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{{Short description|Argument over whether atoms and molecules are real objects, closed by experiments between 1908 and 1913}}
{{About|the argument over whether atoms and molecules exist|the company|Molecular Reality Corporation|the 1972 history of Jean Perrin's work|Molecular Reality (book)}}
'''Molecular reality''' is the question of whether atoms and molecules are physical objects or only useful fictions of chemistry and physics, and the name [[Jean Perrin]] gave to his answer. The question was open for most of the second half of the nineteenth century. For most working scientists it was closed between 1908 and 1913, and the evidence that closed it was the jittering of visible grains suspended in liquids, the motion known as [[Brownian motion]].

Several leading figures had declined to treat atoms as real. [[Ernst Mach]] held that physics should describe what can be observed, and the chemist Wilhelm Ostwald built a system called energetics in which energy takes the place of matter.<ref name="gori" /><ref name="uffink" /> [[Ludwig Boltzmann]], the best-known defender of atoms, argued that the choice should depend on fruitfulness and expected atoms to win on that ground.<ref name="uffink" /> In 1905 Albert Einstein calculated how far a particle a thousandth of a millimetre across should wander in water if water is made of moving molecules.<ref name="einstein1905" /> From 1908 Perrin and his students tested that prediction and others on emulsions of resin grains, and in 1913 he set side by side the values of [[Avogadro constant|Avogadro's constant]] that thirteen different phenomena gave. They fell between 6.0 and 7.5 × 10<sup>23</sup> per mole. The value fixed by international agreement in 2019 is 6.02214076 × 10<sup>23</sup>.<ref name="atoms" /><ref name="nist" />

Ostwald announced his change of mind in the preface to a textbook, dated November 1908. Henri Poincaré said in a lecture published in 1913 that Perrin's determinations had "completed this triumph of atomism", and Perrin received the 1926 Nobel Prize in Physics.<ref name="ostwald" /><ref name="poincare" /><ref name="nobel1926" /> The phrase "molecular reality" is the title of his 1909 memoir on Brownian movement and, in 1972, of Mary Jo Nye's history of his work, [[Molecular Reality (book)|''Molecular Reality'']].<ref name="perrin1910" /><ref name="nye" />

== Background ==
=== Atoms in chemistry ===
Ancient writers had argued that matter consists of indivisible particles in a void. Perrin observed in his Nobel lecture that imagination had been free to choose between that view and a continuous "full" ever since antiquity.<ref name="nobel" /> The first working atomic theory came from chemistry. John Dalton's ''A New System of Chemical Philosophy'' (1808) described each element as made of identical atoms and each compound as a fixed combination of them, which explained why elements unite in fixed proportions.<ref name="chalmers" /> Joseph-Louis Gay-Lussac reported in 1809 that gases combine in simple ratios of volume, and Amedeo Avogadro (1811) and André-Marie Ampère (1814) suggested that equal volumes of gas hold equal numbers of particles. Dalton saw the difficulty: one volume of oxygen and two of hydrogen make two of steam, so a water "atom" would have to contain half an oxygen "atom". The way out was a distinction between atoms and molecules, and chemists did not generally accept it for decades.<ref name="chalmers" />

In September 1860 the first international congress of chemists met at Karlsruhe to settle how atomic weights and formulae should be determined. Stanislao Cannizzaro, who had argued for Avogadro's distinction in a paper of 1858, defended it there, and copies of his pamphlet were handed out to the delegates.<ref name="lindahall" /> The successes of chemistry still said nothing about absolute sizes. In Perrin's words, if all atoms became a thousand times smaller, or a milliard times smaller, "our chemical laws and our formulae would be unchanged."<ref name="nobel" />

=== Molecules in physics ===
Physicists meanwhile had begun to treat a gas as a crowd of molecules in motion. [[James Clerk Maxwell]] showed that the viscosity of a gas ought to be independent of its density, a result that looked odd and that his own measurements supported in 1866; Perrin counted it among the first important successes of the kinetic theory.<ref name="atoms" /> Viscosity gave the distance a molecule travels between collisions, that distance gave a size for the molecule, and the size gave a count. Josef Loschmidt, who is best known for his estimate of molecular size, made an early calculation of that kind in 1865.<ref name="uffink" /><ref name="straumann" />

Perrin summarised the results in his Nobel lecture. The molecular diameters came out between 2 and 5 ten-millionths of a millimetre, and the corresponding values of Avogadro's number between 40 and 120 × 10<sup>22</sup>, with an uncertainty he called "largely 100 per cent". He admired the reasoning but judged that it rested on simplifying assumptions and on the hypotheses it was meant to test. Conviction, he wrote, "will without doubt come to life if entirely different paths lead us to the same values for the molecular sizes."<ref name="nobel" />

== Objections ==
The Stanford Encyclopedia of Philosophy states that atomism "was rejected by leading scientists and philosophers such as Wilhelm Ostwald, Pierre Duhem, and Ernst Mach up to the end of the nineteenth century and beyond."<ref name="chalmers" /> Their reasons differed from one another.<ref name="uffink" />

=== Thermodynamics and energetics ===
Thermodynamics treated heat and chemical change without saying anything about the structure of matter, and it worked. Ostwald, Duhem and Max Planck were inclined to take it as the model of how science should proceed, keeping a secure relation to experiment and avoiding hypotheses of the kind atomism needed.<ref name="chalmers" /> Duhem and Ostwald accepted the structural formulae of chemistry but would not take them as pictures of arrangements of atoms. Ostwald's energetics went further. It took energy as the most fundamental physical entity and described processes as transformations of energy, without mechanical pictures.<ref name="chalmers" /><ref name="uffink" />

In 1895 the annual meeting of German scientists and physicians at Lübeck gave energetics a session. Georg Helm and Ostwald presented it. Boltzmann, who sat on the programme committee, answered with what Jos Uffink calls "devastating criticism", and those present judged him the clear winner. The energeticists, who had expected a discussion in the "British style" with papers circulated beforehand, felt ambushed. Boltzmann and Ostwald remained friends.<ref name="uffink" />

=== Mach ===
Mach's objection dates from the early 1870s and is a form of Occam's razor. One should not credit the unobservable entities of a hypothetical microworld with the properties of observable bodies, and while descriptions can do without atoms they remain, in the summary by Pietro Gori and Luca Guzzardi, "pure things of thought".<ref name="gori" /> Boltzmann told the best-known story of the disagreement in his first lecture on natural philosophy at the University of Vienna, given on October 26, 1903. During a debate on atomism among a group of academicians that included Mach, he said, Mach declared "suddenly and laconically": "I do not believe that atoms exist." The remark "kept going round in my head", Boltzmann said, and led to the only philosophical paper he had written so far.<ref name="boltzmann1903" />{{efn|The German is "Ich glaube nicht, daß die Atome existieren." Boltzmann's retelling gives no year, though accounts of the exchange often date it to 1897. He prefaced the printed lecture by saying that, because he had spoken freely, he could guarantee its sense and could not guarantee its wording. The translations are the editors'.}} Mach is also usually quoted as having asked of atoms, "Have you ever seen one?"{{Citation needed|date=October 2026}}

The reading of Mach as a flat denier is contested. Gori and Guzzardi write that his position "is less straightforward than is often claimed". Some historians think he accepted atomism in his early writings and later allowed it only as a hypothesis for organizing appearances, as he purportedly told Einstein at their meeting in 1910.<ref name="gori" />

=== Boltzmann ===
Boltzmann is often drawn as a lone realist besieged by positivists. Uffink's account describes a more careful man. From the 1880s Boltzmann said that the atomic view gave at best an analogy, a picture or model of reality, and he argued that no approach in natural science which avoided hypotheses completely could succeed. What divided him from Mach was, in Uffink's words, "more a strategic issue".<ref name="uffink" /> In the foreword to the second volume of his ''Lectures on Gas Theory'', dated August 1898, he wrote that the attacks on gas theory rested merely on misunderstandings and that the theory's role in science was far from played out. He was aware, he added, how powerless the individual remains against the currents of the time, and he had therefore put the hardest parts of the theory into the book so that, when people returned to it, not too much would have to be discovered a second time.<ref name="boltzmann1898" />{{efn|The German is "Wie ohnmächtig der Einzelne gegen Zeitströmungen bleibt, ist mir bewusst." The translation is the editors'.}}

Some objections came from men who accepted atoms. Loschmidt, Boltzmann's former teacher and lifelong friend, raised the reversibility objection to Boltzmann's statistical theory in 1876, and Ernst Zermelo raised the recurrence objection in 1896.<ref name="uffink" />

== Brownian motion ==
The motion was already seventy-odd years old. Perrin's history of it names Robert Brown, who observed it in 1827, and later writers who held that the agitation belongs to the liquid itself: Christian Wiener in 1863, William Ramsay in 1876, Delsaulx and Carbonelle, and Georges Gouy in 1888.<ref name="atoms" /> Perrin was careful about the status of that idea. However seductive it was, he wrote, "it is nevertheless a hypothesis only."<ref name="atoms" />

Einstein's paper, received by the ''Annalen der Physik'' on May 11, 1905, derived the motion from the molecular-kinetic theory of heat. "It is possible that the movements to be discussed here are identical with the so-called 'Brownian molecular motion'," he began, but the information available to him about that was "so lacking in precision, that I can form no judgment in the matter." He added that had the prediction proved incorrect, "a weighty argument would be provided against the molecular-kinetic conception of heat."<ref name="einstein1905" /><ref name="einstein-tr" />

The result was a formula for the diffusion of a grain of radius ''a'' in a liquid of viscosity ''η'' at absolute temperature ''T'': ''D'' = ''RT'' / (6π''ηaN''), where ''R'' is the gas constant and ''N'' Avogadro's constant. The mean square displacement along one axis in a time ''t'' is 2''Dt''. Everything in the formula except ''N'' can be measured, so a measurement of how far grains wander yields the number of molecules in a mole. Einstein's own example was a grain 0.001 mm across in water, which should move on average 0.8 µm along one axis in a second and about 6 µm in a minute.<ref name="einstein-tr" /> William Sutherland in Australia reached the same formula at almost the same time, and Marian Smoluchowski published a kinetic theory of the motion in 1906.<ref name="straumann" /><ref name="smoluchowski" />

Perrin learned of Einstein's paper through Paul Langevin. Einstein and Smoluchowski had pointed out that the order of magnitude of the motion seemed to agree with their predictions, but Perrin wrote that nothing more precise could be said until spherules of known size had been prepared.<ref name="nobel" />

== Perrin's experiments ==
=== Emulsions ===
Perrin's first task was to make grains of equal size. He dissolved a resin, gamboge or mastic, in alcohol, added a large amount of water so that spherules of every size precipitated, and sorted them by repeated centrifuging, a process he compared to fractional distillation. In his most careful fractionation, 1 kilogram of gamboge gave after several months a few decigrams of grains of the diameter he wanted, about three-quarters of a micrometre. That is a yield of a few parts in ten thousand.<ref name="atoms" /><ref name="nobel" />

[[File:Perrin_gamboge_column.webp|thumb|right|upright=1.3|alt=Bar chart of four grain counts falling by roughly half at each of four heights|The counts at four heights in one of Perrin's gamboge preparations, drawn by code from the numbers printed in ''Les Atomes''. It is not a copy of any figure in the book.]]
Then he let a drop of the emulsion settle in a sealed cell. The grains behaved like the molecules of a very heavy gas in a very small atmosphere, thinning out with height. In one series, using gamboge grains of radius 0.212 µm in a cell 100 µm deep, he counted 13,000 grains at four levels 30 µm apart and found relative concentrations of 100, 47, 22.6 and 12, close to the geometric progression 100, 48, 23 and 11.1 that the gas laws predict.<ref name="atoms" /> The height at which the number halved, compared with the height at which the density of air halves, gave the weight of a grain as a multiple of the weight of an air molecule. The grain's weight could be measured, so the molecule's weight and the constant followed. "It was with the liveliest emotion that I found, at the first attempt, the very numbers that had been obtained from the widely different point of view of the kinetic theory," he wrote.<ref name="atoms" /> He varied the volume of the grains by a factor of 50, the resin, the liquid (including glycerine 125 times more viscous than water) and the temperature, from -9 °C to 60 °C, and the value held.<ref name="atoms" />

He also followed single grains. A camera lucida drawing of the horizontal position of a mastic grain 0.53 µm in radius, marked every 30 seconds, gives a tangle of straight segments. Perrin remarked that if the positions were marked at intervals 100 times shorter, each segment would be replaced by a polygon as complicated as the whole figure, so that it is meaningless to speak of a tangent to such a trajectory.<ref name="atoms" /> Measured displacements gave a second value of the constant. A third came from rotation, which Einstein had also predicted: a sphere 1 µm across turns too fast to follow, so Perrin made mastic spherules about 12 µm across.<ref name="nobel" />

=== The thirteen determinations ===
In the conclusion of ''Les Atomes'' (1913) Perrin listed the phenomena that had yielded a value of the constant.<ref name="atoms" />

{| class="wikitable"
|+ Values of ''N'' in Perrin's table, in units of 10<sup>22</sup> per gram-molecule
! Phenomenon !! ''N'' / 10<sup>22</sup>
|-
| Viscosity of gases (van der Waals' equation) || 62
|-
| Brownian movement: distribution of grains || 68.3
|-
| Brownian movement: displacements || 68.8
|-
| Brownian movement: rotations || 65
|-
| Brownian movement: diffusion || 69
|-
| Irregular molecular distribution: critical opalescence || 75
|-
| Irregular molecular distribution: the blue of the sky || 60 (marked uncertain by Perrin)
|-
| Black body spectrum || 64
|-
| Charged spheres (in a gas) || 68
|-
| Radioactivity: charges produced || 62.5
|-
| Radioactivity: helium engendered || 64
|-
| Radioactivity: radium lost || 71
|-
| Radioactivity: energy radiated || 60
|}

On this scale the modern value is 60.2214076. Twelve of the thirteen entries lie within 18 percent of it, and the other, critical opalescence, within 25 percent. Perrin wrote that the agreement gave "the real existence of the molecule" a "probability bordering on certainty".<ref name="atoms" /> He also pointed out what the agreement left unsaid. Eliminating the constant between the 13 equations leaves 12 equations connecting only quantities that can be measured, relating for example the viscosity of gases, Brownian movement, the blue of the sky and radioactivity. "The atomic theory has triumphed," the conclusion continues. "Its opponents, which until recently were numerous, have been convinced and have abandoned one after the other the sceptical position that was for a long time legitimate and no doubt useful."<ref name="atoms" />

[[File:Perrin_thirteen_determinations.webp|thumb|right|upright=1.3|alt=Dot plot of thirteen values of Avogadro's constant clustered between 60 and 75 with the modern value at 60.2|The thirteen values in Perrin's table plotted against the modern value, drawn by code from the table above.]]

== Conversions ==
Ostwald's concession came first. The preface to the fourth German edition of his ''Grundriss der allgemeinen Chemie'', signed at Grossbothen in November 1908, says: "I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years." He named two sources of evidence: the isolation and counting of gas ions, which crowned J. J. Thomson's researches, and the agreement of Brownian movements with the kinetic hypothesis, "established by many investigators and most conclusively by J. Perrin". These, he wrote, "justify the most cautious scientist in now speaking of the experimental proof of the atomic nature of matter." The atomic hypothesis "is thus raised to the position of a scientifically well-founded theory, and can claim its place in a text-book intended as an introduction to the present state of our knowledge of General Chemistry."<ref name="ostwald" /> The same preface adds that for stoichiometry alone the atomic theory is a convenient mode of representation, since the facts can be represented without it. In 1909 Ostwald received the Nobel Prize in Chemistry for his work on catalysis and chemical equilibria.<ref name="ostwald" /><ref name="nobel1909" />

Poincaré's endorsement came in a lecture to the Société française de physique, printed in 1913 in ''Dernières pensées''. He wrote that "the brilliant determinations of the number of atoms made by M. Perrin have completed this triumph of atomism", and that what carried conviction was "the multiple agreements between results obtained by entirely different methods". The chemist's atom, he said, is now a reality, which did not mean that its ultimate elements had been touched: the atom is a world.<ref name="poincare" />{{efn|The French is "Les brillantes déterminations du nombre des atomes faites par M. Perrin ont complété ce triomphe de l'atomisme." and "L'atome du chimiste est maintenant une réalité". The translations are the editors'.}}

Mach's record is less tidy. Max Planck, who had favoured thermodynamics over atoms in the 1890s, attacked Mach's philosophy in a lecture printed in 1909, and a study of Mach's last notebook suggests that shortly afterward Mach threatened to leave physics if belief in atoms were required. Einstein met him in September 1910 and tried to persuade him to accept atomism.<ref name="blackmore" /> Einstein's later account, in the autobiographical notes of 1949, nevertheless lists Mach among the sceptics convinced: he wrote that the agreement of his Brownian-motion considerations with experience, together with Planck's determination of molecular size from the law of radiation, "convinced the sceptics ... (Ostwald, Mach) of the reality of atoms", and that the antipathy of those scholars could be traced to "their positivistic philosophical attitude."<ref name="duplantier" />

The conclusion of ''Les Atomes'' ends on the conflict itself: "Equilibrium between the instincts towards caution and towards boldness is necessary to the slow progress of human science; the conflict between them will henceforth be waged in other realms of thought."<ref name="atoms" /> The 1926 Nobel Prize in Physics went to Perrin "for his work on the discontinuous structure of matter, and especially for his discovery of sedimentation equilibrium". Theodor Svedberg received that year's Prize in Chemistry for his work on disperse systems.<ref name="nobel1926" /><ref name="nobel1926c" />

== Historiography ==
Popular accounts often attach a death to the story. Boltzmann died by suicide at Duino, near Trieste, on September 5, 1906, and it is sometimes said that the rejection of atoms drove him to it.<ref name="mactutor" /> Uffink's entry calls that a myth. Boltzmann's reputation was high, he was recruited by one university after another, and, in Uffink's words, "there is no factual evidence for the claim that Boltzmann was ignored or suffered any unusual lack of recognition". In Uffink's reading the suicide "seems to have been due to factors in his personal life", a decline of mental and physical health, with academic matters playing no part.<ref name="uffink" /> Uffink adds that Boltzmann's complaints of a hostile environment in 1896 to 1898 were partly a taste for polemic and partly his health, though the disputes with Ostwald and Zermelo may have contributed to the crisis.<ref name="uffink" />

What Perrin observed were grains of resin, which he called, in his Nobel lecture, "visible molecules". His claim was that thirteen routes to one number made the existence of the molecule overwhelmingly probable, and that the visible consequences could be written down without mentioning molecules at all. Poincaré stopped short of calling atoms ultimate. Alan Chalmers observes that Perrin's argument needs only the central assumptions of kinetic theory, equipartition of energy and the randomness of molecular agitation, with no auxiliary assumptions, and that this made it more telling than other determinations; citing Nye, he adds that Ostwald gave this as the reason for his conversion.<ref name="chalmers" /><ref name="nobel" />

== The phrase ==
Perrin used the words in his 1909 memoir. A section titled "Molecular reality" follows a table of the phenomena that, "taken altogether", form "what may be termed the proof of molecular reality", and begins: "I think it impossible that a mind, free from all preconception, can reflect upon the extreme diversity of the phenomena which thus converge to the same result, without experiencing a very strong impression."<ref name="perrin1910" /> F. Soddy's English translation of the memoir, published in 1910, is titled ''Brownian Movement and Molecular Reality''.<ref name="perrin1910" /> Nye's book of 1972 takes the last two words of that title for its own. The Stanford Encyclopedia of Philosophy uses them again in a section heading, "Brownian Motion and Molecular Reality".<ref name="nye" /><ref name="chalmers" />

In the preface to ''Les Atomes'' Perrin wrote that "a time may perhaps come when atoms, directly perceptible at last, will be as easy to observe as are microbes to-day."<ref name="atoms" />

The company [[Molecular Reality Corporation]] was founded in 2018 as demonpore, inc. and took its present name in 2021.<ref name="records" /> Its 2022 document "[[Our North Star]]: Utility-Scale Molecular Sensing" has a section titled "Increasing Awareness of Molecular Reality".<ref name="northstar" /> The founder's introduction to [[Epic Quest Bio]] says: "We should be 'seeing' molecular reality, from everyone and everywhere, right at home."<ref name="essay" />

== See also ==
* [[Jean Perrin]]
* [[Les Atomes]]
* [[Brownian motion]]
* [[Avogadro constant]]
* [[Ernst Mach]]
* [[Ludwig Boltzmann]]
* [[Maxwell's demon]]
* [[Molecular Reality (disambiguation)]]

== Notes ==
{{Notelist}}

== References ==
{{Reflist|refs=
<ref name="chalmers">{{cite web |url=https://plato.stanford.edu/entries/atomism-modern/ |title=Atomism from the 17th to the 20th Century |author=Alan Chalmers |website=Stanford Encyclopedia of Philosophy |date=2026-02-20 |access-date=2026-10-25}}</ref>
<ref name="uffink">{{cite web |url=https://plato.stanford.edu/entries/statphys-Boltzmann/ |title=Boltzmann's Work in Statistical Physics |author=Jos Uffink |website=Stanford Encyclopedia of Philosophy |date=2024-10-10 |access-date=2026-10-25}}</ref>
<ref name="gori">{{cite web |url=https://plato.stanford.edu/entries/ernst-mach/ |title=Ernst Mach |author=Pietro Gori and Luca Guzzardi |website=Stanford Encyclopedia of Philosophy |date=2026-09-15 |access-date=2026-10-25}}</ref>
<ref name="mactutor">{{cite web |url=https://mathshistory.st-andrews.ac.uk/Biographies/Boltzmann/ |title=Ludwig Eduard Boltzmann |website=MacTutor History of Mathematics Archive |access-date=2026-10-25}}</ref>
<ref name="atoms">{{cite book |last=Perrin |first=Jean |title=Atoms |publisher=Constable |year=1916 |url=https://archive.org/details/atomsper00perruoft |pages=vi-viii, 84-89, 103-104, 114-117, 206-208}} Translated by D. Ll. Hammick from the fourth French edition of ''Les Atomes'' (Paris: Félix Alcan, 1913).</ref>
<ref name="perrin1910">{{cite book |last=Perrin |first=Jean |title=Brownian Movement and Molecular Reality |publisher=Taylor and Francis |year=1910 |url=https://archive.org/details/brownianmovement00perr |pages=90-93}} Translated by F. Soddy from the ''Annales de chimie et de physique'', 8th series, September 1909.</ref>
<ref name="nobel">{{cite web |url=https://www.nobelprize.org/prizes/physics/1926/perrin/lecture/ |title=Discontinuous Structure of Matter (Nobel lecture, December 11, 1926) |author=Jean Baptiste Perrin |website=NobelPrize.org |access-date=2026-10-25}}</ref>
<ref name="nobel1926">{{cite web |url=https://www.nobelprize.org/prizes/physics/1926/summary/ |title=The Nobel Prize in Physics 1926 |website=NobelPrize.org |access-date=2026-10-25}}</ref>
<ref name="nobel1926c">{{cite web |url=https://www.nobelprize.org/prizes/chemistry/1926/summary/ |title=The Nobel Prize in Chemistry 1926 |website=NobelPrize.org |access-date=2026-10-25}}</ref>
<ref name="nobel1909">{{cite web |url=https://www.nobelprize.org/prizes/chemistry/1909/summary/ |title=The Nobel Prize in Chemistry 1909 |website=NobelPrize.org |access-date=2026-10-25}}</ref>
<ref name="ostwald">{{cite book |last=Ostwald |first=Wilhelm |title=Outlines of General Chemistry |publisher=Macmillan |year=1912 |url=https://archive.org/details/outlinesofgenera00ostwrich |page=vi}} Translated by W. W. Taylor from the fourth German edition, whose preface is signed Grossbothen, November 1908.</ref>
<ref name="poincare">{{cite book |last=Poincaré |first=Henri |title=Dernières pensées |publisher=Flammarion |year=1913 |url=https://archive.org/details/dernirespens00poin |pages=197-199}} Chapter 7, "Les rapports de la matière et de l'éther".</ref>
<ref name="boltzmann1898">{{cite book |last=Boltzmann |first=Ludwig |title=Vorlesungen über Gastheorie, II. Theil |publisher=Barth |place=Leipzig |year=1898 |url=https://archive.org/details/vorlesungenber02bolt |pages=v-vi}} Foreword dated Volosca, Villa Irenea, August 1898.</ref>
<ref name="boltzmann1903">{{cite book |last=Boltzmann |first=Ludwig |title=Populäre Schriften |publisher=Barth |place=Leipzig |year=1905 |chapter=Ein Antrittsvortrag zur Naturphilosophie}} The lecture of October 26, 1903 was first printed in ''Die Zeit'', December 11, 1903.</ref>
<ref name="einstein1905">{{cite journal |last1=Einstein |first1=Albert |title=Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen |journal=Annalen der Physik |volume=322 |issue=8 |pages=549-560 |year=1905 |doi=10.1002/andp.19053220806}}</ref>
<ref name="einstein-tr">{{cite book |last=Einstein |first=Albert |title=Investigations on the Theory of the Brownian Movement |publisher=Methuen |place=London |year=1926 |pages=1-18}} Translated by A. D. Cowper.</ref>
<ref name="smoluchowski">{{cite journal |last1=Smoluchowski |first1=Marian |title=Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen |journal=Annalen der Physik |volume=326 |issue=14 |pages=756-780 |year=1906 |doi=10.1002/andp.19063261405}}</ref>
<ref name="straumann">{{cite web |url=https://arxiv.org/abs/physics/0504201 |title=On Einstein's Doctoral Thesis |author=Norbert Straumann |website=arXiv |date=2005-04-27}}</ref>
<ref name="duplantier">{{cite web |url=https://arxiv.org/abs/0705.1951 |title=Brownian Motion, "Diverse and Undulating" |author=Bertrand Duplantier |website=arXiv |date=2007-05-14}} Quotes Einstein's autobiographical notes (1949).</ref>
<ref name="blackmore">{{cite journal |last1=Blackmore |first1=John T. |title=Ernst Mach leaves "the church of physics" |journal=The British Journal for the Philosophy of Science |volume=40 |issue=4 |pages=519-540 |year=1989 |doi=10.1093/bjps/40.4.519}}</ref>
<ref name="nye">{{cite book |last=Nye |first=Mary Jo |title=Molecular Reality: A Perspective on the Scientific Work of Jean Perrin |publisher=Macdonald; American Elsevier |place=London and New York |year=1972 |isbn=0-444-19596-3}}</ref>
<ref name="lindahall">{{cite web |url=https://lindahall.org/stanislao-cannizzaro |title=Stanislao Cannizzaro |website=Linda Hall Library |access-date=2026-10-25}}</ref>
<ref name="nist">{{cite web |url=https://physics.nist.gov/cgi-bin/cuu/Value?na |title=CODATA value: Avogadro constant |website=NIST |access-date=2026-10-25}}</ref>
<ref name="records">{{cite web |title=Company records |publisher=Molecular Reality Corporation |date=October 2026}}</ref>
<ref name="northstar">{{cite web |title=Our North Star: Utility-Scale Molecular Sensing |publisher=Molecular Reality Corporation |year=2022}}</ref>
<ref name="essay">{{cite web |title=Epic Quest Bio |author=Kemmishtree |publisher=Molecular Reality Corporation |date=March 2026}}</ref>
}}

== Further reading ==
* {{cite book |last=Nye |first=Mary Jo |title=Molecular Reality: A Perspective on the Scientific Work of Jean Perrin |publisher=Macdonald; American Elsevier |year=1972 |isbn=0-444-19596-3}}
* {{cite book |last=Perrin |first=Jean |title=Atoms |publisher=Constable |year=1916}}

== External links ==
* [https://www.nobelprize.org/prizes/physics/1926/perrin/lecture/ Perrin's Nobel lecture, "Discontinuous Structure of Matter"] at NobelPrize.org

[[Category:History of physics]]
[[Category:History of chemistry]]
[[Category:Atomic theory]]
[[Category:Scientific controversies]]
[[Category:Brownian motion]]