NOTE-709: Ostwald — Studies on the formation and transformation of solids, I

Contribution

The paper does three things. First, it measures how little solid is needed to set off a supercooled melt or a supersaturated solution, by diluting the solid in milk sugar or quartz powder in homeopathic steps and finding where the effect stops. The limits run from about 10⁻⁷ g for salol to about 10⁻¹⁰ g for sodium chlorate. Second, it fixes the distinction between metastable states, which change only on contact with the new phase, and labile states, where the new phase forms spontaneously. Ostwald had coined “metastabil” earlier, and here he restricts it to the first kind (p. 302). Third, in a short theoretical section (§§32–41, pp. 306–313), it states a general proposition: a system leaving a state reaches the nearest form, not the most stable one. This is the proposition later called the rule of stages. Most of the paper (about 35 of its 42 pages) is about seeds, not about the rule.

Key insight

A supersaturated system has two thresholds, not one. Past equilibrium it enters a metastable zone, where nothing but a seed of the new phase will start the change. Further on it enters a labile zone, where the new phase appears by itself. A less stable form has a narrower metastable zone, so a system driven past equilibrium reaches the labile limit of the less stable form first, and that form appears first (p. 306). What happens next depends on the same two thresholds again. If the new form is only metastable with respect to a still more stable one, it stays until a seed of that one touches it (p. 308). So a seed decides the outcome in the metastable zone, and the rule of the nearest form decides it in the labile zone.

Assumptions

• Seeding is material. Only “eine Spur des fraglichen Stoffes im festen Zustande (oder eines in strengem Sinne isomorphen Körpers)” (“a trace of the substance in question in the solid state, or of a strictly isomorphous body”, p. 289) sets off a metastable melt. He tests this rather than assumes it (§§12, 17).
• Stability is ordered by free energy, and free energy is read off from vapour pressure or solubility: “die Form mit dem grössten Dampfdruck oder der grössten Löslichkeit hat auch die grösste freie Energie” (“the form with the greatest vapour pressure or solubility also has the greatest free energy”, p. 307). The rule needs this order to say what “nearest” means.
• The solid–liquid transition behaves like the liquid–gas one. The argument for the rule (§§32, 40) uses James Thomson’s continuous isotherm and van der Waals’s equation for liquid and vapour, then carries the conclusion to solids “durch Analogie” (“by analogy”, p. 312). He admits the pressure–volume data for solid–liquid are “so gut wie vollständig” missing (“as good as completely”, p. 305).
• The rule covers spontaneous change only. It is stated for leaving a state “freiwillig, d. h. infolge Eintritts in das labile Gebiet” (“spontaneously, that is, as a result of entering the labile region”, p. 307). Seeded change is outside it.

Key results

The rule of the nearest form (§§32–39, pp. 306–310)

The statement, pp. 306–307: “ich möchte die Gesamtheit der bisherigen Erfahrungen über den Gegenstand in den allgemeinen Satz zusammenfassen, dass beim Verlassen irgend eines Zustandes und dem Übergang in einen stabileren nicht der unter den vorhandenen Verhältnissen stabilste aufgesucht wird, sondern der nächstliegende.”

My translation: “I would sum up the whole of experience so far on the subject in the general proposition that, on leaving any state and passing into a more stable one, what is sought out is not the state most stable under the given conditions, but the nearest one.”

He glosses “nearest” at once, p. 307: “Der obige allgemeine Satz besagt dann, dass beim freiwilligen, d. h. infolge Eintritts in das labile Gebiet erfolgenden Verlassen eines Zustandes nicht die Form mit der kleinsten freien Energie erreicht wird, sondern die Form, welche unter möglichst geringem Verlust an freier Energie erreicht werden kann, oder die Form mit der nächstgrössten freien Energie.” My translation: “The general proposition above then says that when a state is left spontaneously, that is, as a result of entering the labile region, the form reached is not the one with the least free energy, but the form that can be reached with the smallest possible loss of free energy, or the form with the next-greatest free energy.”

He calls it “den allgemeinen Satz” (p. 306) and “den Satz von der Bildung der nächstliegenden Form” (“the proposition of the formation of the nearest form”, p. 309). He does not call it a Stufenregel.

How he frames it. p. 308: “Was den Beweis dieses Satzes anlangt, so gebe ich ihn zunächst als den Ausdruck vielfacher Erfahrungen.” (“As for the proof of this proposition, I give it for now as the expression of manifold experience.”) p. 308: “Dass ein derartiges Verhältnis, wenn auch nicht als Gesetz, so doch als häufig zutreffende Regel besteht …” (“That such a relation holds, if not as a law, then as a frequently applicable rule …”). So it is an empirical rule, explicitly not a law. He also gives a graphical argument (below) and says that with vapour or dissociation pressures “kann man übrigens an die Stelle der Analogie in ziemlich weitem Umfange bindende Schlüsse setzen” (“one can, over a fairly wide range, put binding conclusions in place of the analogy”, p. 312). He does not carry that out here.

The mechanism he proposes, p. 306, for sodium chlorate and sodium sulphate: “Man muss also die Erscheinung so auffassen, dass die Lösung bezüglich der unbeständigen Form, obwohl diese weniger weit von der Sättigung entfernt ist, doch eher in das labile Gebiet gelangt, als in Bezug auf die weniger lösliche Form.” (“The phenomenon must therefore be understood thus: the solution, with respect to the unstable form, although it is less far from saturation for that form, reaches the labile region sooner than with respect to the less soluble form.”) The graphical argument (§40, pp. 310–312) concludes that the less stable form “von beiden Seiten ein engeres metastabiles Gebiet haben muss” (“must have a narrower metastable region from both sides”, p. 312). It uses Clausius’s equal-area rule on the vapour–liquid isotherm.

What happens after the first form appears, p. 308, for sulphur cooled from the melt into the labile region: the monoclinic form II appears, not the rhombic form III, “weil diese die nächstliegende ist” (“because it is the nearest”). Then: “Befindet sich dann II gegenüber III im metastabilen Gebiete, so wird es damit sein Bewenden haben, und eine weitere Umwandlung tritt erst ein, wenn das Produkt mit etwas von der Form III in Berührung kommt. Daneben besteht aber auch die Möglichkeit, dass auch II gegenüber III im labilen Gebiete ist; dann wird eine freiwillige weitere Verwandlung eintreten, und schliesslich die beständigste Form III erreicht werden.” (“If II is then in the metastable region with respect to III, matters will rest there, and further transformation occurs only when the product comes into contact with some of form III. But it is also possible that II is in the labile region with respect to III; then a further spontaneous transformation will occur, and the most stable form III will finally be reached.”) A sequence of stages is therefore conditional. It continues on its own only through forms that are labile with respect to the next.

The evidence (§§35–39):

• Mercuric iodide made at room temperature appears first as the yellow form and turns red. The yellow phase lasts a fraction of a second on precipitation from HgCl₂ and KI, days on precipitation from alcohol by water, and sublimed HgI₂ is always yellow at first (p. 308).
• The metastable forms of monotropic substances exist at all: “Solche unbeständige Formen monotroper Stoffe könnten überhaupt nicht vorkommen, wenn die Umwandlung immer zu der beständigsten Form führte” (“Such unstable forms of monotropic substances could not occur at all if transformation always led to the most stable form”, p. 309).
• Fusible substances deposited from vapour or solution below their melting point should appear first as liquid, and do: benzoic acid comes out of its salts as droplets, and sulphur vapour condenses first as droplets (pp. 309–310, citing Frankenheim 1860).
• Phosphorus vapour gives yellow, not red, phosphorus. Cyanuric acid vapour condenses to cyanic acid. Cyanogen gives liquid cyanogen, not paracyanogen. For isomers that give identical vapours he knows “keine Ausnahme” (“no exception”) to the vapours giving “von allen möglichen Formen die unbeständigste” (“of all possible forms the most unstable”, p. 310). Note that this sentence says “most unstable”, which is stronger than “nearest”.
• Chlorine in potash gives hypochlorite, which slowly passes to chlorate; perchlorate is not reached in neutral solution (p. 310). This is his only three-step chain, and it is a chemical reaction, not a polymorph series.

Apparent exceptions (§37, p. 309). Where no intermediate form is seen, one may assume it forms and transforms at once. He adds: “Allerdings ist diese Art, die Widersprüche gegen den Satz zu heben, einigermassen bedenklich, da eine derartige Annahme zwar immer gemacht, aber wenigstens mit den gegenwärtigen Hilfsmitteln nicht immer bewiesen werden kann.” (“Admittedly this way of removing contradictions to the proposition is somewhat questionable, since such an assumption can always be made but, at least with present means, cannot always be proved.”) He hopes that slowing the reaction will often show the intermediate.

Metastable and labile states (§§26–31, pp. 301–304)

• Supercooled salol resists everything except contact with its own crystal, which raises the question how the first crystal arose (p. 301). “Die Antwort ist, dass es allerdings eine Generatio spontanea für feste Körper giebt” (“The answer is that there is indeed a spontaneous generation for solids”, p. 301). Below the melting point there is first a region where only a crystal causes solidification, then, on further cooling, a region where crystals form freely.
• p. 302: “Hier möchte ich diesen Namen [metastabil] ausdrücklich auf solche Zustände beschränkt wissen, … in denen keine andere Ursache, als die Berührung mit der anderen Phase, die Umwandlung bewirkt. Die weiter belegenen Zustände, in denen eine Generatio spontanea möglich wird, sind dann sachgemäss labile zu nennen, da in ihnen umgekehrt die Entstehung der anderen Phase nicht verhindert werden kann.” (“Here I want the name metastable expressly restricted to states in which no cause other than contact with the other phase brings about the transformation. The states lying further on, in which spontaneous generation becomes possible, are then properly called labile, since in them, conversely, the formation of the other phase cannot be prevented.”)
• The labile change is not instantaneous. The labile state “kann … einige Zeit bestehen, bevor er freiwillig in den anderen übergeht”, sometimes “eine sehr grosse” time (“can persist for some time before it passes spontaneously into the other”, p. 302).
• The limit is real but hard to locate. Phenol cannot be supercooled below 24° even with seeds excluded, and above it cannot be made to freeze (B. Moore, pp. 301–302). In sealed capillaries, p-chloronitrobenzene (m.p. 83°) froze spontaneously anywhere between 77° and 63°, differently from run to run in the same tube. He takes the highest value as decisive and puts the scatter down to “Reaktionsgeschwindigkeit” (p. 303). He corrects Violette: the lower limit of supersaturation depends on concentration, and supersaturation and supercooling are the same phenomenon (p. 303).
• He reverses his biological analogy: there is no observed spontaneous generation of life because the earth’s matter is “den lebenden Organismen gegenüber im metastabilen und nicht im labilen Zustande” (“in the metastable and not the labile state with respect to living organisms”, p. 303).

Seeds (§§1–25, 42–79)

Ostwald does not use “Impfen” in this paper. His words are “Keim” (germ, seed), “Einsäen” and “Aussäen” (sowing), “Infektion”, “steril” and “Sterilisieren”, and a “Kulturmethode” copied from bacteriology (p. 318).

• Seeds are material solid. Diluting solid salol stepwise finds a limit, which shows “dass es sich bei diesen Auslösungen des überkalteten Zustandes um materielle, an das wirkliche Vorhandensein des festen Körpers gebundene Wirkungen handelt” (“that these releases of the supercooled state are material effects, bound to the actual presence of the solid body”, p. 294). Salol in an inactive D4 powder was extracted and identified (it froze on contact with a seeded wire): “Damit ist bewiesen, dass die Unwirksamkeit der Verreibung D4 nicht von einer Zerstörung des vorhandenen Salols herrührt, sondern nur davon, dass es die Eigenschaft des festen Stoffes nicht mehr besitzt” (“This proves that the inactivity of the D4 trituration comes not from destruction of the salol present, but only from its no longer having the property of the solid substance”, p. 296). He suggests the salol is adsorbed on the powder as a gas-like layer (pp. 297–299).
• Isomorphous seeds work as well as identical ones. Potash alum seeds ammonium alum to the same dilution: “dass isomorphe Keime bis zu derselben Grenze wirksam sind, wie identische” (p. 323). Chrome alum, which differs in both metals, does too (p. 323). m-Bromonitrobenzene seeds supercooled m-chloronitrobenzene, but the para isomers do nothing (p. 330). He explains isomorphous seeding by solid solution (p. 323) and proposes it as a test of isomorphism that cannot be fooled by similar angles (p. 330).
• How small. Salol: D3 active, D4 not, at about 0.1 mg per test, so about 10⁻⁷ g active and 10⁻⁸ g not, cubes of 0.045 and 0.022 mm (p. 295). Fresh triturations reach further (D5, D6) and fall back to D4 within one or two days (p. 296). Molten sodium thiosulphate: fresh, to D8 or D9, about 10⁻¹² g; the limit recedes over days, which he puts down to decomposition (pp. 299–300). Sodium chlorate: between D5 and D6, about 10⁻⁹ g (p. 316); about 10⁻¹⁰ g by evaporating dilute solution on a platinised spatula (p. 317); 3.2 × 10⁻¹⁰ g by platinum loop (pp. 321–322). Alum: D8 to D10, end not reached because of alum in dust (p. 322). Rochelle salt: D8 active, D10 and beyond inactive (p. 327). Borax: D7 (p. 327). Barium chloride: D9, “unter Vorbehalt” (“with reservation”, p. 328). He sums up that one can detect “bis zu einem Hunderttausendstel Milligramm” (“down to a hundred-thousandth of a milligram”, p. 329).
• Seeds can be lost. A glass hair stroked on salol loses its power in minutes to hours, by evaporation (p. 292). Salts on glass hairs keep it (p. 293). Heating above the melting point sterilises a salol mixture, and it stays sterile until it touches a crystal (p. 298). Sodium chlorate powder in nearly saturated air takes up water and loses its power (p. 314). Weathered salts still seed until heated past the temperature at which the hydrate cannot exist: 34° for Glauber’s salt (p. 325).
• Seeds spread. Once a room has been used for alum, “Es wird dann bald unmöglich, auf dem Objektträger einen übersättigten Tropfen zu haben, der nicht alsbald an einzelnen Stellen auszukrystallisieren beginnt” (“it soon becomes impossible to have a supersaturated drop on the slide that does not soon begin to crystallise at points”, p. 291). A washed and towelled agate mortar kept its seeding power until scrubbed under running water (p. 291). Fresh milk sugar taken from the middle of a batch contained alum (p. 322). Uncontrolled borax gave a false limit of D17 (p. 327). “Ein einziger Keim, der in die Reibschale fällt, genügt, um die ganze sterilisierte Alaunmenge wieder zu beleben” (“a single seed that falls into the mortar suffices to revive the whole sterilised quantity of alum”, p. 324).
• Scratching works by seeding. Rubbing a vessel wall does not change the surface. It leaves crystal fragments that grow along the scratch: “ein wirkliches Aussäen” (“an actual sowing”, p. 313).
• Size matters. Small fragments of salt are more soluble than large ones, so a fine powder beside a saturated solution will slowly dissolve while larger crystals grow (p. 315). A solution can be “in Bezug auf makroskopische Krystalle übersättigt …, in Bezug auf sehr kleine dagegen untersättigt” (“supersaturated with respect to macroscopic crystals, but unsaturated with respect to very small ones”), so the smallest effective seed should depend on the supersaturation. His experiments on this are “noch nicht so weit gediehen” (“not yet far enough along”) to report (pp. 320–321). A very small fragment grows much more slowly than a larger one until it reaches a certain size (p. 320).
• A speculative “Satz”. Because weathered salts keep seeding, he proposes that “die Menge einer einmal vorhandenen festen Phase nicht null werden kann” (“the amount of a solid phase, once present, cannot become zero”), so long as only solid and gaseous phases are involved (p. 326). He leaves open whether this is a solid-solution effect.

Claims

id	claim	strength	support
C1	A metastable melt or solution is set off only by the solid substance itself or a strictly isomorphous solid	strong	many controlled experiments with blank controls (p. 292), for salol, thiosulphate, sodium chlorate, alums, Rochelle salt, borax; the D4 salol extraction (p. 296); isomorphous seeds (pp. 323, 330). Barium sulphate sets off barium chloride (p. 328), but that solution is near the labile region
C2	Seeds as small as about 10⁻⁹–10⁻¹² g are effective, and there is a lower limit	moderate	dilution series with limits that agree across methods within an order of magnitude (pp. 316–322); the limits drift with time, adsorption and decomposition, and dust contaminates the alum and borax series
C3	Beyond equilibrium there is a metastable zone (change only by seed) and, further, a labile zone (spontaneous change)	moderate	phenol (Moore), p-chloronitrobenzene, Glauber’s salt (Löwel, Violette), sodium chlorate (p. 316); the limit itself is not measured with any precision, and he says so (p. 303)
C4	A system leaving a state spontaneously reaches the nearest form (next-highest free energy), not the most stable	moderate as a rule, weak as a general proposition	a handful of cases (HgI₂, sodium chlorate hydrate, sodium sulphate 7-hydrate, borax, sulphur, phosphorus, cyanic acid, cyanogen, hypochlorite) and the existence of monotropic metastable forms; offered as “häufig zutreffende Regel”, not a law (p. 308)
C5	The less stable form has a narrower metastable zone, which is why it appears first	weak	a graphical argument on the liquid–vapour isotherm (pp. 310–312), carried to solids by analogy; he says the solid–liquid data are missing (p. 305)
C6	A metastable intermediate stays until seeded by the more stable form, unless it is labile with respect to it	moderate	stated for the sulphur diagram (p. 308); shown by sodium chlorate cubes consuming the hydrate on contact (p. 301) and by HgI₂ turning red with red seeds excluded (p. 308)
C7	Where no intermediate is seen, it formed and transformed at once	assertion	§37, which he himself calls “einigermassen bedenklich” (p. 309)
C8	Once present, a solid phase cannot vanish entirely from its solid decomposition products	weak	inferred from weathered salts that still seed (pp. 325–326); “ist jetzt noch nicht zu erörtern” (“cannot yet be discussed”)

Method

Bench experiments with simple apparatus. Supercooled drops of salol or molten thiosulphate on microscope slides, and supersaturated drops of salt solution under a low-power microscope (pp. 293–294). Seeds diluted in homeopathic decimal triturations (D1, D2, …) in milk sugar or quartz powder, some made in a small tumbling mill (pp. 295–296) and some by the homeopathic pharmacist W. Schwabe (pp. 295, 322, 327–328). Seeds also made by evaporating dilute solutions on platinum spatulas and loops (pp. 316–322). A “culture method”: sterilised supersaturated solution in stoppered tubes held at 45°, sample dropped in, crystallisation centres counted after minutes to hours (pp. 318–320). Every series had blank controls (p. 292). §§32–41 are argument, not experiment.

Concepts

• Metastabil (metastable): a state that changes only on contact with the other phase, and for no other cause (p. 302). Ostwald coined the word earlier, and here restricts it.
• Labil (labile): a state further from equilibrium in which the new phase forms spontaneously and cannot be prevented, though it may take time (p. 302).
• Generatio spontanea: spontaneous formation of the new phase without a seed. It is possible only in the labile region (p. 301).
• Keim (seed, germ): a particle of the solid phase, or of a strictly isomorphous solid, that sets off crystallisation. It acts by growing. Its effect is the “Auslösung” (release) of the metastable state.
• Nächstliegende Form (nearest form): the form reachable “unter möglichst geringem Verlust an freier Energie”, the form with the next-greatest free energy (p. 307). It is not “the least stable form” in general, though for vapours of isomers he says “die unbeständigste” (p. 310).
• Verreibung D_n: a trituration with 10⁻ⁿ g of active substance per gram (p. 294).
• Steril, Sterilisieren: free of active seeds, and the making so (by heating above the melting point, by solution, by breathing on a slide).
• Monotrop, enantiotrop: Lehmann’s terms for substances with no accessible transition point below the melting point, and with one (pp. 308–309, 312–313).

Connections

The paper says it grew out of repeating known experiments while writing chapters of Ostwald’s Lehrbuch der allgemeinen Chemie (p. 289), and it calls itself “aphoristischen Mitteilungen” (p. 329). The seed experiments extend Gernez, Violette and Lecoq de Boisbaudran (p. 329) and the long study of supersaturated Glauber’s salt (Ziz 1815, Löwel 1850, de Coppet 1871). The theory of §§32–41 rests on James Thomson’s continuous isotherm and van der Waals’s equation of state (p. 304), with Clausius’s equal-area rule (p. 311). Lehmann supplies monotropy and enantiotropy (p. 309). Ostwald notes that Schaum’s Marburg Habilitationsschrift has the same vapour-pressure figure (p. 313).

Later work the record holds touches three parts of it. The size-dependence of solubility (p. 315) and the idea that a fragment can be dissolving at one supersaturation and growing at another (pp. 320–321) are the ingredients of a critical nucleus, which De Yoreo & Vekilov review (LIT-924). Here they are qualitative and the experiments unfinished. The prediction that fusible substances come out of solution or vapour first as liquid droplets (pp. 309–310) is a stage rule with a liquid intermediate, in the neighbourhood of the two-step mechanism (LIT-926, LIT-919). Ostwald’s droplets are a macroscopic liquid phase, not clusters. The dust experiments (pp. 291, 322, 325, 327) are early evidence for the seeding explanation that Dunitz & Bernstein (LIT-917) are cited for. LIT-917, LIT-924 and LIT-926 are not read, so those connections are by what the works are cited for. LIT-919 was read the same day (NOTE-708). It does not cite this paper, though its two-step route through a metastable intermediate is close to the rule in spirit.

Bearing on the record

• CLAIM-181 (a seed fixes the lattice, not the shape). Supported, within a limit the claim does not state. Ostwald shows in detail that in the metastable zone only the solid itself, or a strictly isomorphous solid, starts crystallisation (C1). That a chrome alum seed works in ammonium alum solution (p. 323) is good evidence for the claim’s narrowed form: what the seed passes on is the lattice, not the substance and not the outline. The paper says nothing about habit, so it neither supports nor tests the claim’s second half, that the habit is set by growth conditions. The limit is this: a seed decides only in the metastable zone. In the labile zone the new phase forms without one, and the form is the nearest, whatever seeds are present or absent (p. 307). Carried over, the analogy would say the record’s grammar decides how an argument crystallises only while the exchange is “metastable”. Far enough past that, structure forms on its own and in the nearest form. That is an analogy, and the paper does not license it. Ostwald’s seeds also fade: they evaporate, decompose, dissolve in damp air or are sterilised by heat (pp. 292, 298–300, 314). The record’s schemes do not fade, so the transfer works best for non-volatile seeds like alum.
• CLAIM-176 (recurrence is the nucleation threshold). Complicates it. The paper has two thresholds, and neither is a count of occurrences. The metastable limit is a degree of departure from equilibrium, beyond which the new phase forms spontaneously, and even there the time it takes scatters (p. 303). The minimum seed is a size, about 10⁻⁹–10⁻¹² g, and Ostwald expects it to depend on the supersaturation (pp. 320–321). “Code it the second time it turns up” corresponds to neither. In Ostwald’s terms the record’s filing rule is closer to sowing: a code is a seed put in by hand, which acts only in a metastable state. The claim borrows the word “nucleation” for a different kind of threshold. Ostwald gives it no support, and he does not undercut the rule as a filing rule either. If the analogy is to be kept, the paper suggests the threshold should depend on how far the exchange is from settling, not be a fixed number. That would be a new claim.
• The floated reading of the thesis sequence (CLAIM-017 → CLAIM-115 → CLAIM-133 → CLAIM-139) as successive metastable forms. The paper gives the vocabulary but not support, and parts of the record’s own evidence go against the reading. (1) The rule needs a stability order, which Ostwald takes from free energy measured by solubility (p. 307). The record has no measure of how stable a thesis is, so “each closer to stability than the last” cannot be checked. (2) Ostwald’s stages are irreversible: each form has lower free energy than the last, and a form once left is not formed again spontaneously. The record’s sequence returns. CLAIM-133 brings back the identity clause of Superseded CLAIM-108, and CLAIM-139 brings back CLAIM-017’s invariants. (3) On Ostwald’s account an intermediate stays put unless it is labile with respect to the next form or is seeded (p. 308). Each of the record’s moves came on the owner’s request (“draft a manuscript”, “the current state of our argument”, “tie it all together”). In the analogy those requests would be the seeding, not spontaneous stages. (4) Ostwald himself warns that unseen intermediates “can always be assumed but cannot always be proved” (p. 309). A stage reading of a sequence whose stability order is not measured has the same weakness. What does transfer is the distinction itself. A thesis that persists only until something touches it is metastable, and one that changes with no prompt is labile. That could be asked of each move. It would be a new claim, and this reading does not file it.
• CLAIM-186 (pace sets form). The paper bears on it at an angle. Ostwald says nothing about growth rate, faceting or branching. He does say that the further a system is driven past equilibrium, the more likely the less stable form appears first, because its metastable zone is narrower (pp. 306, 312). If the analogy were extended, a fast exchange would first produce the nearest, least settled thesis, not the most stable one. CLAIM-186 does not say this, and the paper does not test it.
• No THEORY should be filed from this reading. If the record later states a THEORY that leans on the rule of stages, this paper is its primary source, with C4 at “moderate as a rule” and C7 as an open liability.
• No instruction for machine-learning practice.

Limitations

• The rule rests on a handful of cases. Most are single observations from the literature or the bench, and the systematic work in the paper is on seeds, not on the rule. He gives it “zunächst als den Ausdruck vielfacher Erfahrungen” (p. 308).
• The theoretical support is an analogy. The argument from the liquid–vapour isotherm is carried to solids “durch Analogie” (p. 312). The promised “binding conclusions” from vapour and dissociation pressures are not given.
• Exceptions are absorbed, not counted. §37 explains away absent intermediates by instant transformation, and he admits the move is questionable (p. 309). The paper lists no exception.
• “Nearest” and “least stable” are not kept apart. The rule says nearest (next-highest free energy, p. 307). For vapours of isomers he says the most unstable form appears (p. 310). With two forms the two readings agree. With three or more they do not, and the paper does not say which holds.
• The metastable limit is not measured. p-Chloronitrobenzene scatters from 77° to 63° (p. 303), and the systematic study is deferred (“noch keine Zeit gefunden”).
• Experiments are reported in progress. The Rochelle salt and sodium chlorate deliquescence runs are “fortgesetzt” (p. 316). The size-versus-supersaturation study is unreported (p. 321). The bright-platinum anomaly is “nicht weiter verfolgt” (p. 322).
• Slips. Two sections are numbered 32 (pp. 304 and 306). The six figures were not seen in this reading.

Open questions

• Is the first-formed phase the nearest in free energy, or the least stable available? A system with three or more accessible forms, driven into the labile region, would settle it. Ostwald’s own sulphur example (p. 308) is stated, not observed.
• Does the narrower metastable zone of the less stable form hold for solid–liquid transitions, not only by analogy? Measured metastable limits for both forms of a dimorphic substance would close it.
• Does the smallest effective seed depend on the supersaturation, as Ostwald predicts (pp. 320–321)? His second paper might report it. The record does not hold the later Abhandlungen.
• For the record: what would count as a measure of a thesis’s stability, against which a stage reading of the thesis sequence could be tested?