanics) that is undated but must have been written after April 1856 (the date of one of the articles Hinrichs cites), and the other entitled Entwurf der Atomechanik that is dated August and September 1858. The latter consists of 16 chapters, totaling 74 pages plus index.

Neither document contains any kind of periodic system. The earlier document does contain an inserted sheet, evidently added after the main text was written, summarizing an 1857 article [43] on the atomic weights of the elements by the German analytical chemist Heinrich Rose (1795–1864). Another inserted sheet, also bearing a reference to an article from 1857, gives atomic weights for 13 elements, all given on an H = 2 basis; these doubled atomic weights are based on a unit equal to half of a hydrogen atom.

The 1858 document contains an attempt to devise formulas for the (doubled) atomic weights of the elements, similar to the analysis he published eight years later in 1866. The logic behind the formulas, however, is far from clear: hydrogen = 2 = 1²·2, fluorine = 38 = 3²·4 + 2, chlorine = 71 = 2² + 3²·7 + 2², bromine = 160 = 4²·10, iodine = 254 = 5²·10 + 2², lithium = 14 = 2²·3 + 2, sodium = 46 = 3²·5 + 1; and potassium = 78 = 3²·7 + 5 [sic].

The earlier version of the Entwurf may be the one referred to in the next section of the Programme:

1856. In October of this year, I thought I was sufficiently advanced in my work to rewrite the publication. I ended up sending shorter reports to many of the existing men of science and also to some academies, expecting this to open up closer scientific communication. I had miscalculated in that. Passive resistance and the lack of help were to persuade me to further develop atomechanics.

The Programme then lists the scientific leaders Hinrichs had contacted in order to inform them of his ideas and to enlist their help in arranging for publication. The historical forward also describes the responses he received. Among those he contacted were Forchhammer (his former teacher), John Tyndall, J. C. Poggendorff (both mentioned above), the French editor Eugène d’Arnoult (fl. 1830s–1873; founder of l’Institut, Journal Universel des Sciences), the German chemist and physicist August Karl Krönig (1822–1879; known for his kinetic theory of gases, and then secretary of the Physical Society in Berlin), the Austrian mineralogist Wilhelm Haidinger (mentioned above; member of the Imperial Academy of Sciences in Vienna), the German physician and physicist Emil du Bois-Reymond (1818–1896), the Austrian chemist and mineralogist Anton Schrötter (1802–1875), the Danish-born German astronomer Peter Andreas Hansen (1795–1874), and the Prussian naturalist Alexander von Humboldt (1769–1859).

Although Hinrichs writes that he was grateful for the (mostly meager) responses he received, he accuses Krönig of plagiarizing some of his ideas in a monograph Neues Verfahren zur Ableitung der Formel einer Verbindung aus den Gewichtmengen der Bestandtheile (New procedure for deriving the formula of a compound from the weights of the constituent parts) [44]. On p. 53 of Krönig’s monograph, as part of an eight-page section entitled “On the atomic weights of the elements,” Krönig states: “As for the atomic weights I have assumed, I have used only Berzelius’s numbers, taking into account the necessary corrections, based on half an atom of hydrogen as a unit…. So I set H = 2, O = 32, Cl = 71, and for example Ca = 80. Thus, all atomic weights appear as whole numbers.” Krönig later refers to “the primordial particles, from which I think all bodies are composed, and of which 2 should form an atom of hydrogen, 32 an atom of oxygen, 71 an atom of chlorine, 80 an atom of calcium.”⁶

In the historical forward to the Programme, Hinrichs implies that this “half-hydrogen” basis for atomic weights had been included in the reports that Hinrichs circulated privately beginning in late 1856. Hinrichs further quotes from a letter he received back from Krönig dated April 15, 1857, in which Krönig said that he had read Hinrichs’s report carefully and offered to circulate it to members of the Physical Society in Berlin who were part of Krönig’s reading circle.

Even if we accept Hinrichs’s implication that his circulated report contained his half-hydrogen hypothesis, it is perhaps forgivable if by 1866 Krönig had forgotten that he had first encountered the idea in a still-unpublished report sent to him nine years earlier by an obscure correspondent. Even more to the point, however, the idea that atomic weights are multiples of some fraction of a hydrogen atom had been proposed before 1856. The first to do so was Prout himself, in a letter sent on September 12, 1831 to the English chemist Charles Daubeny (1795–1867), and printed by Daubeny as an appendix in his textbook of that same year, Introduction to the Atomic Theory [45]. In his letter, Prout states that: “there seems to be no reason why bodies still lower in the scale than hydrogen … may not exist, of which other bodies may be multiples, without being actually multiples of the intermediate hydrogen.”

In 1843, the Swiss chemist Jean Charles Marignac (1817–1894) was even more explicit [46]:

In reality, so far, among all the bodies whose equivalent has been able to be determined with some precision, chlorine alone is obviously the exception. But still, by making a slight modification to Prout’s law, this anomaly could be eliminated. It would suffice to admit that for some bodies, and chlorine would be in this case, the equivalent would be a multiple, not of the equivalent, but of the half-equivalent, of the hydrogen atom.⁷

In 1846, the French chemist Edme-Jules Maumené (1818–1898) promoted the same idea [47].

By 1867, however, almost all of the former advocates of Prout’s hypothesis, even in such a modified form, had abandoned it. For example, Marignac, who had been the foremost skeptic of Stas’s 1860 work [28] on atomic weights, was convinced by Stas’s follow-up 1865 monograph [29]. That same year, in a review of the latter work, Marignac stated [48]:

I can now no longer raise any doubts about the accuracy of the above numerical results, and I perfectly recognize with Mr. Stas that the atomic weights of bodies do not strictly offer among them the simple relationships that Prout’s hypothesis would require.⁸

Hinrichs concludes the historical forward by mentioning his 1866 article in the American Journal of Science, and adds that in the Fall of 1866 he had come to an agreement with the editor-in-chief, James Dwight Dana (1813–1895), that Hinrichs’s further work would be published in the same journal. But he adds, “I wanted to start with the crystallographic part, [and] work inductively to the pantogen…. Circumstances have caused the current publication.”

The “circumstances” were a dispute with Dana; evidently, Hinrichs took offense at suggested changes in the manuscript that Dana and the referees suggested [12]. Hinrichs was later [49] to accuse Dana of plagiarizing his ideas in an 1867 article Dana wrote [50] on the relationship of crystalline form to chemical composition.

4.2 Introduction (§ 1–5) and Pantogen and the Elements (§ 6–35)

Beginning in Sect. 7.3, Hinrichs proposes that “everything of a material nature has arisen from a former substance. We may call this original element pantogen.” He proposes that free pantogen “probably occurs in the outermost solar atmosphere (appears light-producing) and in the planetary nebulae. Hydrogen is closest to it. The relationship to the luminiferous ether remains undecided.” But later in the Programme Hinrichs seems to use the word pantogen not only to mean this original form of matter, but also as matter as it exists today on the atomic scale.

Hinrichs continues by making the a priori assumption that atoms are composed of fundamental units which he calls pantatoms,⁹ which mutually attract one another. The atomic weight of an atom is then proportional to the number of pantatoms it consists of. To account for the non-integral atomic weight of chlorine (35.5) when scaled to the atomic weight of a hydrogen atom, Hinrichs further assumes (unlike the assumption made in his 1866 paper) that the weight of a pantatom must be 0.5—i.e., half the atomic weight of hydrogen—so that, for example, there are 2 pantatoms in hydrogen, and 71 pantatoms in chlorine.

In paragraph 10, Hinrichs introduces his additional assumption that atoms consist of layers of pantatoms that are stacked to form prisms. He begins this proposal with the statement:

There are only two possible compound arrangements in a plane for equal material points: at the corners of an equilateral triangle or a square. Accordingly, there are two kinds of pantogen compounds or elements; namely trigonoids and tetragonoids.

Hinrichs then discusses various ways to arrange pantatoms into plates based on triangular and square grids. He begins by depicting and counting the number of pantatoms included in plates based on triangular grids having equal-length sides (Fig. 7.5, parts a–i): for six-sided plates (i.e., regular hexagons) the numbers are 1, 7, 19, … and for four-sided plates (i.e., diamond shapes) the numbers are 4, 9, 16, …. But he also analyzes certain irregular hexagons with unequal-length sides (examples include those with 13, 23, 30, and 34 pantatoms).

Fig. 7.5

Various rafts or layers of pantatoms from paragraph 11 of Programme der Atomechanik

For the plates based on square grids (Fig. 7.5, parts k–m), Hinrichs mentions both plates with equal-length sides (i.e., squares), as well as rectangular plates having unequal sides (examples include those with 12, 16, and 20 pantatoms). Hinrichs does not mention the fact that the four-sided plates based on triangular grids (Fig. 7.5, parts d–f) are slanted versions of (with the same number of total points as) square plates with the same length side: e.g., a plate with 4, 9, or 16 points can be represented either way. This is just one of the many degrees of freedom in Hinrichs’s system.

Hinrichs then suggests that “by placing these pantatom plates vertically above one another, prisms emerge as the atoms of the elements.” The number of pantatoms in the base of the prism he calls the atomare (symbol a), and the number of layers—i.e., the height of the prism—he calls the atometer (symbol m). Therefore, “if there is only one prism, then the sum total of the pantatoms in the element atom or the atomic weight = atogram g = m·a”.

Hinrichs proposes a Linnean nomenclature (order, genus, species, variety) for classifying elements:

[the elements] divide into 2 orders (the trigonoids and the tetragonoids) according to the mutual association of the pantatoms on average. This order divides into genera according to the external form of the figure…. The species (the element) is determined by the atometer m. Varieties (very closely related elements [having] nearly the same atomic weight) are created by merging the subsequently determined caps onto the prism.

Hinrichs’s orders divide all the elements into two large categories (see below); his genera are the equivalent of our groups (alkali metals, halogens, etc.); his species are the elements within a group. In allowing for varieties, Hinrichs acknowledges that pure prismatic structures cannot be assigned for some atoms; it is sometimes necessary to add caps (“Aufsätze”) of additional pantatoms.

Hinrichs says shortly thereafter that trigonoids are metalloids (what we would call non-metals) and tetragonoids are metals. Thus, fluorine, oxygen, and nitrogen (along with their heavier congeners) are trigonoids, whereas all other elements are tetragonoids.¹⁰ Hinrichs evidently made this choice (rather than the reverse) because he believed it led to a more consistent set of pantatomic structures for the various atoms, and thus a more consistent classification scheme. Of course, Hinrichs’s proposal that there was any such correlation was another of his a priori assumptions.

A key assumption in Hinrichs’s system is that atoms of elements that belong together in a group have similarly shaped prismatic structures with the same base: “Thus the general character of the element will be determined by a, while the particular determination of this character will be expressed by m, the height”.

Based on this assumption, Hinrichs fits the atograms (i.e., twice the atomic weights) of the elements within a group to a common formula, much like he had done in his 1866 paper, except now the formulas correspond to stacks of plates based on triangular or square grids (rather than square grids only), and the basic unit has an atomic weight of ½ rather than ¼ or 1 on a H = 1 scale. Examples of some of his proposed arrangements of pantatoms are as follows (see Fig. 7.6):

Fig. 7.6

Atoms as stacks of pantatom layers, from paragraph 34 of Programme der Atomechanik

• H (2) = 2 layers of 1 pantatom

• F (36) = 5 layers of 7-pantatom hexagons +1

• N (28) = 4 layers of 7-pantatom hexagons

• O (32) = 8 layers of 4-pantatom double triangles (diamonds)

• K (78) = 2 layers of 7-pantatom hexagons + 4 layers of 4 × 4 squares

• Ca (80) = 2 layers of 4 × 4 squares + 2 layers of 4 × 6 rectangles.

From the fact that Hinrichs proposes that calcium is composed of 80 pantatoms, it is apparent that in the year between 1866 and 1867 he has switched over entirely to the system of atomic weights advocated by Cannizzaro and others.

Note that the most straightforward proposal for the structure of calcium would be five layers of 4 × 4 squares, but instead Hinrichs proposes a more complicated structure involving the stacking of both square and rectangular plates (Fig. 7.6). He does this in order to devise a formula that also applies to the congeners of calcium: strontium and barium. Also, despite Hinrichs’s proposal that metals are tetragonoids, he proposes that potassium (Ka), along with the other alkali metals, consists of hexagon-shaped triangular plates on top of square plates. We will return to this point later.

This section of Hinrichs’s monograph contains a series of 13 tables, one for each of his different groups of elements: the pantoids (containing only hydrogen), the chloroids (halogens), phosphoids (pnictogens¹¹), sulphoids (chalcogens), kaloids (alkali metals through Rb and perhaps also including In, Cs, and Tl), calcoids (heavier alkaline earths starting with Ca), kadmoids (Mg, Zn, Cd, and Pb), ferroids (Al, Fe, Rh, Ir), molybdoids (Cr, Mo, V, W), cuproids (Cu, Ag, Au),¹² titanoids (C, Si, Ti, Pd, Pt, and perhaps also including Zr, Sn, Ta, and Th), sideroids (Cr, Mn, Fe Ni, Co, and U), and “undetermined” (B, Be, Hg). Chromium and iron each appear in two of these groups. Hinrichs also mentions but does not give formulas for two additional groups, rhodoids (Rh, Ru) and iridoids (Ir, Os), claiming that too little is known about their atograms (i.e., atomic weights). In fact, this is not correct: accurate atomic weights for these elements had been reported for Ru in 1845 by the Russian chemist (and discoverer of Ru) Carl Ernst Claus [52] (1796–1864) and for the other three elements in 1828 by the Swedish chemist Jöns Jacob Berzelius [53] (1779–1848).

Each of the 13 tables contains a general parameterized formula for the atogram (i.e., twice the atomic weight), along with the values of parameters in the formula that correspond to each element. For example, the table for the chloroids (i.e., halogens), the general formula is (1) + m·(p), where (p) denotes a six-sided raft (not necessarily with equal sides) containing p pantatoms arranged in a triangular grid. Fluorine has m = 5 and p = 7, chlorine has m = 10 and p = 7, bromine has m = 12 and p = 13, and iodine has m = 11 and p = 23. The “predicted” atomic weights for fluorine and bromine show a discrepancy of 1.0 and 1.5, respectively, with respect to the then-accepted values.

Although Hinrichs states that elements in the same group have similar shapes with the same base, the table for the halogens shows that his “atomic structures” conform to a looser rule: elements in the same group are represented by the same formula, but the base can change from, for example, a regular hexagon of 7 or 13 pantatoms to a six-sided (but not regular) plate of 23 pantatoms.

The formulas for the atograms of all 13 groups of elements according to Hinrichs’s classification scheme can be found in Table 7.1.

Table 7.1 Hinrichs’s formulas for the atograms (i.e., doubled atomic weights) of the elements^a

4.3 Hinrichs’s Chart of 1867 (§ 36–56)

In paragraph 37 of the Programme, the chart shown in Fig. 7.7 appears. Hinrichs introduces his chart as follows:

Fig. 7.7

Hinrichs’s 1867 chart of the elements from paragraph 37 of his Programme der Atomechanik. Image courtesy of the University of Dresden

To illustrate the mechanical or rational classification of the elements contained in the foregoing [tables], I present them in the following drawing. The pantogen forms the midpoint, the genera are represented by rays from this point, and the species are recorded in these rays where the distance from the center equals the atogram g ….

Because the distance from the center is the atogram (=twice the atomic weight), the dotted lines in Hinrichs’s diagram have usually been referred to as a spiral [6, 8, 9, 54]. But such a description is actually only half-true. In (unnumbered) paragraph 54, Hinrichs states explicitly that the dotted lines in his diagram form a spiral, but with a twist:

…the known elements in our chart follow one another in spiral lines. See in 37 [i.e., his chart] the lines H-Li-C-O-N-Fl-Na–Mg-Al–Si-S-P-Cl-Ka-Ca–Ti and then in the opposite direction Ti–Fe-Zn-In-Br-As-Se-Pd-Rh-Cd-Cs-Jo-Sb-Te.

The words and then in the opposite direction (“in entgegengesetzte Richtung”) indicate that Hinrichs considered that the elements form two spirals, not one (Fig. 7.8). Elements from H to Ti lie on a clockwise spiral, but from Ti through Te the spiral proceeds counterclockwise. The change in direction of the spiral upon reaching titanium can be understood by reference to the modern periodic table: titanium is the first of the d-block transition elements. Hinrichs knew that the next elements after titanium in order of increasing atomic weights were all metals, and he concludes that the spiral must reverse direction in order to place these succeeding transition elements within his tetragonoid sector.

Fig. 7.8

Hinrichsʼs chart, in which two spirals have been added as described in unnumbered paragraph 54 of Atomechanics, the inner spiral proceeding clockwise, the outer one counterclockwise, with the change in direction occurring at titanium

The elements Rb, Sr, Ba, and Mo are skipped in Hinrichs’s sequence, and indeed they do not fall on the dotted lines in the chart; Hinrichs makes no comment on these omissions. The heaviest elements, Pt, W, Ir, Au, Pb, and Tl, are placed on their own dotted line; Hinrichs does not say in which direction he intended this portion of the curve to spiral, and it seems likely that he couldn’t decide. Cu and Ag are also omitted from the list, even though these element do lie on the dotted lines.

A key feature of any classification of the elements that can be called periodic is the recognition that the similarities of the elements have a two-dimensional character: not only do the properties of elements vary regularly within a group,¹³ there are regularities that relate different groups (which Hinrichs called genera). Hinrichs recognizes this two-dimensional character in paragraph 53: “…nearly equal values of g [i.e., Hinrichs’s atogram] can correspond to different forms; that is, near equal g give species of different genera. Our chart § 37 shows this quite clearly.” This sentence is followed by a table (Fig. 7.9) that emphasizes recurrent similarities in the atomic weights of elements from different genera.

Fig. 7.9

Table showing inter-group relationships of Hinrichs’s doubled atomic weights.Footnote

Hinrichs sometimes uses Tτ and sometimes (as here) Tι to denote the titanoid group; for clarity, I use only Tτ.

From paragraph 53 in Hinrichs’s Programme der Atomechanik

Thus, the elements O–N–F all have atograms near 30, the heavier congeners S–P–Cl all have atograms near 66, and so on for the subsequent members of those three groups. Similarly, Hinrichs points out that the elements Na–Mg–Al–Si all have atograms near 51, although the heavier congeners show quite a bit more scatter, in part because some of the elements Hinrichs includes are today recognized as belonging to other groups.

The table in Fig. 7.9 is significant because, as a (partial) tabular representation of Hinrichs’s periodic system, it more closely resembles other periodic systems devised in the 1860s, and thus makes comparisons a little easier. This table includes all three of the trigonoid groups, but only four of the tetragonoid groups. The latter include the alkali metal groups and the three tetragonoid groups which Hinrichs calls in paragraph 49 “the 3 main genera with a rectangular base, namely the ferroids, … the titanoids …, and the kadmoids ….” We will return to this idea of there being a smaller number of “main” tetragonoids below.

Two further aspects of Hinrichs’s chart deserve comment: the first is why the halogens, chalcogens, and pnictogens (Hinrichs’s Χ, Θ, and Φ groups, respectively) are out of order when compared with the modern table, and the second is why the spokes appear where they do (i.e., what is the basis for their angular positions). The first of these aspects has long been noted [8] but never explained.

The reason Hinrichs chose the order chalcogens–pnictogens–halogens (i.e., O–N–F) rather than pnictogens–chalcogens–halogens (N–O–F) can be deduced from a diagram he gives in paragraph 100 (Fig. 7.10). This diagram, which appears in the next section on the chemical properties of the elements, immediately follows a summary of combining ratios with hydrogen and the halogens.

Fig. 7.10

Diagram showing the combining ratios of elements with hydrogen and the halogens (inner circle) and with the chalcogens (outer circle). A circle has been added to emphasize what Hinrichs calls “point A”. From paragraph 100 in Programme der Atomechanik

In reference to this diagram, Hinrichs states,

In the adjacent figure, the main result of the compound ratios is compiled. The number indicates how many atoms of X (inner circle) or Θ (outer) unite with one atom of the different genera (their symbol in the outermost circle) to [give] the main compound.¹⁵ One can see that the ratio in both the X [i.e., halide] and the Θ [i.e., chalcogenide] compounds grows regularly from [point] A in every direction, reaching its maximum at Θ [O-S-Se-Te group] among the trigonoids [and] at Tτ [C-Si–Ti-Pd-Pt group] among the tetragonoids.

Point A in Hinrichs’s diagram occupies a place that today would be filled with the noble gases, which have a characteristic combining ratio of zero. Starting from this location, Hinrichs places the groups of elements in order of increasing combining ratios. Indeed, if one moves column by column away from the lighter noble gases in the modern periodic table, the valence of E in the EH_n hydrides increases in the order 1, 2, 3, 4… in both directions (i.e., increasing and decreasing atomic number).

Hinrichs had previously stated in paragraphs 92 and 95–98 that the various groups have combining ratios with the chloroids (X) as follows: XX for F and its congeners, ΘX₂ for O and its congeners, and ΦX₃ for N and its congeners (these are the trigonoid groups), and TτX₄ for C and its congeners, ΣιX₂, ΣιX₃, or ΣιX₄ for Al and its congeners, XαX₂ for Mg and its congeners, and KαX for Li and its congeners (these are the tetragonoid groups listed in his table in paragraph 53; Fig. 7.9). In the diagram in paragraph 100, Hinrichs chose ΣιX₃ as the “main” composition of the group of elements headed by Al. Had Hinrichs based his chart on these trends in combining ratios, he would have placed the F, O, and N groups in the correct order.

Instead, Hinrichs evidently places greater weight on the combining ratios with chalcogens (oxygen in particular). In the 1860s [55], the highest known chlorine oxide was Cl₂O₃; although I₂O₅ and I₂O₇ had been claimed, the evidence in support of these higher oxides was ambiguous (and even today the existence of I₂O₇ is doubtful).¹⁶ Thus, Hinrichs mentions that F and its congeners form binary compounds whose maximum chalcogen content is embodied in the formula Χ₂Θ₃, whereas N and its congeners form binary compounds up to Φ₂Θ₅ (such as P₂O₅ and As₂O₅), and among O and its congeners the compounds SO₃ and SeO₃ exist. Correspondingly, in his diagram, Hinrichs arranges the F–N–O groups in order of increasing (maximum) combining ratio with oxygen: 3/2, 5/2, and 6/2.

Thus, it is clear that, to Hinrichs, atomic weights play an important role in determining what elements belong together in the same groups, but they play a lesser role in determining how the groups are ordered with respect to one another. Hinrichs focuses more on the similarity of the atomic weights of elements from different groups, and less on arranging them in strict order of increasing atomic weight. Instead, Hinrichs places greater importance on combining ratios when deciding on the relative arrangement of the groups in his periodic system.

Almost all of Hinrichs’s atomic weights are close to the modern values but, like everyone else in the 1860s, he used wildly incorrect atomic weights for vanadium, tantalum, and uranium (137, 137.6, and 120, respectively, vs. modern values of 51, 181, and 238). Of these, only vanadium appears in his chart, and not surprisingly this element is located farthest from any of the arcs of his spiral. It is interesting that this deviation did not prompt Hinrichs to consider whether his assigned atomic weight of vanadium might be wrong.

As to the second aspect of Hinrichs’s chart, i.e., the basis for the angular positions of the various spokes, Hinrichs says nothing in the Programme.¹⁷ But the diagram in paragraph 100 also helps explain why the spokes are where they are.

Evidently, Hinrichs intended the trigonoids collectively to subtend approximately 120° of arc, and the same for the tetragonoids; he places these two arcs symmetrically within a circle, separated by 60° (Fig. 7.11). Hinrichs chose the alkali metal and chalcogen spokes to define the horizontal axis of his chart. He does not give reason for this arrangement, but one possibility is that Hinrichs orients the spokes in this way so that the maximum valence (as given by the outermost values in Fig. 7.10) increases from right to left.

Fig. 7.11

Possible structure of Hinrichs’s chart. Compare with Fig. 7.10

Hinrichs considers the molybdoids Mλ (Cr, Mo, V, W) and the cuproids Χυ (coinage metals) as subordinate to the ferroids Σι (Al, Fe, Rh, Ir): in paragraph 47 he states “the molybdenoids and cuproids are … only side branches of the ferroids.” This subordinate role is reflected in his omission of the molybdenoids and cuproids from his list of the “main” tetragonoids, as given in the table in paragraph 53 (Fig. 7.9), and also in his construction of the chart. Thus, the spokes for the three trigonoid groups and the four “main” tetragonoids are spaced equally, by 60° of arc for the trigonoids, and 40° for the tetragonoids. The subordinate molybdoids and cuproids lie on partial spokes that flank the spoke for the ferroids.

Hinrichs justifies his designation of the molybdenoids and cuproids as side branches because their atograms can be represented by formulas of the type a + md where m is odd, whereas the ferroids have formulas a + md where m is even. The flanking relationship of the molyboids and cuproids is evident in Hinrichs’s chart in paragraph 37: these flanking spokes are labeled “m = ungerade (odd)” whereas the ferroid spoke is labeled “m = gerade (even)”.

We can speculate that, because vanadium was on one of these flanking partial spokes, it was of less concern to Hinrichs that this element did not lie on any of the dotted spiral lines. But Hinrichs is silent as to the reasons that Rb, Sr, and Ba also do not lie on his dotted lines.

4.4 Chemical Characteristics (§ 57–110)

The next section of the Programme deals with the chemical characteristics of the elements. He begins with a statement about chemical bonding: “The chemical bonding between two atoms A and B, viewed as a mechanical phenomenon, can only consist of the side-by-side arrangement (juxtaposition) of atoms, AB.” He then devotes a lengthy discussion to the geometries of molecules (three-atom molecules are triangles, etc.) and to the contraction in volume that occurs when, for example, hydrogen and oxygen gases react to form water.

Hinrichs then tries to explain the atomicities (i.e., valences) of the atoms in terms the pantatomic structures he has assigned. The following is taken from his English abstract [2]:

• I. One atom of any chloroid combines with one of hydrogen; for (1)+m(p) shows one prominent centre of attraction.

• II. One atom of a sulphoid is saturated by two atoms of H: for the atomare¹⁸ 2 2² of O shows two equal centres of attraction.

• III. One atom of any phosphoid requires three atoms of H for saturation; for the regular hexagon gives as foci the centre of gravity of the three rhombs into which it is divisible.

Thus, Hinrichs proposes that the halogens have pantatomic structures in which the single capping pantatom is responsible for the valence of one, the divalent chalcogens have structures that consist of two identical halves, and the trivalent pnictogens have structures based on hexagons, which can be considered as consisting of three joined rhombuses. Here is another example of Hinrichs formulating ad hoc hypotheses, which in this case are not even internally consistent.

Hinrichs’s “explanations” of gas volume changes in chemical reactions and interatomic bonding are outside of the scope of the present discussion. Those interested in these aspects of Hinrichs’s theories are encouraged to consult the appendix to the present article.

I will, however, mention one aspect of Hinrichs’s theory of atomic structure, which as far as I am aware has not been pointed out previously. This is Hinrichs’s explanation of the cause of isomorphism.

Hinrichs proposes that, in the ammonium ion (NH₄⁺), the N atom (4 layers of 7-pantatom hexagons) is attached to four H atoms (each consisting of 2 pantatoms), which he places below the N atom as four “legs” that define a square-based parallelepiped (the overall shape is reminiscent of NASA’s lunar module). His model for potassium (shown in his paragraph 34; Fig. 7.6) consists of 2 layers of 7-pantatom hexagons on top of 4 layers of 4 × 4 squares. Therefore, according to Hinrichs, ammonium and potassium commonly form isomorphous compounds because these chemical species have about the same three-dimensional shape (Fig. 7.12).

Fig. 7.12

Hinrichs’s explanation of the isomorphism of ammonium and potassium salts. From paragraph 89 of Programme der Atomechanik

Similarly, cyanide and chlorine also form many isomorphous compounds, and Hinrichs accounts for this phenomenon in a similar way (Fig. 7.13). The cyanide ion he depicts as a nitrogen atom on top of a carbon atom; the height and cross section of the resulting shape are similar to those of his proposed structure of chlorine (10 layers of 7-pantatom hexagons plus 1).

Fig. 7.13

Hinrichs’s explanation of the isomorphism of cyanide and chloride salts. From paragraph 90 of Programme der Atomechanik

Hinrichs evidently kept the phenomenon of isomorphism in mind as he made his choices for the arrangements of pantatoms within atoms. Although he would have disagreed strongly with the comparison,¹⁹ this part of Hinrichs’s Programme is similar in intent to the work of the French chemist and crystallographer Marc Antoine Gaudin (1804–1880), who devoted his life (unsuccessfully) to working out the arrangements of atoms within molecules and molecules within crystals [57, 58].

4.5 Physical Characteristics (§ 121–228), and Morphological Characteristics or Crystal Forms (§ 229–399)

The last two sections of the Programme contain detailed discussions of trends and mathematical relationships between chemical formulas and various properties of the elements, such as specific weights (i.e., densities), specific heats, melting points, boiling points, refraction equivalents (i.e., the refractive index minus unity, divided by the density and multiplied by the atomic weight), spectral lines, and the axial ratios, external forms, and optical properties of crystals. In a few cases, Hinrichs notes regular trends in these properties as a function of increasing atogram (atomic weight): for example, he mentions that the melting points of Li, Na, and K decrease in that order. But other than a few scattered examples, Hinrichs is silent on the relationship of these properties to his periodic system.

Hinrichs also published his ideas on these topics in two contemporary summaries [2, 59].

5 Hinrichs’s Charts of 1869

Two years later, in 1869, Hinrichs published modified versions of his periodic system; one of them (Fig. 7.14) appeared in the July 1869 issue of a rather obscure Chicago-based journal, The Pharmacist [3], whereas the other (Fig. 7.15) was presented at the August 1869 meeting of the American Association for the Advancement of Science and published in their proceedings [4]. Hinrichs also issued his AAAS paper separately as a privately printed offprint [5]. The two new versions are very similar, the one presented at the AAAS meeting including fewer of the transition elements.

Fig. 7.14

Hinrichs’s chart from The Pharmacist (1869) [3]

Fig. 7.15

Hinrichs’s 1869 chart from Proceedings of the AAAS Meeting (1869) [4]

The tables also resemble Mendeleev’s first table of 1869, in that the elements within a group are arranged in rows rather than columns. Mendeleev’s table had appeared in the Zeitschrift für Chemie and the Journal für praktische Chemie a few months before Hinrichs’s tables appeared, but it is unclear whether Hinrichs had seen it.

Several features of Hinrichs’s 1869 tables have been discussed in some detail [6,7,8,9] and here I will just summarize some of the main conclusions.

• (1) Hinrichs chose fusibility and volatility, i.e., “the deportment of the elements in increasing temperature, as the basis of classification. For heat is merely motion of the particles, in fact this classification is a mechanical one, expressing the relative mobility of the atoms of the elements …” [3] In a textbook Hinrichs published in 1871 [60], he elaborates:

  The order of the genera … is determined [as follows]. The least fusible and volatile is placed in the middle. The most fusible and volatile are at the top and at the bottom; the metals standing above, the metalloids below. The upper elements in this table are decidedly electropositive; the lower equally electronegative.

• (2) Unlike his 1867 system, in which combining ratios played a dominant role, Hinrichs now uses his new organizational principles, fusibility, volatility, and electronegativity to reverse the relative ordering of the nitrogen and oxygen groups, so that in his 1869 system these groups are in the modern order, C–N–O–F. Although Hinrichs does not emphasize the point, this rearrangement also gives an order in which the atomic weights increase monotonically.

• (3) Hinrichs points out [4] that

  in this table the elements of like properties, or their compounds of like properties, form groups bounded by simple lines. Thus a line drawn through C, As, Te, separates the elements having metallic lustre from those not having such lustre.

With regard to the last feature, it is relevant to point out that, in terms of overall structure, Hinrichs’s 1869 system can be regarded as a long-form periodic table. Two aspects of the table support this conclusion. First, except for Pd and Pt, the transition elements are not co-mingled with pnictogen, chalcogen, or halogen groups: for example, V is not grouped with the pnictogens, Cr is not grouped with the chalcogens, and Mn is not grouped with the halogens, as they are in short-form tables. Second, the first-, second-, and third-row transition elements (except for Pd, Pt, and the elements in the Zn and Cu groups) collectively occupy the three places corresponding to the next three heavier congeners of aluminum. Hinrichs thus treats the transition elements the same way as the lanthanide and actinide elements are handled in many forms of today’s periodic tables (i.e., as collectively occupying the two places after yttrium in group 3). This way of handling the transition elements is not like that in the short form of the periodic table; instead, Hinrichs’s 1869 system is best regarded as a compacted version of a long-form periodic table.

Hinrichs points out that, in his 1869 table, a line can be drawn that separates the metals from the non-metals. This is the first recognition by anyone of this advantage of the long-form periodic table (although Gmelin had come close in 1843 [61]). Interestingly, Mendeleev emphasized that his system placed similar elements in adjacent locations, and he occasionally published long-form periodic tables (most notably in 1872 [62]), but as far as I know he never explicitly pointed out that the long form makes it possible to divide the metals and the non-metals with a single line. Hinrichs’s idea was not resurrected until the Scottish chemist James Walker (1863–1935) independently recognized this advantage of the long-form table in 1891 [63].

In the longer of his two 1869 articles [4], Hinrichs proposes new formulas for the atomic weights of elements within a group. Instead of polynomials based on integers, Hinrichs now proposes formulas that include exponential quantities, but of course even these formulas do not match the experimental values exactly. He comments

We do not mean to have the observed values corrected, for what here appears us “corrections” may in fact represent the links which hold together the various portions of the resulting atom. A negative correction would thus indicate that some projecting point had been removed before combination was effected.…

So here Hinrichs is proposing that his formulas give a sort of idealized atomic weight, which is modified when the atom engages in chemical combinations. He further says:

Most chemists seem to think that the chief importance of the painstaking work of Stas is to disprove and forever reject the so-called hypothesis of Prout; and with the destruction of this hypothesis they seem to think all the palpable harmonies of the atomic weights, and particularly all relating to “pantogen” is annihilated. We are inclined to think that just such careful determinations will demonstrate the correctness of the law of a common divisor (equal one-half the atomic weight of hydrogen?) for all elements, and prove some essential features of the structure of the element atoms.

Hinrichs was nothing if not steadfast in his views.

Several additional aspects of the 1869 charts are worthy of comment. One is why the transition metals in Hinrichs’s 1869 tables are listed in reverse order and in slanted columns. Van Spronsen has speculated [7, 8], I think correctly, that the reverse order “might also be explained by the fact that Hinrichs wanted in any case to see the elements Zn, Cd, and Pb classified as a group next to Mg.” My sense is that the reverse order can also be viewed a holdover from his 1867 system, in which he proposed a reversal in the direction of the spiral beginning with titanium.

In reference to the arrangement in slanted columns, Hinrichs says in his 1869 AAAS article: “By printing their symbols at distances from that of the genus, nearly proportional to the atomic weight, we obtain the following chart ….”²⁰ This sentence explains the slanting of the block of elements formed by the transition metals: the atomic weights of Zn, Cd, and Hg/Pb are the largest in their respective d-block rows, and thus they are placed farthest to the right.

But this explanation raises the question why the main group elements are not arranged with distances from the leftmost column “nearly proportional to the atomic weight”. I found a possible answer in a copy of the handwritten original of his 1869 AAAS paper, which is present among the Hinrichs papers at the University of Illinois (Fig. 7.16).

Fig. 7.16

Handwritten original of Hinrichs’s 1869 paper given to the American Association for the Advancement of Science. Courtesy of the University of Illinois at Urbana-Champaign

The dotted lines that precede each column of elements are slightly slanted with respect to the double line in the “genera” column, as they should, because the atomic weights increase in a period. I think it is possible that Hinrichs meant to have all the columns slanted in the printed table (i.e., with the bottoms of the columns set further right than the tops), but the typesetters didn’t notice this subtlety and Hinrichs didn’t insist on correcting it.

Another aspect of Hinrichs’s 1869 tables is that they contain numerous gaps, but in neither of his 1869 publications does Hinrichs comment on the gaps in any way. Even if he had proposed that these gaps represented elements still to be discovered, however, his predictions would not have been borne out. For example, his placement of Ti, Pd, and Pt in the same group with C and Si made it impossible for him to predict the existence of germanium, and his grouping of aluminum with a number of transition metals (but not with boron) made it impossible for him to predict the existence of either scandium or gallium.

I will end with one aspect of Hinrichs’s work that has largely been overlooked, which is his use of his system to illustrate periodic trends (Fig. 7.17). In a book he wrote in 1894 [56, pp. 231–239], Hinrichs gives examples of “some of the charts which were exhibited before the Salem Meeting of the American Association in August, 1869.” In these charts, Hinrichs maps various chemical properties onto his 1869 table: among the properties he plots are atomic volume, fusing (i.e., melting) points, and specific gravity (i.e., density), but also the method and date of discovery of the elements, and reactions in the wet and dry way.

Fig. 7.17

Diagrams showing atomic volumes and melting points, mapped onto Hinrichs’s 1869 table of the elements. From G. D. Hinrichs, The Elements of Atom-Mechanics, St. Louis, 1894

Hinrichs’s atomic volume plot is especially notable for its anticipation of the important role that atomic volumes played in the formulation of the periodic systems of Lothar Meyer and Dmitri Mendeleev [64]. Of course, Hinrichs’s plot was not published in 1869 and became available to the scientific public only after a lapse of 25 years.

6 Conclusions

Hinrichs used a number of chemical properties to construct his 1867 and 1869 periodic systems, including atomic weights, electronegativities, volatilities, valence, and specific gravities. In his 1869 article in The Pharmacist, Hinrichs states his approach as follows: “all the previous attempts [to classify the chemical elements] were founded upon only some one property of the elements, and hence necessarily led to an artificial classification.” He was thus led “to propose a classification which we believe to be natural, because it does rest upon fundamental and essential properties, and because all other properties of the elements not directly involved in this classification nevertheless harmonize therewith” [3]. In a real way, he anticipated the holistic approach Mendeleev took when constructing his periodic system.

Both Hinrichs and Mendeleev used atomic weights as well as combining ratios to create their periodic systems, but Mendeleev placed greater importance on atomic weights as an organizing principle. As a result, Mendeleev’s system not only more closely resembled today’s periodic table, it facilitated his ability to make predictions about undiscovered elements, to correct incorrect atomic weights, and more generally to convince others that the system was useful.²¹ Hinrichs’s placing of greater importance on combining ratios led him initially to invert the relative locations of the nitrogen and oxygen groups, and his system was sufficiently flawed that it made it difficult for him to duplicate Mendeleev’s achievements.

Hinrichs had a very ingenious theory for isomorphism, in which he proposed that chemical units such as ammonium and potassium, or cyanide and chloride, had similar shapes and sizes and thus formed crystals with similar shapes. He was entirely correct in general, but entirely wrong in his particular explanation.

The finding that Hinrichs’s chart of 1867 is actually a double spiral—which begins in a clockwise fashion but then reverses direction and continues in a counterclockwise direction—stems simply from reading what Hinrichs wrote. The additional proposal that the transition elements in his 1869 system are arranged in a slanted fashion to reflect their relative atomic weights—whereas other elements are not arranged in this way owing to a printer’s oversight—comes from a consultation of his original manuscripts.

Hinrichs was not well connected to other chemists, and was evidently unaware of (or uninterested in) many of the considerable developments that had taken place in chemistry in the decade or so leading up to 1867. There is, for example, no hint of the “new” structural organic chemistry in any of his publications before 1870. It seems that, at the time he constructed his Atomechanics, Hinrichs’s knowledge of chemistry was based almost entirely on what he learned as a student in the early 1850s, augmented by some selected reading of more recent chemical papers (Dumas’s 1858 paper for example).

Hinrichs never carried out chemical research of his own and, after he moved to the United States, he was scientifically isolated and kept busy with his instructional and organizational duties. Very likely, he had little time or opportunity to keep up with the newest ideas. Thus, in the field of chemistry Hinrichs was, to a great degree, intellectually frozen in the 1850s. From this perspective, it is even more remarkable that he was able to devise a periodic system at all.

To call Hinrichs a crank, as some have, is in my opinion an oversimplification. To be sure, he invented novel comprehensive systems in vastly divergent areas of science, often proposing new vocabulary that proved more of a barrier than an aid to understanding. He was often guilty of forcing data to fit a preconceived idea, and finding more meaning in correlations and trends than actually exist. He resorted to private publication when he could not get his ideas into the mainstream scientific press; furthermore, he distributed his Atomechanics, his magnum opus, as a lithographed handwritten manuscript rather than a printed monograph. He sent his work to influential people, such as Darwin and Humboldt, even when it was far outside their area of expertise. He accused established scientists of either ignoring his ideas or trying to steal them.

Such behavior is certainly displayed by true cranks, but many of these tendencies are also displayed by those who, like Hinrichs, are outside the scientific mainstream. For example, not long before, in the 1840s, both Julius Robert Mayer (1814–1878) and Hermann Helmholtz (1821–1894) resorted to private distribution of their philosophical (and rather hand-wavy) ideas on the conservation of energy when they could not get them published; also like Hinrichs, their ideas were largely ignored at the time, and both later became involved in priority disputes [65].

In my view, Hinrichs was a polymath with an encyclopedic (if not completely up-to-date) knowledge of the natural world. His unpublished work, as it survives in the University of Illinois archives, is massive in quantity (multiple large handwritten volumes) and impressive both in scope and content. Although ultimately his penchant for uncritical systematizing prevented him from devising a more compelling periodic system, Hinrichs deserves credit for being one of the first to organize the chemical elements into a useful two-dimensional arrangement having both groups and periods based on increasing atomic weights, and to point out that many properties of the elements change in systematic ways not only within a group but also between them.

Appendix: Transcription and Translation of Hinrichs’s 1867 Monograph