Tabula Affinitatum (s)
A framed copy of French physician and chemist Étienne Geoffroy’s 1718 affinity table, entitled: Table of Affinities Between Different Substances (Inter Differentes Substantias); captioned: Not invented, or thought involved, but to be seen what the nature of the issue, or does (Non Fingendum Aut Exogit Andum, Sed Videndum Quid Natura Ferat; Aut Faciat), at Museo Galieo, Florence, Italy. [7]
In chemistry, an affinity table, or "table of affinities", is an arrangement of chemical species ordered such that the species at the head of each column (header species) has a chemical attraction, and ability to combine via chemical reaction, with each species listed directly below (reactant species), with each potential reactant listed in order of decreasing force of affinity to the header species, enabling the chemist to predict the course of react.


The affinity table was the spark of the chemical revolution. The beginnings of the chemical revolution centered around the revival of Leucippusatomic theory through the works Rene Descartes (1637), French mathematician Pierre Gassendi (1649), English chemist Robert Boyle (1661), and English physicist Isaac Newton (1686). In this revival, the concept of the ‘molecule’, from French word molécule, originating from the Modern Latin molecula, a diminutive of Latin word moles or ‘mass’, was born, generally defined as a small unit of mass or structure comprised of two or more atoms. [3]

Unique among this group was Newton, who conceived of molecules as being structures of atoms attached together by a chemical force of affinity. He outlined his atomic chemical force affinity bonding theory in the ‘Queries’ section to his Opticks (the last and final "Query 31", to be precise). To cite the core example of Newton’s description of a gradient of affinity reactions, he states: [4]

Is it not for want of an attractive virtue between the parts of water () and oil, of quick-silver ()(Hg) and antimony ()(Sb), of lead ()(Pb) and iron ()(Fe), that these substances do not mix; and by a weak attraction, that quick-silver ()(Hg) and copper ()(Cu) mix difficultly; and from a strong one, that quicksilver ()(Hg) and tin ()(Sn), antimony ()(Sb) and iron ()(Fe), water () and salts, mix readily?

In 1718, during a translation into French of Newton’s Opticks, French physician and chemist Étienne Geoffroy used Newton’s descriptions of affinity tendencies or reactions, such as above, to construct the world’s first affinity table, as shown below (and adjacent), titled “Table of Affinities: Between Different Substances”, with the caption:

“Not invented, or thought involved, but to be seen as what the nature of the issue is, or does.”

The table containing twenty-four reacting species, detailing specifically what affinity reactions would occur between various combinations of reactants. This table might be readily defined as the pinnacle example of chemical determinism (see also: determinism), an issue at the center of discussion in German polymath Johann Goethe's extrapolation of this logic to human affairs (below). In any event, Geoffroy's table would go on to seed or rather, as some have argued, "launch", what would become the chemical revolution. [5]

Geoffroy's affinity table | 1718
See main: Geoffroy's affinity table
The original "affinity table" was the 1718 Table Concerning the Different Affinities Observed in Chemistry between Different Substances (Tableau des différentes Rapports Observées entre Différentes Substances), sometimes translated as "Table of the Different Relations Observed between Different Substances", a 16-column (9-row) affinity table made by French physician-chemist Étienne Geoffroy, which ordered chemical species according to the following rule, often categorized as Geoffroy's first law of affinity:

“Whenever two substances are united that have a disposition to combine and a third is added that has a greater affinity with one of them, these two will unite, and drive out the other.”

This is the prime example of the "laws of affinity", a methodology that traces back to Plato's notion of "likes attract; opposites repel", and before that to Empedocles' chemical aphorisms. Based on his so-called first law, as derived from Newton's Query 31, Geoffroy made the following affinity table:

Geoffroy's 1718 affinity table (1000px)

In Geoffroy’s table, to elaborate, at the head of each column is a header species with which all species below can combine or have a rapport with. The latter are so placed such that any higher species replaces all others lower in the column from their compounds with that at the head of the table. In other words, the species at the head of the table can potentially react with any species below it. All the species below the header species are ranked by chemical affinity preferences relative to the top species, with a higher rank corresponding to a higher affinity tendency. The species at the bottom of each column, for instance, have the least amount of affinity for the header species. If the bottom species is in a weakly bonded relationship with the header species, any species above it can potentially displace it from its attached partner. [2]

This table led to the development of the science of affinity chemistry and to the various laws of affinity; numbering up to ten, depending on which chemist was sourced. The best known is Plato’s ‘like attracts to like’ affinity law, e.g. water-to-water or fire-to-fire, etc.

Grosse's affinity table | 1730
In 1730, German chemist Jean Grosse (someone whom Geoffroy had inducted into the Academy in 1731), made a revised table of 19-columns (16-rows) for the use of his students: [5]

Grosse's affinity table (new)
Macquer's Elements of Chemistry | 1749
In 1749, French chemist Pierre Macquer, published his Elements of the Theory of Chemistry (Elemens de Chymie Theorique), in which he began to incorporate affinity table logic into his outlines of general chemistry. The following diagram, from the 1753 second edition, is the famous illustration of three putti, in a chemistry laboratory, studying Geoffroy's affinity table: [5]
Macquer putti studying affinity table (1753)

Gellert's affinity table | 1750

In 1750, German metallurgical chemist Christlieb Ehregott Gellert (1713-1795), who had begun to associate with the German chemists in 1744, produced a 28-column (17-row) affinity table: [5]

Gellert's affinity table (1750)
In figures one and two, in the lower right hand corner of Gellert's table, we begin to see the preliminary notion of the chemical reaction diagram, the dotted line indicative of the force of chemical affinity.

Rudiger's affinity table | 1756
In 1756, Mr. Rudiger produced a 15-column (9-row) affinity table: [5]

Rudiger's affinity table (1756)

Cullen's reactions diagrams | 1756
See main: Cullen reaction diagrams
In the midst of the the science of "affinity chemistry", anchored in the construct of chemical reactions governed by "affinity tables", the origin of the concept of the ‘chemical reaction’ was born, in specific regards to chemical notation and diagram, in the sense of "reactants" (initial state) transforming to "products" (final state). This idea stems from these affinity tables through the work of Scottish physician and chemist William Cullen. [2] Specifically, in 1756, in lecture, Cullen utilized Geoffroy’s affinity table wherein he pioneered the use of chemical reaction diagrams by using reaction arrows ‘→’, to represent the affinity preference or force, and bonding brackets ‘{‘, to represent the chemical bond, to show the mechanistic steps in each elective affinity reaction. [6] In modern notation, although Cullen didn't use letters to represent chemical species (something latter done by Torbern Bergman), Cullen introduced the following notational representation for chemical reactions:

18th centuryModern
Cullen reaction diagram

AB + C → BC + A

In this diagram (left), a system originally containing the chemical "AB" is put into contact with reactant "C", whereby virtue of the fact that B has a stronger force of "affinity" for that of C over that of it's bonded partner "A", it will, owing to these new chemical arrangements, displace or rather detach from A and form a new bonded union with C, in the form of "BC", leaving A to go off on its own (typically as a gas). This lecture method was passed along to Cullen's famous student Joseph Black, who expanded on this notation use.

Limbourg's affinity table
In 1758, the Academy of Rouen offered a prize competition on the following topic: "Determine the affinities that are found between the principals and mixts as M. Geoffroy did, and find a physico-mechanical system of these affinities. The idea of the prize was for someone to unite the physical and the chemical sides of the affinity issue (hence the birth of the science of physical chemistry, as James Partington categorizes things). [5] Not finding an essay that addressed both aspects, the prize was awarded (divided between) to physician Jean Philippe de Limbourg (a former doctor of medicne from Liege and former student of Herman Boerhaave, Musschenbroek, and Rouelle), and Swiss mathematical physicist Georges Le Sage. Le Sage supplied a mathematical exposition of affinity in line with the concept of gravity; Limbourg produced the following extended 33-column affinity table: [5]

Limbourg's affinity table

Marherr’s affinity table
In 1762, a Mr. Marherr produced a 120-column (3-row) affinity table. [5]

Rouelle’s affinity table | 1763
In 1763, French chemist Guillaume-Francois Rouelle (1703-1770), former teacher of Denis Diderot during the years 1754-1757, produced the following affinity table as found predominately in Diderot’s Encyclopedia:

Rouelle's affinity table

Spielmann’s affinity table | 1763
In 1763, Jacob Reinbold Spielmann (1722-1783), who had learned chemistry at Berlin’s Medical Surgical College from Pott and Margraf and spent some time in Paris with Jean Grosse and C.J. Geoffroy in the early 1740s, proposed a 28-column table. [5]

Demachy’s affinity table
In 1769, a Mr. Demachy produced a 20-column affinity table. [5]

Demachy's affinity table (1769)

De Fourcy’s affinity table
In 1773, a Mr. De Fourcy produced a 36-column affinity table. [5]

Bergman's affinity table | 1775
See main: Bergman's affinity table; See also: Bergman's reaction diagrams
The peak of the science of affinity chemistry culminated in the publication of the popular 1775 textbook A Dissertation on Elective Attractions by Swedish chemist Torbern Bergman (and expanded 1785 edition). The center piece of Bergman’s book, was a 59-column (50-row chemical affinity table, the largest ever assembled, showing thousands of possible chemical reactions, in both the "wet way" (aqueous) and "dry way" in schematic form between various chemical species, a portion of which (upper right and corner) is shown below:

Bergman affinity table (portion)

The full table was attached as a "map size" fold out to the appendix of his 1775 textbook. Bergman's table listed 25 acids, 15 earths, and 16 metallic calces; in comparison in the four acids, two alkalis, and nine metals in Geoffroy's original table. With this table, and accompanying reaction diagram schematic sheet (Cullen style), Bergman showed how chemical reactions, such as, for example, the famous ‘double elective affinity’ (
double displacement reaction), where two chemical units, AB and CD, exchange or displace partners to form two new evolved species AC and BD. [2]

AB + CD → AC + BD

could be quantified, diagrammed, and studied.

Diderot's affinity table | 1778
The following is French encyclopedist Denis Diderot's 1778 affinity table: [14]

Diderot's affinity table (1778)
Walker | 1802
In 1802, English science lecturer Adam Walker, in his lecture four "On Chemistry", produced the following affinity table:

Walker affinity table (1802)

This logic was taught to a young Percy Shelley, then aged 11, who would later use this model to develop his own unique atheism-based “elective-affinity scheme” of human relationships, as his second wife Mary Shelley would later refer to it.

Goethe's affinity table | 1809
See main: Goethe's affinity table; See also: Goethe's human chemistry
In the years 1796 to 1809, German polymath Johann Goethe used Torbern Bergman's 1785 physical chemistry textbook (and affinity table and reaction diagrams) to make a "human elective affinity table" (of human elective affinities), at least conceptually in his mind, if not most likely on paper. Verifiable evidence that Goethe did actually make an "affinity table" with people listed as reactants and products will never be known, being that, contrary to his usual practice (being the most prolific author behind Shakespeare), he destroyed all of his notes to his human elective affinity theory, leaving only the finished product, his famous 1809 novella Elective Affinities, wherein each chapter is said to be based on a different type of affinity reaction and each person is viewed as an interchangeable type of chemical species (see: Otto). The following re-construction outline is what Goethe did, in short:

Goethe reaction

The following is a re-construction, first printed in American electrochemical engineer Libb Thims' 2007 Human Chemistry (pg. 398), of what Goethe's affinity table would have most likely looked like:

EduGoethe 75 newChaCharlotte von Stein 75 newOtt
Minna Herzlieb 75
Buchholz 75
LucMitCouKarl August 75Bar
Luise Auguste 75
Riemer 75
OttMinna Herzlieb 75EduGoethe 75 newEdu
Goethe 75 new
EduGoethe 75 new
Goethe 75 new
Luise Auguste 75
CouKarl August 75OtoAugust von Goethe (1793)OttMinna Herzlieb 75OttMinna Herzlieb 75
CapBuchholz 75Cap
Buchholz 75
Charlotte von Stein 75 new
ChaCharlotte von Stein 75 new
Charlotte von Stein 75 new
EduGoethe 75 newEduGoethe 75 newOttMinna Herzlieb 75

ChaCharlotte von Stein 75 newOtt
Minna Herzlieb 75
OtoAugust von Goethe (1793)

CapBuchholz 75ChaCharlotte von Stein 75 newChaCharlotte von Stein 75 new

Luise Auguste 75
August von Goethe (1793)

OttMinna Herzlieb 75

CouKarl August 75
Riemer 75


OtoAugust von Goethe (1793)BarLuise Auguste 75CapBuchholz 75

LucCouKarl August 75Gar


BarLuise Auguste 75

OttMinna Herzlieb 75CouKarl August 75

(add discussion)

Free energy tables
See main: Free energy table
In the decades 1775-1840s, it was increasingly becoming apparent that the "affinity table" approach to the quantification of chemical reactions had its limitation. One, Bergmann's multi-page map size affinity table was approaching the limit in functionability. Two, and most importantly, it was becoming apparent that that reactions seemed to depend on temperature, meaning that one would have to construct a different affinity table for each temperature, and hence make hundreds of affinity tables. Third, and most importantly, was the puzzling nature of heat, which between 1780s to 1830s, had its roots in the now defunct so-called "caloric theory of heat" which held that heat was a type of fluid-like indestructible particle (caloric).

In the late 1850s and into the 1870s, the so-called
"thermal theory of affinity" was proposed, which held that heat release was the measure of affinity and hence the true measure of the driving force of chemical reactions. This theory, however, soon showed limitations: for instance, it could not explain endothermic reactions.

In 1882, German physicist Hermann Helmholtz, in his seminal paper "On the Thermodynamics of Chemical Processes", showed that the true measure of affinity is not "heat" but rather "free energy", which depended on reaction conditions, as shown below:

Thermal theory of affinity
Thermodynamic theory of affinity

Driving force / Measure of affinity (isochoric-isobaric reactions)Q U – TS
Driving force / Measure of affinity (isothermal-isobaric reactions)Q U + PV – TS

Helmholtz's proof that
overthrew the thermal theory of affinity of thermochemistry, updating things with the newly-forming science of chemical thermodynamics. In the decades to follow affinity tables were soon replaced by free energy tables. The first outlines of which were made by German physical chemist Fritz Haber in regards to gas phase reactions. [1] In more detail, according to Gilbert Lewis (1923), "the first systematic study of all the thermodynamic data necessary for the calculation of the free energy of chemical substances in a group of important reactions was done by Haber", as presented in his 1905 work Thermodynamics of Technical Gas Reactions. [8] Haber, however, did not make actual free energy tables, but rather made tables of equilibrium constants, discussing reaction energies, which is nearly synonymous with free energy, loosely speaking.

The work of Haber gave way to the construction of the first so-called “table of free energies” made in 1914 by American physical chemists Gilbert Lewis and Merle Randall, giving free energies of formation values for oxygen, hydrogen, and a few oxides of hydrogen. [9] This formed the basis for their expanded-followup 1923 “Table of Standard Free Energies of Formation at 25 °C”, giving free energies of formation for 28 cations and a few metallic compounds and 111 non-metallic compounds and anions. [8]

Human free energy tables
The above logic, as outlined by Goldstein, that one can calculate the energies and entropies of the reaction mechanism steps involved in the formation or synthesis of an animated entity such as a mouse, gives way to the view that each person can be viewed, likewise, as a "molecule" (human molecule) or chemical species (human chemical species) with a measurable human molecular formula, as has been recently calculated (Sterner and Elser, 2000; Thims, 2002, New Scientist, 2005). The basic idea that each person was formed during a great process, involving a large number of mechanistic steps, was first outlined in 1789 by French philosopher Jean Sales, with his statement:

“We conclude that there exists a principle of the human body which comes from the ‘great process’ in which so many millions of atoms of the earth become many millions of human molecules.”

This premise constitutes what is called the "human molecular hypothesis" (akin to the atomic hypothesis).

The basics of the idea of the "human free energy tables" was first outlined in American chemical engineer Libb Thims' 2007 Human Chemistry textbook, as a subject to be worked out in the future; the first stepping stone of which is to study the approaches (and pitfalls) of the 500+ thinkers on the HT pioneers timeline-table, so to get basic framework as to how people historically have attempted to calculate the energies, entropies, internal energies, enthalpies, temperatures, pressures, volumes, and free energies of humans.

Free energy selection method
See main: Thims thought experiment
In circa 1995, after taking courses in chemical thermodynamics and physical chemistry, and learning how reactions between different chemical species are predicted energetically, Thims began to muse about how this would be done chemical thermodynamically in regards to humans, even nearing the point of asking the question openly by raising his hand in his chemical engineering thermodynamics class. The following is the reformulated free energy based selection method table Thims hand in mind at this point (which, to note, is equivalent to Goethe's affinity table, affinity and free energy connected via the Goethe-Helmholtz equation):





1Thims 75 new

Lisa | 5.0

Baby icon 75

2Thims 75 new

Sarah | 6.2

Baby icon 75

3Thims 75 new

Jessica | 6.1

Baby icon 75

4Thims 75 new

Fay | 5.6

Baby icon 75

5Thims 75 new

Tina | 7.2

Baby icon 75

6Thims 75 new

Ashley | 5.8

Baby icon 75

7Thims 75 new

Mary | 5.9

Baby icon 75

8Thims 75 new

Sophia | 6.7

Baby icon 75

9Thims 75 new

Ava | 6.4

Baby icon 75

10Thims 75 new

Chloe | 4.3

Baby icon 75

11Thims 75 new

Samantha | 5.3

Baby icon 75

12Thims 75 new

Allison | 5.2

Baby icon 75

13Thims 75 new

Addison | 4.6

Baby icon 75

14Thims 75 new

Julia | 6.0
Baby icon 75

15Thims 75 new

Brooke | 6.0

Baby icon 75

16Thims 75 new

Lauren | 6.2

Baby icon 75

17Thims 75 new

Claire | 6.6

Baby icon 75

18Thims 75 new

Ella | 7.7

Baby icon 75

19Thims 75 new

Aubrey | 5.3

Baby icon 75

The units listed above, to note, are retrospect units, in the sense that in circa 1995 Thims only had +/- conception of free energy change in his mind, i.e. that a negative free energy change is needed for a spontaneous, favorable, of feasible reaction, and that the more negative the value in magnitude the greater the spontaneity or favorableness of the reaction, as defined by the spontaneity criterion:


DG lz cReaction is spontaneous in the forward direction.

E DG gzReaction is nonspontaneous (reaction is favored in the opposite direction).
 dG = 0 \, System is at equilibrium (there is no net change).

Hence, if the above values of Gibbs free energy change, per each human chemical reaction, were accurate, as based on measurement, then reaction #14 would be the most thermodynamically favored (Thims marrying Julia and making a family); reactions: #11 (-125 MJ/hmol), #1 (-80 MJ/hmol), #9 (-75 MJ/hmol), #7 (-50 MJ/hmol), #6 (-30 MJ/hmol), #15 (-40 MJ/hmol), #17 (-25 MJ/hmol), #5 (-20 MJ/hmol), and #19 (-15 MJ/hmol) would each also be favored energetically, albeit each to a lesser degree, respectively; reaction #3 (0 MJ/hmol) would be at equilibrium or characterized by no free energy change and hence one that was equally favored in the forward and backwards direction; and reactions: #4 (+10 MJ/hmol), #13 (+10 MJ/hmol), #16 (+10 MJ/hmol), #18 (+10 MJ/hmol), #2 (+25 MJ/hmol), #10 (+50 MJ/hmol), #8 (+125 MJ/hmol), and #12 (+200 MJ/hmol) would each be non-favored reactions, with increasing amounts, respectively, i.e. reactions that are thermodynamically impossible, unless energy were added to the reaction to make each go.

The "hmol" in the above table, to note, is assumed to be three human molecules and wherein a normal reproduction reaction is approximated as involving an average of 1,500 cal per day at 365 days per 18 years times 3 people involved in the reproduction and one child rearing process, which amounts to about 125 megajoules of energy.

See also
Affinity of reaction
● Human free energy table

1. (a) Cahan, David (1993). Hermann von Helmholtz and the Foundations of Nineteenth-Century Science (Ch. 10: "Between Physics and Chemistry - Helmholtz's Route to a Theory of Chemical Thermodynamics" by Helge Kragh). University of California Press.
(b) Quote: "Given the unlimited validity of Clausius' law, it would then be the value of the free energy, not that of the total energy resulting from heat production, which determineds in which sense the chemical affinity can be active." (Source: Helmholtz, H. v. "Die Thermodynamic chemischer Vorgange," SB, pg. 23, pg. 22-29, in Wissenschaftlich Abhandlundgen von Hermann von Helmholtz. 3 vols. Leipzig: J.A. Barth, 1882-95.)
(c) Leicester, Henry M. (1956). The Historical Background of Chemistry, (pg. 206). New York: Dover (reprint).
2. (a) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), (ch. 10: “Goethe’s Affinities” and ch. 11: “Affinity and Free Energy”, pgs. 371-468) Morrisville, NC: LuLu.
(b) Thims, Libb. (2008). The Human Molecule, (preview), (pgs. 3-5). Morrisville, NC: LuLu.
3. Molecule (from Fr. moléclue (1678), from Mod.L. molecula, dim. of L. moles "mass, barrier"); Online Etymology Dictionary.
4. Newton, Isaac. (1704). Opticks (Query 31: On the small particles of bodies); London: Printers to Royal Society. Note: several editions published between 1704 and 1730.
5. Kim, Mi Gyung. (2003). Affinity, That Elusive Dream – A Genealogy of the Chemical Revolution. Cambridge, Mass: The MIT Press.
6. Crosland, M.P. (1959). “The use of diagrams as chemical equations in the lecture notes of William Cullen and Joseph Black.” Annals of Science, Vol. 15, No. 2, June.
7. Tabula Affinitatum: Inter Differentes Substantias (Table of Affinities between different substances) – Florence, Italy.
8. Lewis, Gilbert N. and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances (pgs. 5-6; Table of Free Energies, pgs. 607-08). McGraw-Hill Book Co., Inc.
9. Lewis, Gilbert and Randall, Merle. (1914). “The Free Energy of Oxygen, Hydrogen, and the Oxides of Hydrogen”, Journal of American Chemical Society, 35:1964.
14. Diderot’s Affinity Table (1778) –

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