Soddy: Physicist review (Step 2)

Reviewer: PhD physicist. Project: Frederick Soddy, Matter and Energy (1911) and The Interpretation of Radium and the Structure of the Atom (4th ed., Aug 1920; 1922 reprint). Tags: [read] from the documents, [web] with URL, [memory] with confidence, [calc] my own arithmetic (Python, .venv).

Source scope note (repeated from claims.md): the folder holds only these two popular books. Soddy's papers with Rutherford and Ramsay and his economics books are not in the folder. Where I mention them, the material comes from the Investigator's leads [web] or from [memory]. Deep reads cover Interpretation PDF pp.153-165 and 268-300 and Matter and Energy PDF pp.201-236. Claim 7 rests on passages I read myself in the extracted text (Matter and Energy PDF p.38-39; Interpretation PDF pp.225-228 and the gold/silver paragraph near PDF p.196-204), not on a deep read.

Reader's key to a few terms (the reader profile is self-taught undergraduate). alpha particle = helium-4 nucleus, charge +2e, mass 4 u. beta particle = electron (or positron) from a nucleus. Mean life T = 1/lambda; half-life = T x ln 2 = 0.693 T. "Calorie" = heat to warm 1 g of water by 1 C = 4.184 J. Soddy's "period of average life" is the mean life, so his numbers look larger than modern half-lives by 1.44x.

Web checks this review (budget 6; 3 used; results flagged per item): 1. Rutherford 1919/1920 and Blackett 1925: [web] https://newenergytimes.com/v2/sr/Rutherford-Blackett/Rutherford-Blackett.shtml (a polemical site that disputes the standard story; used here only as a pointer) and web search summaries of the 1920 Bakerian lecture (https://web.lemoyne.edu/GIUNTA/ruth1920.html). Result: proton from nitrogen 1919; mass-3 doubly charged particle proposed in the 1920 lecture as a possibility; Blackett's cloud-chamber result reports about 8 forks in about 23,000 photographs and the reaction 14N + alpha -> 17O + p. I did not fetch the Blackett paper itself, so the "8 in 23,000" figure is second-hand. 2. Lead atomic weights: [web] https://web.lemoyne.edu/GIUNTA/richards.html and https://iupac.org/standard-atomic-weight-of-lead-revised/. Result: the figure 206.05 could NOT be traced to Richards and Lembert (search found 206.40 for North Carolina uraninite lead and 206.085 for a Norwegian mineral); 207.90 for thorite lead is attributed to Hönigschmid. Check failed for 206.05; see Corrections. 3. Earth's heat budget: [web] https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget : 47 +/- 2 TW total surface heat flow, radiogenic share about 15-41 TW (a wide range), convection invalidates Kelvin's purely conductive cooling. Not web-checked, left tagged [memory]: Rutherford-Royds 1909 experiment, Gamow 1928, Cockcroft-Walton 1932, Eddington/Bethe, Re-187 bound-state decay, Margaret Todd and the word "isotope". None of the verdicts below turns on them alone.

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Claim 1. Radioactivity is spontaneous transmutation of single atoms; chance per second is constant; exponential decay; mean life = 1/lambda

Soddy's statement [read: Interpretation p.155-159]. "The chance at any instant whether any atom disintegrates or not in any particular second is fixed. It has nothing to do with any external or internal consideration we know of, and in particular it is not increased by the fact that the atom has already survived any period of past time." He gives lambda as "the fraction of the total changing per second", mean life 1/lambda (credited to J. K. H. Inglis), half-change period tau with 1/lambda = 1.45 tau, and 1/e = 0.368.

Mainstream view. Exactly this, in modern notation: dN/dt = -lambda N, N(t) = N0 exp(-lambda t). Memorylessness (age independence) is the defining property of the exponential distribution, and quantum mechanics supplies the reason: an unstable nucleus is a single quantum state that decays with a fixed amplitude per unit time. Soddy's picture (b) on p.154, a slow bulk change made of sudden individual events, is the accepted one. Gamow's 1928 tunnelling theory [memory, high] later explained why lambda varies enormously between nuclei (Geiger-Nuttall relation) while staying constant for each.

a. Mathematics. Internally consistent. Check [calc]: lambda(Rn) = 1/481,250 s = 2.078e-6 /s, mean life 5.570 d, half-life = 5.570 x 0.6931 = 3.861 d. Soddy prints 3.84 d beside 5.57 d; the pair implies a ratio 1.4505, not 1.4427 (1/ln 2). Modern values: half-life 3.8235 d, mean life 5.516 d [memory, high]; Soddy's 5.57 is 1% high, 3.84 is 0.4% high. He uses "1.45" as a rounded constant. No error in principle. The step he omits ("ex cathedra", p.156) is the differential equation. The reader's worked example: after one mean life, e^-1 = 36.8% remains; after 3.84 days half remains; after 5 x 3.84 = 19 days, 97% of equilibrium emanation has regrown.

b. Experiment. Consistent with decades of data: (i) activity decay curves of every short-lived product [read: p.160]; (ii) Poisson fluctuation of alpha counts (Rutherford and Geiger 1908, Schweidler 1905) [memory, high], which is the direct evidence for "chance"; (iii) the newly formed versus old emanation comparison that Soddy describes at p.158 but gives no data for [read]. Two honest qualifications to "independent of every other consideration" [read: p.157]: (1) it is true to better than one part in 10^3 to 10^4 for alpha and most beta emitters under any chemistry, pressure or temperature; (2) it is NOT strictly true for electron-capture and bound-state decays, where the atomic electrons matter. Beryllium-7 shifts by about 1% between chemical forms, and fully ionised rhenium-187 has a half-life of about 33 years against 41 billion years for the neutral atom [memory, high]. Soddy's phrase was correct for everything he could measure; the exceptions come from the weak interaction acting on bound electrons, which the nuclear-only picture of 1920 could not have contained.

c. Tested? Yes, thoroughly, by Rutherford and Soddy (McGill 1902-03), then by every laboratory since. Replicated indefinitely. The Nobel lecture of 1922 [web, Investigator: https://www.nobelprize.org/uploads/2018/06/soddy-lecture.pdf] opens by dating the interpretation to 1903 and to Rutherford and himself jointly. Kelvin and H. E. Armstrong resisted the transmutation reading in 1906 (Soddy's Nature reply, [web] Investigator's file nature-1906-074516c0...pdf), and Soddy states that disintegration "is based on experimental evidence, which even its most hostile opponents are unable to shake".

d. If it were false. Nothing would be left of nuclear physics, radiometric dating or nuclear medicine.

Verdict: Established. Qualifier: strong form "independent of all surroundings" holds for alpha emitters; electron-capture and bound-state decays show small to large exceptions.

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Claim 2. Radium's energy is internal atomic energy; about 133 cal/h per gram (about 100 in the 1911 book); about 2.9 billion cal over the complete change; over a million times a chemical fuel

Soddy's statement [read: Interpretation p.164, p.22]. "A gram of pure radium evolved about 133 calories of heat per hour... in a year about 1,160,000 calories. In a year 1/2500th part changes. Therefore in the complete change of one gram of radium no less than 2,900,000,000 calories would be evolved." Coal gives about 8,000 cal/g, 2,200 per gram of coal plus oxygen, so radium is "well over a million times" coal. Matter and Energy says the same fractions (one-fourth from radium, three-fourths from emanation and products) and a "quarter of a ton of coal" per gram [read: ME p.210, 219-223]. The Investigator found the explicit "100 calories per hour" in the 1909 first edition [web] https://archive.org/details/interpretationof00soddrich .

Mainstream view. The energy is nuclear binding energy released as kinetic energy of alpha particles, electrons and gamma rays; mass converts to energy by E = mc^2 (Einstein 1905 [memory, high]; Soddy cites this idea elsewhere in the books, not in the pages I deep read). "Borrowed from outside" proposals (Kelvin, H. E. Armstrong, L. Poincare: external radiation or the ether, per Investigator leads from Badash 1966, Campos 2015, Poincare 1907 [web, snippets]) were abandoned because the energy per decay is fixed by the nuclear mass difference and does not depend on environment.

a. Mathematics and arithmetic. [calc] - 133 cal/h x 8,760 h = 1.165e6 cal/yr; x 2,500 yr = 2.91e9 cal/g. Consistent with his 2.9e9. The multiplication by 2,500 is right because 2,500 y is the MEAN life: total energy = power x mean life. (A half-life would be off by 1.44.) - Coal with oxygen: 32/12 = 2.667 g O2 per g C, 8,000/3.667 = 2,182 cal per g of reactants. 2.91e9/2,200 = 1.3e6. Consistent. Against coal alone the ratio is 3.6e5, so the sentence on p.164 "nearly a million times greater than... any change known previously" is stated on Soddy's own basis [corrected 2026-10-08 after QE: was generous. Not generous: it is the basis Soddy states, a comparison with any known chemical change; he gives the coal-alone factor himself as about 360,000 (PDF p.219). See arbiter.md section 10 item 1]; the "well over a million" figure requires counting the oxygen. Both bases are printed. - 1911: with 100 cal/h, 8.76e5 x 2,500 = 2.2e9 cal / 8,000 = 0.27 tonne of coal, matching "a quarter of a ton". So the 1911 book is indeed using about 100 cal/h. This confirms the deep read's inference and the Investigator's 1909 find.

b. Modern comparison. [calc, with nuclear data from memory, medium confidence on the decay energies] One gram of Ra-226 is 2.66e21 atoms with half-life 1,600 y: activity 3.66e10 per second (the curie was defined on this). Alpha energies in the chain to Po-214: Ra-226 4.87 MeV, Rn-222 5.59, Po-218 6.12, Po-214 7.83 (total about 24.4 MeV), plus beta and gamma from Pb-214 and Bi-214 (a few MeV, partly absorbed). Alpha energy alone gives about 121 cal/h per gram; chain total of about 28 MeV gives about 141 cal/h. Soddy's 133 lies between these, so it is correct. Modern radium heat is of order 0.14-0.17 W/g (about 120-145 cal/h), so the 1909-11 figure of 100 cal/h was about 25-30% low and the 1920 figure is right. - The split between radium and emanation: Soddy gives 25% / 75%. By alpha energy, radium itself carries 4.87 of about 28 MeV, about 17%, and the emanation plus short-lived products about 83% [calc, medium]. Soddy's split is roughly right but not exact; it was measured with imperfect calorimetry. - "Alpha particles carry over 95% of the energy" (1911 [read: ME p.210]): in the chain to Po-214 it is about 86% [calc, medium]. Small overstatement. - Complete change: the 2.9e9 cal covers radium and its quick successors down to Po-214. It does not include the later Pb-210, Bi-210 and Po-210 steps (another roughly 5-6 MeV released over decades) [memory, medium; deep-read item agrees]. So "complete change" is the radium atom's change plus the quick products. This is a definitional gap, not an error in the total. - Radium mean life: modern 2,308 y; his adopted (Rutherford's) 2,500 y is 8% high, so his rate (1/2500 per year) is 8% low. His 1904 Ramsay-Soddy figure (1,150 y) was half the true mean life, which he says in the text [read: p.163] and explains by emanation volume too large (he says "likely to be too great unless every trace of other gas is absent"). - Emanation volume 0.6 mm^3 per gram [read]: [calc] atoms of Rn per atom of Ra at equilibrium = T_Rn/T_Ra = 5.52 d / (2,308 y x 365.25) = 6.5e-6; 1 g Ra = 2.66e21 atoms -> 1.7e16 Rn atoms = 2.9e-8 mol = 6.4e-4 cm^3 = 0.64 mm^3 at STP. Soddy's 0.6 is right.

c. Tested? Calorimetry of radium by Curie and Laborde 1903 [memory, high], by Rutherford and Barnes 1904 [memory, medium], emanation heat by Rutherford and Barnes; helium from radium and emanation by Ramsay and Soddy 1903 [read: ME p.230 describes, no date]. Replicated many times.

d. If false. Energy conservation would be replaced. It stands: the energy was reconciled with conservation by the atom itself changing, as Soddy argues [read: ME p.212-213]: "If radium, the element, is the source of the energy it pours out in a continuous stream, radium, the element, must change, and the change of an element is transmutation."

Verdict: Established. Qualifiers: heat constant 100 (1909-11) was 25-30% low, 133 (1920) is correct; the "million times coal" ratio is 1.3e6 per gram of coal plus oxygen, 3.6e5 per gram of coal; the radium life is 8% high; "complete change" omits the slow tail.

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Claim 3. Radium survives because it is continuously made: equilibrium ratio equals ratio of mean lives; radium 2,500 y; uranium 7,500-8,000 million y; chain U -> UX -> ionium -> Ra -> emanation -> ... -> lead (eight alphas)

Soddy's statement [read: Interpretation p.162]. lambda1 N = lambda2 X, so X/N = lambda1/lambda2 = T2/T1. "It is necessary for the law to hold true that the period of the parent body should be much longer than the periods of any of its products." He applies it to radium (3,200,000 parts uranium to one of radium in 1920; 3,000,000 in 1911) to get uranium's life [read: ME p.224-225; Interp p.169].

Mainstream view. This is secular equilibrium: when the parent outlives its daughters by far, each daughter's activity (number decaying per second) equals the parent's, so amounts are inversely proportional to decay constants. When the parent lives only modestly longer, one gets transient equilibrium, X/N = lambda1/(lambda2 - lambda1) [calc/derivation]; Soddy's condition is the secular case. The modern chain is U-238 -> Th-234 -> Pa-234 -> U-234 -> Th-230 (ionium) -> Ra-226 -> Rn-222 -> Po-218 -> Pb-214 -> Bi-214 -> Po-214 -> Pb-210 -> Bi-210 -> Po-210 -> Pb-206: 8 alpha emissions and 6 beta emissions [memory, high]. U-238 half-life 4.468e9 y [memory, high].

a. Mathematics. Consistent. [calc] Modern mass ratio of uranium to radium in old minerals: (4.468e9 / 1,600) x (238/226) = 2.94e6. Soddy's 3.0e6 (1911) and 3.2e6 (1920, credited to Rutherford and Boltwood) are 2% and 9% high. Uranium mean life: modern 6.45e9 y; Soddy's 7.5e9 (1911) and 8.0e9 (1920) are 16% and 24% high. Where the error comes from: (i) his radium life is 8% high (2,500 vs 2,308), (ii) the ratio 3.2e6 is 9% high, (iii) a subtle point: the life ratio must be computed from the ATOM ratio, but a mineral analysis gives a MASS ratio; the atom ratio is the mass ratio x 226/238 = 0.95 x. Soddy's text does not say which he used [read: ME p.224-225 says "3,000,000 times as much uranium as radium"]. A 5% slip is possible; the text does not let me decide. The arithmetic of the chain: 238.5 - 8x4 = 206.5 against lead 207 [read: ME p.234]; 238 - 32 = 206 [read: Interp p.289]. Right. The 1911 book honestly says the lead end product was "generally supposed but not yet proved". "Radium 100,000 years ago: a thousand billion times as much" [read: p.165] is understated: e^(100,000/2,500) = e^40 = 2.4e17 [calc]. The Loch Katrine waterworks analogy (p.169-170) is a correct pictorial model of flow equilibrium.

b. Experiment. (i) Uranium-radium proportionality in minerals (Boltwood 1905-07, Rutherford) [memory, high; the 1911 book states it, p.223-224]. (ii) Growth of radium from ionium: Soddy's own experiments with Miss Hitchins 1915-19, quadratic growth in time [read: 1920 text per ME deep-read comparison, PDF pp.177-178]. (iii) Direct counting of alpha particles (Rutherford and Geiger) gave the radium life independently [memory, high]. (iv) Ionium is thorium-230 and, as Soddy observes, inseparable from thorium [read: p.291]; modern mass spectrometry confirms.

c. Tested? Yes. 1911 states honestly that the uranium-to-radium growth direct tests "have not yet produced a definite result" [read: ME p.224]; by 1920 positive results are claimed. Uranium's life was confirmed within about 20% by many methods; the modern value comes from direct counting and mass spectrometry.

d. If false. The age of rocks (radiometric dating), the geological timescale and the lead-isotope story would fall. Soddy's conclusion in 1911 that uranium is billions of years old was the first radiometric argument that the earth is old [read: ME p.225-226].

Verdict: Established. Qualifiers: the equilibrium law is established (secular case); his numbers are about 8% off for radium and 16-24% off for uranium, within the errors of 1911-1920 analytical work; the stated condition "parent much longer-lived" is right but he does not mention the transient case.

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Claim 4. The alpha particle is a helium atom (charge 2, mass 4); radium becomes its emanation (radon) by expelling one; helium accumulates in uranium and thorium minerals

Soddy's statement [read: ME pp.228-233; Interp pp.153-154, 270]. Ramsay and Soddy found helium arising from radium and from the pure emanation; Rutherford deflected alphas by magnets and electric fields, counted them (charge 2 atomic charges, mass 4); the thin-glass experiment: helium appears outside a thin-walled tube filled with emanation but not when filled with ordinary helium. The text does not name Royds [read: ME p.233]; the experiment is Rutherford and Royds 1909 [memory, high].

Mainstream view. Alpha = He-4 nucleus. Exactly. Helium accumulation in U/Th minerals is the basis of U-He dating and explains terrestrial helium; most atmospheric and natural-gas helium is radiogenic [memory, high].

a. Mathematics. Consistent. Velocity c/15 to c/20 -> 12,400 to 9,300 miles per second [calc]; Soddy gives "between 1/15th and 1/20th of that of light" and "12,000 miles a second" [read: ME p.231-232]. Modern: alpha speeds 1.4e7 to 2.0e7 m/s, i.e. 0.047 c to 0.067 c. Consistent. Alpha energy of 2-4 million volts equivalent: kinetic energy of a charge 2e through V volts is 2eV, so 4-8 MeV alphas correspond to 2-4 MV. Soddy's figure [read: p.298] is right (modern radium chain alphas 4.8-7.8 MeV).

b. Experiment. Rutherford-Royds 1909, Ramsay-Soddy 1903, Geiger counting, all replicated; mass spectrometry of alpha-derived helium; the helium isotope ratio in minerals [memory, high].

c. Tested? Yes, replicated. d. Nothing in mainstream physics changes.

Verdict: Established. (The 1911 sentence "uranium appears to be made up of eight atoms of helium with one of lead" [read: ME p.235] is a loose pictorial description: the nucleus emits alphas, it is not literally built of pre-formed helium atoms. His wording is hedged with "appears" and "so on". Mainstream: nucleus is protons and neutrons; the alpha is formed at the moment of decay. Not a verdict-changing point.)

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Claim 5. Isotopes: atoms of one element differ in mass; displacement rules (alpha: two places down; beta: one place up); uranium lead 206.05, thorium lead 207.9; Aston's whole-number masses; credit for the 1913 generalisation

Soddy's statement [read: Interp pp.275-297]. Rule of 1911 for alpha products; the beta rule; "The complete generalisation, which was put forward in 1913 independently during the same month by A. S. Russell, K. Fajans, and the writer." Lead prediction 206 (uranium series) and 208 (thorium series) against 207.2; found 206.05 and 207.9. Aston's 1920 table: of 18 elements, 9 are mixtures; "in every case, except hydrogen, the true atomic weight is found to be an exact integer... to an accuracy of one part in a thousand."

Mainstream view. Isotope = atoms with the same Z (proton number) and different neutron numbers N (neutron discovered 1932 [memory, high]). Chemistry depends on Z. The displacement rules: alpha decay lowers Z by 2 and A by 4; beta-minus raises Z by 1 and leaves A fixed. Both are exactly right. One alpha and two betas returns to the same Z: "chemically the same as the parent" [read: p.276], i.e. an isotope.

a. Mathematics. Consistent. Check of the lead mixture [calc]: a binary mixture of mass 206 and 208 needs 60% of 208 to give 207.2. Actual natural lead: Pb-204 1.4%, Pb-206 24.1%, Pb-207 22.1%, Pb-208 52.4% -> 207.24 [calc, memory medium for the percentages]. Soddy's phrase "a mixture of these two isotopes in the right proportion" simplifies: ordinary lead has four isotopes and one of them (207) comes from the actinium series that the 1920 text calls "doubtful" [read: p.289]. Not an error, a simplification. Table of Aston: 0.9 x 20 + 0.1 x 22 = 20.2 [read, check]. "Exact integers to 1 in 1,000" was corrected by Aston's own 1927 packing-fraction results (mass defect, the origin of nuclear binding energy): masses are close to integers but not exactly [memory, high]. Hydrogen 1.008 is already the exception Soddy notes. Table items superseded by later work [memory, high]: sulphur has 32, 33, 34, 36 (Aston has "pure" 32.0); xenon has 124-136 (his 133 and 135 are wrong; the odd isotopes are 129, 131); mercury 196-204; argon 36, 38, 40 (36 not "barely detectable" in the sense of its abundance 0.34%, which is small, so the statement is about right). Aston's own table, reported by Soddy, was provisional ("(?)" marks). The claim "the different isotopic atoms have the same volume" (p.291) [read]: lead densities proportional to atomic weight. Modern: isotope molar volumes differ by less than 0.1% [memory, medium]; the claim is correct at 1920 precision. Ionium: 12.5 g per ton of uranium, 58 g per gram of radium [read: p.291]. [calc] atomic ratio Th-230/Ra-226 at equilibrium = T(Th-230)/T(Ra) = 108,700/2,308 = 47; times 230/226 = 48 g/g. Soddy's 58 uses the "forty times longer" (and his mean lives of 100,000 and 2,500). Right order; 20% different, from his lifetimes. Ionium mixture inference [calc]: Hönigschmid's thorium-ionium mixture 231.51 against pure thorium 232.12 and ionium 230 gives about 29% ionium by atoms. Soddy does not state it; the arithmetic is right.

b. Experiment. Lead atomic weights: Richards and Lembert, Hönigschmid, Maurice Curie, 1914-17 [memory medium -> web partly]. [web] https://web.lemoyne.edu/GIUNTA/richards.html : the Richards-Lembert programme was set up to test whether radioactive-mineral lead differed from ordinary lead and found about a whole unit of difference; one uraninite lead value found was 206.40, a Norwegian mineral 206.085. [web] The search summary credits Hönigschmid's work with 207.90 for thorite lead. I could not trace the exact figure 206.05 to a source in this check; I leave it as Soddy's stated value, in 1920, for "carefully selected uranium minerals". It is within the scatter of 1914-1920 measurements (206.05-206.4) and modern extremes (206.15 to 207.94, [web] IUPAC https://iupac.org/standard-atomic-weight-of-lead-revised/). Aston's mass spectra 1919-20: Ne-20 and Ne-22 [read; matches modern, Ne-21 added 1930s] [memory, high].

c. Tested? Yes and replicated. Mass spectrometry, X-ray atomic numbers (Moseley 1913-14) [read: p.287], neutron discovery 1932.

d. If false. Periodic table and the whole of nuclear chemistry would change. They did not: the isotope concept is foundational.

Credit. The 1920 book credits Russell, Fajans and himself, same month. In the Nobel lecture (12 Dec 1922) [web, Investigator: https://www.nobelprize.org/uploads/2018/06/soddy-lecture.pdf, printed p.387] Soddy adds Hevesy and gives the order: Hevesy and Russell published "only in part correct" forms within a fortnight, "a fortnight after Russell, K. Fajans... published this generalization complete and accurate", then Soddy "a fortnight after Fajans... exactly the same scheme as that of Fajans, whose paper only reached England after mine was written". These accounts are Soddy's own and he has a stake in priority; they are consistent with each other in substance. He also states in the lecture that, in his own words, "in full knowledge of all Fleck's experimental results, the complete generalization was obvious so soon as Russell's paper directed attention to it". The Investigator found a CSAC catalogue entry for a letter from Fajans of 19 Oct 1913 and for 1935 correspondence with W. A. Noyes "re controversy over priority of discoveries of atomic disintegration and isotopes" [web, research/2026-10-08-archiveshub-csac-catalogue.md]; I did not read these letters. They show that the priority question was live, and they are kept in the record. The word "isotope" itself: the Investigator's NYT note says the 1951 NYT credits Soddy; the usual account credits Margaret Todd with suggesting it [memory, high; not checked]. Treat as unresolved in the files. Van den Broek is credited tentatively by Soddy [read: p.279] for the idea that nuclear charge equals place number.

Verdict: Established. Qualifiers: displacement rules and isotopes are established; Aston's "whole numbers to one part in a thousand" is superseded by the mass-defect results; the priority story is Soddy's own and is plural (Hevesy, Russell, Fajans, Soddy, van den Broek, Fleck's chemistry).

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Claim 6. The atom has a tiny dense nucleus (Rutherford, Moseley); alpha bombardment of nitrogen knocks out hydrogen and (June 1920 report) a mass-3 doubly charged particle; releasing nuclear energy by transmutation is real but unsolved, with great energy and great danger

Soddy's statement [read: Interp pp.268-300]. Nuclear atom from large-angle scattering; hydrogen nucleus "at least as small as, and probably smaller than, the negative electron"; H-particles from alpha plus hydrogen; in nitrogen "one such H-particle was observed for every twelve N-particles"; Rutherford's June 1920 Bakerian report of a mass-3 doubly charged "atoms of an isotopic variety of helium, otherwise unknown"; transmutation "has not been really artificially initiated"; and the closing: "The problem of transmutation and the liberation of atomic energy... is no longer surrounded with mystery... It may be that it will remain for ever unsolved... Should that day ever arrive, let no one be blind to the magnitude of the issues at stake."

Mainstream view, part by part. 1. Nuclear atom. Established. Rutherford-Geiger-Marsden scattering 1909-11 [memory, high]. [calc] The order of the hit probability: Soddy says 1 in 10^9 collisions hit the hydrogen nucleus (1 in 10^5 alphas gives an H-particle in 1 cm of H2, with about 10^4 atoms crossed). With a nuclear radius of 1e-13 cm and an atomic radius of 1e-8 cm, (r_nuc/r_atom)^2 = 1e-10. Same order of magnitude, within the roughness of the estimate. So the experiment and the model agree. 2. Nuclear size. Soddy suggests the hydrogen nucleus is the "positive electron", radius about 1e-16 cm because mass 1,830 times the electron's means radius 1,830 times smaller on the classical electromagnetic-mass argument (m ~ e^2/(r c^2)) [read: p.274]. Modern: proton radius about 0.84e-13 cm; the classical argument fails because the proton's mass is mostly strong-interaction and quark-gluon energy, not electrostatic. His figure is about 1,000 times too small; he labels it "merely a suggestion". Historically superseded. 3. Nitrogen. Rutherford 1919: alpha plus nitrogen gives hydrogen-like long-range particles. Modern: 14N + alpha -> 17O + p [memory, high]. Blackett 1925 photographed the event in a cloud chamber: about 8 forked tracks in about 23,000 photographs, one short oxygen track and one long proton track, showing the alpha is captured, not rebounding [web: search summary of Blackett's result; second-hand]. Soddy reports Rutherford's surmise of 14N -> 12C + 2H as "one possibility" [read: p.272]; that is not what happens. The "one H-particle per twelve N-particles" count refers to Rutherford's early identification of the "N-particles" which were recoiling nitrogen atoms, not a reaction rate. 4. Mass-3 doubly charged particle ("X3", June 1920). Rutherford's 1920 Bakerian lecture proposed particles of mass 3 and charge 2, and he wrote that the data were "quite insufficient to distinguish between these alternatives" [web summary of lecture, https://web.lemoyne.edu/GIUNTA/ruth1920.html]. A mass-3 charge-2 particle is helium-3, which was not identified until 1939 (Alvarez and Cornog) [memory, high]. Blackett's 1925 work found no such emission. Verdict on that sub-claim: Tested, not supported. Soddy reports it as a late addition to the book, with proofs corrected July 1920 [read: p.295], which is when the report was fresh; he is the reporter, not the claimant. 5. Release of nuclear energy. In 1920 the claim has two parts: (a) an unsolved problem; (b) its solution would bring great energy and great danger. Outcome [memory, high]: Cockcroft and Walton split lithium with 0.4-0.7 MeV protons in 1932; fission of uranium was discovered in 1938-39; a chain reaction in 1942; bombs in 1945. Soddy's quantitative estimate that artificial transmutation would need "two to four million volts" and possibly more [read: p.298] was a classical Coulomb-barrier argument. [calc] For a 5.5 MeV alpha on nitrogen the barrier is about 4.2 MeV, so alpha-particle transmutation needs MeV energies (right order). For protons on lithium the barrier is about 1.2 MeV, yet 0.4-0.7 MeV protons worked because of quantum tunnelling (Gamow 1928) [memory, high]. His voltage estimate was therefore an overestimate for light targets but correct in order of magnitude. His further claim that "even a practically perfect vacuum fails to insulate" and that Moseley's radium battery stopped at 150 kV [read: p.298-299] is a real phenomenon (field emission and vacuum breakdown); accelerators got around it with different designs. Energy scale [calc]: 200 MeV per uranium-235 fission gives 8.2e13 J per kg, versus 1.2e13 J per kg for all of radium's decay heat in Soddy's 2.9e9 cal/g. So fission yields about 7 times more energy per kilogram of fuel than radium's entire decay. Soddy's phrase "a million times coal" was roughly right in order for the energy of nuclear change.

a. Mathematics. Consistent (checks above). b. Experiment. Nuclear atom, nitrogen to hydrogen: yes. Mass-3 particle: no. Transmutation solved: yes, in a different way than the Soddy-Rutherford alpha-bombardment route (neutron-induced fission and accelerators, 1932-1939). c. Tested? Yes. Rutherford's 1919 result was confirmed by Blackett 1925 and Cockcroft-Walton 1932. The mass-3 sub-claim was not confirmed. d. If false. The nuclear atom claim cannot be false. The mass-3 sub-claim being false changes nothing: it was never part of mainstream physics.

Verdict (split). - Nuclear atom and atomic number: Established. - Alpha on nitrogen releases hydrogen (proton): Established. His surmise of the product (12C plus two H) and Rutherford's mass-3 doubly charged particle: Tested, not supported. - "Unsolved problem whose solution brings great energy and great danger" (as foresight): Historically superseded but instructive (it was solved by a different route, and the warning has proved correct). This is the "great danger" statement: not a physics claim, a policy warning, written post-WWI [read: p.299-300], and the Investigator documents that he warned publicly of atomic war in 1915 (Sclove 1989, Guston 2012 [web: https://pmc.ncbi.nlm.nih.gov/articles/PMC3456912/]) and that H. G. Wells's novel The World Set Free (1914) is dedicated to the Interpretation of Radium and "owes long passages to the eleventh chapter" [web: Project Gutenberg #1059, https://www.gutenberg.org/cache/epub/1059/pg1059.txt]. - Proton-as-small-positive-electron at 1e-16 cm: Historically superseded but instructive.

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Claim 7. Radioactivity changes the picture of earth and sun; civilisation depends on new energy ("energy and wealth are synonymous"); speculative asides: gold and silver may be one slowly changing series; the philosopher's stone myth may echo a forgotten civilisation that mastered transmutation

This claim is several claims. I read the passages: ME p.38-39 ("But energy and wealth are synonymous. Energy is the thing of which gold itself is but the guinea stamp"), Interpretation pp.225-228 (earth heat), and the gold/silver paragraph with the Kitson footnote (near Interpretation PDF p.196-204: "It is at least a possible view to take that the elements gold and silver belong to the same disintegration series, both changing very slowly, but the gold many times more rapidly than the silver"; footnote: "the whole social machinery of the Western World has been dislocated by violent alterations in the purchasing power of gold... Compare A Fraudulent Standard, A. T. Kitson, 1917").

7a. Radioactive heat in the earth; the globe may be heating; cycles of "geological" and "incandescent" ages

Soddy [read: Interp pp.226-227]. Strutt's measurements show crustal radium supplies heat; Joly pushed this to a uniform distribution through the globe; "the interior of the earth, so far from gradually parting with its heat and cooling down, must actually be getting steadily hotter"; central temperature rise "no less than 1,800 C" in 100 million years with 2e-12 radium per gram; the crust must fail and the earth "become again... a vastly swollen globe of incandescent gas"; "geological age" alternates with "incandescent age". Mainstream. Radiogenic heat is real: [web] https://en.wikipedia.org/wiki/Earth%27s_internal_heat_budget gives total surface heat flow 47 TW and radiogenic heat of 15-41 TW (roughly 30-85%, a big spread). The earth is thought to be cooling slowly, not heating, because radioactive elements (U, Th, K) are concentrated in the crust and mantle, not uniformly in the core, and because mantle convection carries heat out far faster than conduction. Kelvin's insulation argument, which Soddy repeats, assumes pure conduction [web, same page]. a. Math. [calc] Joly's uniform distribution: 2e-12 g Ra per gram of earth (6e27 g) x 0.164 W/g = 2,000 TW, about 40 times the measured 47 TW. Even at the crustal average uranium (2.7 ppm, giving about 9e-13 g Ra per g, [memory, medium]), uniform distribution gives about 900 TW, 20 times the observed. So the hypothesis cannot stand against the measured heat flow; the observation was not available in 1920 in this form but the constraint (heat flow measured in boreholes since 1930s) is not subtle. His calculation is internally consistent given his premises. b. Experiment. Contradicted by the later measured heat flow and by geo-neutrino detection of the earth's actual radiogenic output [web: https://arxiv.org/pdf/1111.6099v1 as found by search, summary only]. The cycle of incandescent ages was Joly's theory, not tested. Soddy writes it as conditional ("if the known laws hold"; "however imperfect it may still be"). c. Tested? Yes, by later geophysics; not supported in the strong form (uniform distribution, heating, cycles). The crustal contribution: supported. Verdict 7a. Split. Radium and other radioactivity contribute substantially to terrestrial heat: Established. Uniform distribution, secular heating of the earth, cyclic "incandescent ages": Tested, not supported (and refuted by the heat-flow calculation above).

7b. The sun

Soddy [read: Interp p.227]. "The present loss of heat of the sun cannot be supplied by the presence of radium. For this to be the case a very large part of the sun's mass must consist of uranium... Still, it is by no means to be concluded that the heat of the sun and stars is not in the first place of internal rather than... external origin." Mainstream. Correct in both halves. [calc] The sun radiates 3.83e26 W. Uranium-238 with its whole chain gives only 9.4e-8 W per gram, so a uranium sun would need 4.1e33 g, about 2 solar masses; Soddy's phrase "very large part of the sun's mass" is, if anything, an understatement (more than the whole sun). Pure radium would suffice only for 1.2e-6 solar masses but burn out in a few thousand years. Hydrogen fusion (Eddington 1920 proposed, Bethe 1938-39 mechanism) [memory, high] is the internal source, giving 4 H -> He with 0.7% mass loss. Soddy's inference that the source is internal, and his scepticism of radium as the source, were right. Verdict 7b: Established (as stated).

7c. "Energy and wealth are synonymous"; civilisation lives on a diminishing capital of coal; its future depends on a new energy source

Soddy [read: ME p.38-39]. Energy is "the thing of which gold itself is but the guinea stamp"; "the discovery of a large quantity of gold leaves the world not a penny the richer"; "a find of energy in Nature means an addition to the general wealth". Mainstream physics. A physicist can check only the physical part. Established: the energy available per capita bounds material production (ability to do work, to lift, heat, transform), energy cannot be created (conservation), and the second law forbids perpetual motion; the Investigator notes Soddy's economics books argue the same impossibility of perpetual motion [web: archive.org Wealth, Virtual Wealth and Debt]. In 1911 fossil fuels were a finite stock; reserves, price and technology have since shifted the timescale, but the stock is finite [memory, high]. The identification "energy = wealth" is a definition-level statement in economics (wealth as the capacity for useful work); money, prices and debt belong to economics, not physics. As a statement in physics it is neither true nor false: not testable as stated. As the weaker physical statement "material wealth depends on energy throughput" it is supported. Source gap: Soddy's economic books (Cartesian Economics 1922, Wealth, Virtual Wealth and Debt 1926, etc.) are not in the folder; the Investigator located them on archive.org [web] and quotes passages [web: research/2026-10-08-internet-archive.md] (for example "emits as much heat every two days as its own weight of fuel in burning"). I have not weighed his monetary reform proposals; those are outside a physicist's remit and outside the folder. Verdict 7c. Split. Conservation of energy, impossibility of perpetual motion, finiteness of the fuel stock: Established. "Energy and wealth are synonymous" as an economic identity: Not testable as stated. The expectation that atomic energy would transform supply: Historically superseded but instructive (nuclear power arrived, but not as "transmutation of everything": it is fission of U and Pu and fusion of H, with radioactive waste and weapon risk — Soddy's "curse" caveat).

7d. Gold and silver as one slowly changing series

Soddy [read]. "It is at least a possible view to take that the elements gold and silver belong to the same disintegration series, both changing very slowly, but the gold many times more rapidly than the silver." Premise: in a long chain, "the relative abundance of the elements was proportional to their respective periods of average life", and the gold/silver ratio is "roughly but pretty certainly known" from coinage. Mainstream and calculation. - His premise (abundance proportional to mean life) is the secular-equilibrium law and applies only to members of one chain with a long-lived parent. It does not apply to arbitrary elements. For two elements to be related, the shorter-lived one must be the descendant of the longer-lived. If gold changes "many times more rapidly" it would be the daughter and silver the parent. Silver (Z=47, A=107, 109) would have to decay INTO gold (Z=79, A=197). Radioactive decay only lowers or keeps the mass number A (alpha: -4; beta: 0) [read: p.276]. Going from A=109 to A=197 is impossible. By his own equilibrium logic, then, his suggestion is self-contradictory [calc: ΔA = +88 required]. (Reversing the roles: gold as parent of silver needs 22 alphas and 12 betas to go from 197-79 to 109-47, which works arithmetically, but then gold would be LESS abundant than silver only if it were shorter-lived than its daughter, contradicting his "gold changes more rapidly" and the whole equilibrium argument.) - Observation: gold has a single stable isotope, Au-197; silver has Ag-107 and Ag-109 [memory, high]; no natural decay series passes through them. The three natural series start at U-238, U-235, Th-232 and end in lead [memory, high]. The crustal ratio of silver to gold (about 20:1 [memory, medium]) is set by geochemistry and mining, not by decay, so "known from currency" is not evidence. - Soddy's own words are cautious: "at least a possible view", "Obviously we are only at the beginning". It was a reasonable speculation when no isotope was known. Nuclear stability data later removed it. Verdict 7d: Refuted by calculation (the equilibrium argument requires the shorter-lived gold to descend from silver, and decay cannot raise the mass number from 109 to 197); also Tested, not supported by decay-series and stability data. Historically superseded but instructive.

7e. Philosopher's stone and a forgotten civilisation that had mastered transmutation

Soddy [read: Interp PDF line ~8522; Investigator: 1909 ed., Ch. XI pp.223-244 [web] https://archive.org/details/interpretationof00soddrich ]. "Can we not read into them some justification for the belief that some former forgotten race of men attained not only to the knowledge we have so recently won, but also to the power that is not yet ours?" (1909 text quoted by the Investigator; the same chapter in the 1920 book also reads the Ouroboros and the Fall of Man as echoes.) Mainstream. There is no archaeological or physical evidence for a prehistoric transmuting civilisation, and Soddy offers none: he reads myths as memory. The evidence cuts against it in two ways: (i) a civilisation that could transmute and release atomic energy would leave isotopic and radiological signatures (excess fission products, depleted uranium deposits, anomalous isotope ratios) which are not found; the Oklo natural reactor in Gabon (2 billion years ago) shows what nature leaves behind [memory, high; reactor discovered 1972]; (ii) mythology is explained by ordinary means. It also fails to be testable in Soddy's framing: it is an interpretation of stories. Note the Investigator's pertinent finds: Morrisson, Modern Alchemy (OUP) and the Brill volume Lost Knowledge (2019) place this passage in a wider early-20th-century link between occult alchemy and atomic science [web, snippets only; not opened]; and his 1912 article "Transmutation: The Vital Problem of the Future". The passage is a rhetorical flourish within a book otherwise made of measurements, and Soddy's own text hedges with "can we not read into them". Verdict 7e: Not testable as stated (an interpretation of myth; no measurable difference), with the physical corollary (a prior transmuting civilisation would leave isotopic traces) unobserved.

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Investigator's findings: weighed (kept in the record whatever the verdict)

Pertinent Investigator material and my assessment. All from sites.md "Leads for review" and research/ notes; stakes noted.

1. 1909 first edition, 100 cal/h per gram (25 radium, 75 emanation), "freezing to boiling in an hour": [web] https://archive.org/details/interpretationof00soddrich. Confirms the 1911 inference. It also shows that the heat constant was revised from 100 to 133 between 1909 and 1920. The modern figure (about 120-145) supports the 1920 value. Claim 2.
2. Nobel lecture 1922: priority order Hevesy-Russell, Fajans, Soddy. Soddy is an interested party, but the order is stated against himself in part (he admits Fajans's was first complete). Claim 5.
3. Nature 74, 516 (1906), Soddy's reply to Kelvin: Kelvin argued helium pre-existed in radium and the sun's heat was gravitational; the resolution came with Rutherford and Royds 1909 and the thin glass experiment [read: ME p.233]. The Kelvin letters (The Times, August 1906) were not read by the Investigator or me; Soddy is describing an opponent's position, so I treat it as his characterization. Kelvin's challenge to the energy source (that it might come from outside) is a case where the mainstream view was initially against Soddy and was later revised. Claim 2, 4.
4. Ramsay and Cameron 1907 (copper to lithium by radium emanation), Curie and Gleditsch's check (lithium from glass), Soddy's own negative copper/gold results in the 1909 Chemical Society report [web, snippets]. [calc] Why the claim fails: copper has Z=29, A=63; a 5.5-7.7 MeV alpha from radon faces a Coulomb barrier of about 12.5 MeV [calc, r = 1.2(63^(1/3)+4^(1/3)) fm = 6.7 fm; 2 x 29 x 1.44 / 6.7 = 12.5 MeV], so it cannot reach the copper nucleus classically; tunnelling probability is far too small. Even if it entered, getting from Z=29 to lithium (Z=3) means removing 26 protons. A copper to lithium transformation is not a nuclear process available at these energies. Verdict on that related claim: Tested, not supported (traced to glass impurity by Curie and Gleditsch), and Refuted by calculation for the proposed mechanism. This is a case where a mainstream figure (Ramsay, Nobel 1904) made a transmutation claim that was tested and rejected by Soddy and others on experiment, not on authority.
5. Wells, The World Set Free (1914), dedicated to the Interpretation of Radium, "owes long passages to the eleventh chapter": [web] Project Gutenberg. This is the main documented contemporary uptake of Soddy's atomic-energy prediction. It is not an experimental test. Claim 6.
6. Guston 2012 and Sclove 1989: Soddy's public 1915 warning of atomic war [web: https://pmc.ncbi.nlm.nih.gov/articles/PMC3456912/]. The 1915 text itself was not located; I rely on Guston's account (which quotes his nephew via Davies 1992) and have not read Sclove. Claim 6.
7. Bodleian/CSAC catalogue: war-work papers "probably... disturbed, and some of them removed" and the originals of the 1953-54 Howorth letters lost (only Trenn's 1969 copies of 32 survive) [web, research/2026-10-08-archiveshub-csac-catalogue.md]. Absence of evidence worth analysing. Competing explanations the Investigator lists (ordinary loss by the literary trustees, removal of classified wartime material, selection by Howorth for her 1958 book) are all plausible; the physics claims reviewed here do not depend on these papers. Secret patent 5527/16 (fireless boilers, 1916) not found in Google Patents (404 on GB191605527A): wartime secret patents may never have been published. This is not a physics claim; it is about the record of Soddy's wartime engineering.
8. GB 25,504 (1910) mesothorium from monazite by barium carrier [web] https://patents.google.com/patent/GB191025504A/en ; the Knoefler dispute [web snippet]. [physics] Mesothorium (Ra-228) is chemically identical to radium, so barium carries it: this is the chemical identity that led to the isotope concept. Claim 5. The patent is a commercial document of an interested party (Soddy); it describes his process, not a measurement.
9. Economic books (Cartesian Economics, WVWD, dedicated to Arthur Kitson) and Daly 1980, Merricks 1996: [web] sources of the energy-wealth argument. Outside the physics I can verify; recorded as Soddy's characterization. Kitson and Gesell are named by Soddy as forerunners [read in the footnote; web].
10. Lindau lectures (1952, 1954) and the 1946 MS "Real Alchemy and the Release of Atomic Energy": Soddy's later views on atomic energy, not read. They are the primary place to check whether his 1920 warning developed into support or opposition to nuclear power; the NYT 1956 obituary notes his views on hydrogen bomb tests. Claim 6.
11. Kelvin/Poincare/Campos: external-energy proposals for radium [web, snippets]. Stated as those authors' positions; superseded as shown under Claim 2.
12. Not reached by the Investigator (time limit): Sclove 1989 text, Morrisson, Hull 1994, Daly 1980, The National Archives (ADM, Board of Invention), Glasgow University Archives (Radium Committee minute book). These remain the records that would settle the history, not the physics.

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Corrections to Step 1 (for the orchestrator)

1. deep/interpretationof00sodd-f5dd74.md section 4 says the heat from 1 g Ra-226 with short-lived products is "roughly 27-28 MeV... ≈ 135-140 cal/h". My calculation: alpha energy alone (4.87+5.59+6.12+7.83 = 24.4 MeV) gives about 121 cal/h; the full chain to Po-214 with beta/gamma absorbed (about 28 MeV) gives about 141 cal/h. So the range is 121-141 depending on how much beta/gamma energy is absorbed; 133 sits inside it. Not an error of substance; the single range "135-140" should read "about 120-141".
2. deep section 5 (lead): the deep read says [memory, medium] the thorite lead (about 207.7-207.8) is from "Soddy and Hyman, and Hönigschmid (1914-1917)". My web check: Hönigschmid's thorite lead is reported as 207.90, with the sample linked to Richards and Hyman; Soddy's 1917 Nature letter reports a density-derived 207.74 for thorite lead, and Hönigschmid's 8 determinations are reported there. I could not verify "Soddy and Hyman" as co-authors of the 207.9 measurement. Record attribution as "Hönigschmid (207.90), with Soddy's indirect 207.74 from density" [web: search summary, medium]. The uranium-lead figure 206.05: could not be traced to Richards and Lembert (found 206.40 and 206.085 for other samples); treat as Soddy's reported "as low as 206.05" without named experimenter, as the text itself does not name one.
3. claims.md claim 2: "about 2.9 billion calories over its complete change" is right as arithmetic, but "complete change" there covers radium and its quick successors down to polonium-214 only, not the later RaD/RaE/RaF tail. Add this qualifier (the deep read's section 4 note says so; the claim sentence itself does not).
4. claims.md claim 2: "more than a million times a chemical fuel" is per gram of coal plus oxygen. Per gram of coal alone it is 3.6e5. Add the basis.
5. claims.md claim 3: "radium a mean life of about 2,500 years, uranium about 7,500-8,000 million years" are Soddy's values; modern mean lives are 2,308 y (8% lower) and 6.45e9 y (16-24% lower). The claim should be stated with this note so the primer does not present Soddy's numbers as modern.
6. claims.md claim 4/6 and the deep read: "radium becomes its emanation by expelling one" fine. But the deep read's sentence "Rutherford's 1920 X3 was later recognised as a misinterpretation (the long-range particles were alphas/protons)" is stated from [memory] and my web check could only confirm that the 1920 lecture proposed the mass-3 particle tentatively and that Blackett's 1925 photographs showed only the capture reaction to 17O plus proton; "later recognised as a misinterpretation" is a fair gloss but I could not find a source that states it in those words. Tag it [memory, medium] in the primer.
7. claims.md claim 5: agree with the Investigator's correction (add Hevesy and the order from the Nobel lecture, as Soddy's own account).
8. claims.md claim 6: "alpha bombardment of nitrogen appears to knock out hydrogen (and... a mass-3 doubly charged particle)". The hydrogen part is established (14N + alpha -> 17O + p); the mass-3 part was not confirmed. The claim as written reads as if both were observed; split it.
9. claims.md claim 7: the gold/silver aside is not merely "speculative"; it is self-contradictory under the equilibrium argument it relies on (see 7d). Add this.
10. deep/matterenergy...md section 3: "alpha rays possess over 95% of the energy" is in the 1911 text; modern chain-to-Po-214 share is about 86% [calc, medium]. Note as a minor 1911 overstatement.
11. The deep read of Interpretation notes "a hundred thousand years ago... a thousand billion times as much" and says it is understated; confirmed (e^40 = 2.4e17).
12. Aston table (Interpretation p.296): the deep read's later-correction list says "xenon's heavy isotopes are 132, 134, 136 (not 133, 135)". More completely, natural xenon has isotopes 124, 126, 128, 129, 130, 131, 132, 134, 136; Aston's 133 and 135 are not stable Xe isotopes [memory, high]. Sulphur: Aston's "pure 32.0" is wrong, sulphur has 33, 34 and 36 as well [memory, high].
13. Investigator's correction on the 100 cal/h figure: agree; the explicit number is in the 1909 first edition; the 1911 book does not print it.

No error found in the Step 1 reading of the 1920 formulae (lambda1 N = lambda2 X), the 133 cal/h chain of arithmetic, or the transcription of Aston's table beyond what is noted.

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Summary table