William Cullen

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William Cullen.png

In existographies, William Cullen (245-165 BE) (1710-1790 ACM) (IQ:175|#267) (PR:20,808|65AE / physician:264) (GCE:17) (CR:75) (LH:3) (TL:78) was a Scottish physician and chemist, noted for his 1757 introduction of the crochets or brackets: " { " to signify a bond, uniting two chemical species, and darts: "" or "Cullen dart.jpg"to signify the direction of the force (or chemical affinity) guiding a species to its preferred bonding direction, when a reaction occurs.


In 1717, Newton, in "Query 31" of his Optics, his last and final query, outlined the following logic:

“Is it not for want of an attractive virtue [ΔG > 0] 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 (ΔG ≈ 0), that quick-silver (☿)(Hg) and copper (♀)(Cu) mix difficultly; and from a strong one [ΔG < 0], that quicksilver (☿)(Hg) and tin (♃)(Sn), antimony (♁)(Sb) and iron (♂)(Fe), water (∇) and salts, mix readily?”
— Isaac Newton (1718), “Query 31”, in: Optics (shown alchemical symbols[1] and Gibbs energy ΔG quantifiers added; pg. 383);

In 1718, Etienne Geoffroy, during his translation into French of Newton's Queries, rendered the logic of "Query 31", into the so-called first law of affinity, which reads as follows:

“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 unit, and drive out the other.”
— Etienne Geoffroy (1718), “Concerning the Different Affinities Observed in Chemistry Between Different Substances” (pg. 68), Aug 27[2]

Geoffroy, on this basis, made the following "affinity table"[3], itself but a visual tabulation of the logic defined in Newton's Query 31:

Geoffroy affinity table.png

Cullen lectures

In 1757, Cullen, during his chemistry lectures at Glasgow University, building on Geoffroy, began to employ crochets or brackets: " { " to signify a bond or chemical bond, operating between chemical species, and darts: "" or "Cullen dart.jpg"to signify the direction of the force (or chemical affinity) guiding a species to its preferred direction. In the Cullen scheme, the following notation means that species A and species B are attached in a bonded union, the { signifying the bond:

which equates to AB in modern terms; although, to note, the A, B, C, etc., generic letter notation for chemical species was not introduced until 1775 by Torbern Bergman, who, in his Dissertation on Elective Attractions, presented an updated and expanded version of what Geoffroy and Cullen began. Thus, a reaction wherein species C is introduced to bonded species AB would have been something along the following lines:

In other words:

AB + C → AC + B

Cullen, however, at this point in time, being essentially "the" sole pioneer or inventor of the chemical reaction notation scheme[4], didn't use the arrow or "dart", as he called it, to signify reactants going to products, as we do in modern times, but rather to illustrate the direction of the affinity "force" or attractive virtue or power that moves small bodies, in this case from species A attracted to or directed towards species C:

Cullen reaction (AB + C).png

In detail, as Cullen would have explained in his classroom lecture notes, when the bonded species AB, symbolized by Cullen via the notation: AB bonded.png , where the bonding bracket or "crotchet" signified the "force" of attachment or "chemical bond", in modern term, was brought into contact with an unbonded species C, symbol: Unbonded species.png , wherein species C had more attractive force for A than A had for B, then, via the nature of the interaction or reaction, A would break from B and form a new bond with C, as shown below:


thereby displacing species B, making it a new unbonded species.

In other words, Cullen's "dart" Cullen dart.jpg , in short, was meant to symbolize what Newton refered to as a certain "power, virtue, or force acting" between small particles through a distance, the direction of the arrow indicating the direction of the force or pointing nature of the affinity; in Newton's own words:

“Have not the small particles of bodies certain ‘powers’, ‘virtues’, or ‘forces’, by which they act at a distance, act at a distance, not only upon the rays of light for reflecting, refracting, and inflecting them, but also upon one another for producing a great part of the phenomena of nature? What I call ‘attraction may be performed by impulse, or by some other means unknown to me. I use that word here to signify only in general any force by which bodies tend towards one another, whatsoever be the cause. For we must learn from the phenomena of nature what bodies attract one another, and what are the laws and properties of the attraction, before we enquire the cause by which the attraction is performed. .”
— Newton (1718), “Query 31” (pgs. 375-76)
An expanded and annotated visual column #3 of Geoffroy's affinity table, showing the bonds involved in the first three Cullen reactions (1757), exemplifying the so-called "first law of affinity" (Geoffroy, 1718), according to which, via the introduction of any single column (column three in this case) row species, situated "above" any other species, in the same column, of the Geoffroy affinity table (1718), in a bond to the top row (R1) species, will disrupt the bond, and causing the top row species to detach from its bonded partner, and form a new bond, with the newly introduced species. Hence, in the first reaction copper, a row three species (R3), is introduced to the silver-neter union (bond 1), which breaks the bond, forming copper-neter (bond 2). Next, iron, a row two species (R2), is introduced to the copper-neter union, breaking it, and forming the iron-neter product (bond 3).The fourth reaction, is when zinc is introduced to neter-iron ♂🜕> union (bond 3), causing neter 🜕> to displace iron , and to form a new bond (bond 4) to zinc, in the form of zinc-nitrate, symbol: 🜕>, formula: Zn(NO3)2. Neter, in sum, has the following neter affinity preferences: Less affinity | Ag < Cu < Fe < Zn | More affinity. Neter, accordingly, is able to bond to four different species, but by simple contact, each species will be displaced by a more powerfully-affined species, in the order shown.

Hence, a core example, in Cullen's lecture notes, used is the list of species in the third column of Geoffroy’s affinity table, as shown in expanded form adjacent.[5] The top row species, in the Geoffroy scheme, is the so-called reactant-centric species, the one that can react with all species listed below it, in the same column.

At the head of the third column, i.e. row-one, column-three (R1:C3), is neter or nitric acid (symbol: 🜕>) (Cullen, 1757) (formula: HNO3), or "acide nitreux" (symbol: >🜕) (Geoffroy, 1718). Subsequently, the relative affinities, or forces of reaction, of nitric acid, the top row species, with respect to chemical contact to each of the other species listed in rows below, according to Geoffroy, are in the order: iron (R2:C3), copper (R3:C3), lead ђ (R4:C3), mercury (R5:C3), and silver (R6:C3).

Reaction 1 | Silver nitrate + copper

The first (of six) so-called "column three reactions", discussed in lecture by Cullen, using his newly-invented chemical reaction notation and diagram, is the situation wherein, at first, nitric acid 🜕> (R1:C3), is bonded in chemical union to silver (R6:C3), as indicated below by the bonding bracket { or crochet:[5]

Silver nitrate.jpg

This chemical bond notation, in modern terms, would be equivalent to one of the following:


wherein the dash (-), or dash implicit (☾🜕> or AgNO3), would be representative of the "force" attaching or holding the two species in proximity, e.g. exchange force (Heitler, 1927), valence bond, covalent bond, ionic bond, etc., depending on the level of understanding and force theory employed, and the proton core and electron shell nature of the species involved in the union. Cullen then describes the introduction of copper (R3:C3) into the silver nitrate system, ☾-🜕> or AgNO3, as follows:

Silver nitrate + copper.jpg

wherein, according to Cullen, the dart: "" signifies the greater "affinity", or force of attraction, that neter 🜕> has for copper , as compared to its bonded affinity to silver . Hence, owing to the greater relative affinity, of neter to copper, than neter to silver, a chemical reaction ensues, wherein the the bond between neter and silver is broken, and a new bond between neter and copper is formed.

This reaction, in modern notation, is shown below:

♀ + ☾🜕> → ♀🜕> + ☾


wherein we see copper ( or Cu) newly bonded to the neter, symbol: 🜕>, formula: NO3, in the form of: ♀🜕> or Cu(NO3)2, with the silver precipitating out.

Reaction 2 | Copper nitrate + iron

The next reaction Cullen demonstrates, so to demonstrate how affinity powers are ranked into each row of Geoffroy's affinity table, is that of copper nitrate, formula: Cu(NO3)2, or symbol: ♀🜕>, plus iron (Fe) (R2:C3), as shown below:

Copper nitrate + iron.jpg

where, according to Cullen, the neter (🜕> or NO3) has a stronger affinity attraction to iron than to copper, which is signified by the "dart" pointing from neter to iron, and hence reaction ensues, and iron nitrate, formula: Fe(NO3)2, symbol: ♂🜕>, forms as a product, along with copper (Cu) precipitating out.

The modern equivalent is shown below:

+ 🜕> ♂🜕> + ♀


where copper Cu precipitates out of the solution.

Reaction 3 | Iron nitrate + zinc

The third reaction Cullen employs is iron nitrate, formula: Fe(NO3)2, symbol: ♂🜕>, plus zinc (Zn), symbol: Zinc 25x26.jpg, wherein for a third time the neter is displaced from its bonded partner owing to a strong affinity force, in this case for the zinc, having a greater force of attraction to the zinc that compared to the bonding force of its union with iron :

Iron nitrate + zinc.jpg

The modern equivalent is shown below:

Zinc 25x26.jpg + ♂🜕> Zinc 25x26.jpg🜕> + ♂


wherein zinc nitrate Zn(NO3)2 is formed and the iron Fe precipitates out of the solution.


In 1775, Torbern Bergman, in his Dissertation on Elective Attractions, building on Cullen and the other affinity table makers, presented the largest affinity table to date.[6] In 1785, Bergman's textbook was translated into German.


A summary of the reaction diagrams of William Cullen (1757), Torbern Bergman (1775), Johann Goethe (1809), and Jacobus Hoff (1883), the later of whom upgraded Cullen's one-way reaction "dart", with a two-way reaction arrow, to signify that in a reaction beaker or system, there are both forward and reverse path reactions occurring simultaneously.

In 1794, Goethe, in his "Third Lecture on Anatomy", began speaking of the chemical affinities in respect to human relations.

In 1808, Goethe, in his mind, if not in draft print, made the human affinity table:[7]

Geoffroy affinity table (1718) and Goethe affinity table (1808).png

In 1809, Goethe, in his Elective Affinities, presented Cullen-Bergman reaction logic, extrapolated up to the human reaction level, via 36 coded chapters, wherein each chapter is a new human chemical reaction.



Cullen was influenced by: Etienne Geoffroy, Hermann Boerhaave, and Georg Stahl.


Cullen influenced: Joseph Black, his student, Torbern Bergman, and Johann Goethe.


Cullen was friends with: David Hume.[8]


Quotes | On

The following are quotes on Cullen:

“After Boerhaave's decease, the lectures on chemistry were continued at Leyden by his pupil Gaubius, whose lectures on that subject seem to have been circulated extensively in manuscript, and to have been much sought after by Cullen.”
— John Thomson (1832), An Account of the Life, Lectures and Writings of William Cullen, Volume One (pg. 38)[9]

Quotes | By

The following are quotes by Cullen:

Chemistry is an art that has furnished the world with a great number of useful facts, and has thereby contributed to the improvement of many arts; but these facts lie scattered in many different books, involved in obscure terms, mixed with many falsehoods, and joined to a great deal of false philosophy; so that it is no great wonder that chemistry has not been so much studied as might have been expected with regard to so useful a branch of knowledge, and that many professors are themselves but very superficially acquainted with it. But it was particularly to be expected, that, since it has been taught in universities, the difficulties in this study should have been in some measure removed, that the art should have been put into form, and a system of it attempted—the scattered facts collected and arranged in a proper order. But this has not yet been done; chemistry has not yet been taught but upon a very narrow plan. The teachers of it have still confined themselves to the purposes of pharmacy and medicine, and that comprehends a small branch of chemistry; and even that, by being a single branch, could not by itself be tolerably explained. I do not choose the invidious task of derogating from established reputations; but were it necessary, I could easily show that the most celebrated attempts towards a system or course of chemistry are extremely incomplete, as examining but a few of the objects of chemistry; that of those examined a very scanty and imperfect account of their relations to other bodies is given ; and that, even what is given, is in a method inconvenient and faulty. Now this is the case with the generality of the books on chemistry; but I must take notice, however, that Dr Stahl is one who has endeavored to avoid these faults; he has taught chemistry with a more general view, and attempted to collect the chemical facts, and to range them in a better order. Perhaps we have the substance of Dr Stahl's lessons, in a book published by a disciple of his, Dr Juncker of Halle, under the title of Conspectus Chemiae. This is the fullest collection that I have met with, and I have made a good deal of use of it, and you may do so too; but I must notice at the same time, that it is written in such a clumsy manner, is mixed with so much pedantic, trifling philosophy, and is often so inaccurate and superficial in describing experiments, that it will not contribute much to the propagating of chemical knowledge.”
— William Cullen (c.1748), “Fragment of Early Chemistry Lecture”[9]

End matter

See also

  • History of chemical equations [4]


  1. Alchemical symbol – Wikipedia.
  2. (a) Geoffroy, Etienne. (1718). “Concerning the Different Affinities Observed in Chemistry Between Different Substances: Table of the Different Relations Observed between Different Substances” (Tableau des différentes Rapports Observées entre Différentes Substances), Memoires de l’Academie Royale des Sciences (quote, pg. 203), 202-12, Aug 27; in: A Source Book in Chemistry, 1400-1900 (editors: Henry Leicester, Herbert S. Klickstein) (pgs. 67-74). Harvard University Press.
    (b) Adler, Jeremy. (1990). "Goethe's use of chemical theory in his Elective Affinities" (§18, pgs. 263-79; Geoffroy’s law of affinity, pg. 265); in: Romanticism and the Sciences (editors: Andrew Cunningham and Nicholas Jardine). Cambridge.
    (c) Geoffroy’s law of affinity – Hmolpedia 2020.
  3. Geoffroy’s affinity table – Hmolpedia 2020.
  4. 4.0 4.1 History of chemical equations – Hmolpedia 2020.
  5. 5.0 5.1 Thims, Libb. (2007). Human Chemistry, Volume Two (pgs. 385-388). LuLu.
  6. Bergman affinity table – Hmolpedia 2020.
  7. Goethe affinity table – Hmolpedia 2020.
  8. William Cullen (WB) – JamesLindLibrary.org.
  9. 9.0 9.1 Thomson, John. (1832). An Account of the Life, Lectures and Writings of William Cullen, Volume One (chemistry lectures, pg. 35-; sought after, pg. 38; lecture fragment, pgs. 40-41; double elective affinities, pg. 5##-). Blackwood.

External links

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