Rutherford-Ernest: Physicist review (Step 2)

Reviewer: PhD physicist. Project: Rutherford-Ernest (E. Rutherford, 1903-1930 papers and books; Chadwick and Ellis co-authors of the 1930 book). Written 2026-10-09.

Tags: [read] = from the project documents or deep reads (page given where useful); [read: page image] = rendered page; [web] = Internet source, URL given; [memory] = recall, confidence high/medium/low; [calc] = my arithmetic. Interested parties: Rutherford is the author and originator of the theory he reports (and of the experiments by his own students: Barnes, Soddy, Gates, Bronson). Chadwick is a co-author of the 1930 book that reports his own experiment. Le Bon, Moray and others quoted below are interested parties in their own priority claims.

Source note: all main works are text-extractable (no Source gap). Limits I inherit from Step 1: the 1930 book Ch. IX-XI (artificial disintegration of light elements, attempts to change decay rates, satellite theory) and 1904 book Ch. VIII-XI are digest-only; the 1913 book's alpha-ray chapter (PDF pp.131-192) deep read was lost. Where a verdict leans on those, I say so. I did read the Investigator's saved copies of the 1904 Bakerian Lecture (text layer) and Rutherford's 1919 "Atomic Projectiles" paper (page images, OCR).

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0. The mainstream view in brief, and how this project sits against it

Everything Rutherford claimed in these documents is either part of today's textbook physics or was a reasonable position later replaced. This is not an alternative-science project. The reader should still learn it because it shows how a new theory was built from measurements, with each step checkable: Rutherford and Soddy's decay law (1902-03), the heat of radium (1903-04), the alpha-particle scattering law (1911) and the first artificial transmutation (1919). It also shows where the pre-nuclear picture was wrong (alpha mass, charge, atomic number, the cause of decay, the sun) and was corrected by the author himself.

Two passages are of special interest to readers who come to Rutherford through other projects in this review (Moray, Le Bon): the 1904-1906 discussion of "external energy" and of a possible "detonator" (claim 7). I keep them in full below.

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Corrections to Step 1 (and to earlier documents)

1. claims.md claim 4: "the central charge of gold ... equals the atomic number (79) by Chadwick's 1920 measurements". Wrong attribution. Chadwick (Phil. Mag. 40, 734, 1920) measured copper, silver and platinum: 29.3e, 46.3e, 77.4e against Z = 29, 47, 78 [read: 1930 book, p.231-232, page image]. Gold (Z = 79) was measured later, by Rutherford and Chadwick, Phil. Mag. 50, 889 (1925), who found "a nuclear charge for gold less than 2 per cent. different from the atomic number" [read: 1930 book, p.234]. Correct both the claim and the matching facts.json text for the 1930 book.
2. claims.md claim 4: "Coulomb's law holds to about 3e-12 cm". As worded it reads as a measured scale of the force law. The 1930 book states it as an upper bound on nuclear radius: Coulomb's law holds at the closest distance reached (3.2e-12 cm for gold, 2e-12 silver, 1.2e-12 copper), "we may conclude, therefore, that the radius of the gold nucleus is not greater than 3.2e-12 cm" [read: 1930 book, p.235]. I verified these three numbers as the closest approach at 135 degrees for 7.5 MeV alphas ([calc], agrees with the deep read). The modern radius of gold is about 7e-13 cm [memory, high], so these were never tests of the nuclear surface.
3. claims.md claim 4, "the central charge ... a central charge later called the nucleus (1911)" and "about 100 e in 1911": correct, but state that Rutherford's 1911 paper never uses the word "nucleus", leaves the sign of the charge open ("it has not so far been found possible to obtain definite evidence to determine whether it be positive or negative", p.17), treats the charge as "distributed through a very small volume" (the point-charge assumption is a calculation device valid below 1e-12 cm), and allows "satellites" [read: deep/structureatom, sections 8-9]. "Positive nucleus carrying most of the mass" is the 1913 book's statement [read: 1913 book p.644 page image], not the 1911 paper's.
4. claims.md claim 7: "by 1930 no change in decay rate had been achieved by 3000 C, 20,000 atmospheres, electric, magnetic or gravitational fields, or intense radiation". This is digest-only (1930 Ch. XI) and I could not verify the list. Also, the claim that "no known agent changes the rate" needs a historical caveat and a modern caveat. Historical: in the 1904 Bakerian Lecture Rutherford himself wrote of Curie and Danne's heated-wire result that "the rate of change of the product C is not a constant, but is affected by differences of temperature. This is the first case where temperature has been shown to exert an appreciable influence on the rate of change of any radioactive product" [read: research/files 1904 Bakerian, text layer, section 21]. Bronson (1905, in Rutherford's laboratory) showed the effect was selective volatilization of radium B from C, and the 1906 book reports this [read: deep/Radioactive-Transformations, section 2.5]. The Investigator's lead is confirmed. Modern: electron-capture decays do change by a fraction of a percent with chemical environment or pressure (below).
5. claims.md claim 2 and the 1904 deep read: the "more than two-thirds of the heat from the emanation" calculation in Radio-Activity (1904) divides 1.26 cal/h by 30 mg of radium bromide, giving 42 cal/h per gram of radium BROMIDE, not per gram of radium as printed; the ratio (42/65 = 0.65) is unaffected [read: deep/radio-activity, section 5; calc]. The 1906 book's figure is "about three-quarters". Use 65-75 percent with the stated unit.
6. facts.json / claims.md note on the 1913 uranium half-life: the 1913 book prints 5.2e21 atoms per gram of uranium, twice what its own Section 63 implies (2.6e21); the final 4.8e9 years stands only if the counted alphas are shared between two uranium components [read: deep/Radioactive-Substances A11]. Not a Step 1 error, but a published slip to flag.
7. Digest/structureatom corrections already listed in claims.md are confirmed by my reading of the deep read (energy equation sign, the count scales as (Ne)^2, three z/A^1.5 quotients that do not follow, the silver row of the Crowther table, p1 = 0.0007 not 0.0004 at p2 = 0.1). I add: the 1911 paper's own b = 3.4e-12 cm for N = 100 and 2.09e9 cm/s is about 6 percent above what its own later constants give (3.19e-12), a harmless rounding [read: deep, section 2; calc].
8. A single slip in my sources worth recording: the 1913 book's radium D maximum "in 81 years" should be about 115 years with the book's own periods [read: deep/Radioactive-Substances A8; calc]. The 1930 book's Schonland table has a factor-10 inconsistency among the p values [read: deep/Radiations section 6.5].

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Claim-by-claim review

For each claim: (a) mathematics, (b) consistency with experiment, (c) tests and replication, (d) what mainstream physics would have to change if it were true. Then the verdict.

Claim 1. Radioactive atoms spontaneously disintegrate into atoms of other substances, at a rate no known agent changes, following an exponential (probability) law

Mainstream view. This is the modern law of radioactive decay. If N is the number of atoms of one kind present and lambda (the decay constant) is the chance per second that any one of them decays, then dN/dt = -lambda N, so N = N0 e^(-lambda t). The half-life is T = ln 2 / lambda and the mean life is 1/lambda. For a chain A to B to C, the Bateman equations give each member as a sum of exponentials. Parent and daughter in equilibrium obey lambda_A N_A = lambda_B N_B (the activities are equal).

(a) Mathematics. Consistent. Every derivation I read checks: the decay and recovery curves I/I0 = e^(-lambda t) and 1 - e^(-lambda t); the successive-change solutions (the 1913 book's equations 5-20 were verified with SymPy by the deep reader, with two misprints, b = -lambda1/(lambda2 - lambda1) and a missing 1/lambda4 in equation 13, neither propagating) [read: deep/Radioactive-Substances A3-A6; calc]. Worked example with the book's numbers: thorium X, half value 4 days, so lambda = ln 2 / 96 h = 0.0072 per hour; after 1 hour the recovered fraction is 1 - e^(-0.0072) = 1/139 (the book says 1/140), after 1 day 0.159 (book "1/6"), after 4 days 0.5 [read: 1904 book p.205, page image; calc]. For radium B and C the maximum of C after a short exposure is at t = ln(lambda2/lambda1)/(lambda2 - lambda1) = 35.2 minutes, which matches the observed maximum [read: 1906 book p.119-120; calc]. The 1906 book's one internal inconsistency here, the statement that radium B is rayless and independent of A, is withdrawn in the book's own footnote after Schmidt (1905) found B emits soft beta rays [read: deep/Radioactive-Transformations, section 2.4]. The "life of radium" and thorium rate estimates were rough and some were wrong by factors of 2 to 600 (e.g. "one atom per 1e15 per second" for thorium against a true 1.6e-18 per second) but were labelled "not more than" and "cannot be calculated except roughly" [read: Harper's 1904 p.5; calc].

(b) Experiment. Agreement with all later work. The parent-daughter chemistry is confirmed: thorium X is radium-224 (3.66 days), uranium X is thorium-234 (24.1 days), the emanation is radon-222 (3.82 days) [memory, high]. Rutherford's measured values (3.77-3.99 days for the emanation, about 22 days for uranium X, about 4 days for thorium X) are within 10 percent. Boltwood's mineral table (21 minerals, uranium content varying 250-fold, radium-per-uranium column constant at 215-228 except some monazites) establishes secular equilibrium [read: deep/Radioactive-Substances A10]. A check against modern half-lives gives the equilibrium ratio (1600/4.468e9) x (226/238) = 3.40e-7 g radium per g uranium, equal to Rutherford and Boltwood's 3.4e-7 [calc]. The exponential law, and its meaning as an atomic probability, is established; Rutherford adopted the probability reading explicitly by 1906 ("probably governed purely by the laws of probability", p.281) and 1913 (the law "an expression of the law of probability").

"No agent changes the rate." Two halves. (i) For alpha and beta emitters the claim stands for temperatures from liquid air to red heat, vacuum, chemical combination and intense radiation [read: 1904 book p.208-211; 1906 book p.279]; in a modern reading it holds to better than 0.1 percent for ordinary decays. (ii) It is not strictly true for decays by capture of an inner electron, where the rate depends on the electron density at the nucleus. Beryllium-7 in C60 cages has a half-life 0.83 percent shorter than in beryllium metal (52.68 against 53.12 days); high pressure raises the Be-7 rate by about 0.5 to 1 percent at 270 to 400 kilobars [web: https://physicsworld.com/a/radioactivity-speeds-up/ and the summary of Ohtsuki 2004, Hensley 1973, Liu and Huh 2000 retrieved by search 2026-10-09; the retrieval was a search summary, not the papers]. This is a small, understood effect (electron density) and not a failure of the law. Claims of larger, solar-correlated variations (Jenkins, Fischbach and others) are disputed; the Investigator located but did not read a Texas A&M thesis analysing them [read: Investigator, research/2026-10-09-oaktrust-tamu.md]; I have not evaluated those claims and do not rest anything on them.

The 1904 temperature episode. Rutherford's acceptance (Bakerian Lecture, section 21) that heating changes radium C's decay constant, constant about 1.4 times normal after about 1100 C (Investigator, p.210; I read p.198-199 only), was an experimental artifact. Curie and Danne's heated wire lost radium B (more volatile) faster than C; Bronson (1905) with a sealed tube found "a rise of temperature up to 1100 C has no appreciable effect on the rate of transformation" [read: 1906 book pp.131-132]. I count this in Rutherford's favour as an example of self-correction, and in the record because the Investigator rightly kept it.

(c) Tests. Many, independent, repeated: Rutherford and Soddy (1902), Crookes and Becquerel for uranium X, P. Curie, Bumstead and Wheeler, Sackur (emanation decay 3.77-3.99 days), Boltwood, McCoy, Geiger counting alpha particles (2.37e4 per second per gram uranium) [read: 1913 book]. Reproducible today in a student laboratory (Geiger counter and a thoriated mantle).

(d) If it were false. Nuclear physics, geochronology (uranium-lead dating), nuclear medicine and reactor physics would all have to be rewritten. Nothing has to change because it is true.

Verdict: Established. Split: exponential law, parent-daughter chains, and insensitivity to temperature, chemistry and ordinary radiation: Established. "No agent whatever changes the rate": Established to about 0.1 percent for alpha and beta decay; for electron-capture decays the rate changes by up to about 1 percent with electron environment (small, explained).

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Claim 2. The energy released (about 100 cal per hour per gram of radium, about three-quarters from the emanation and its products, a store of about 3.7e9 cal per gram) is the atom's own internal energy, vastly larger than chemical, not taken from the medium

Mainstream view. The energy is nuclear: the mass of the parent nucleus exceeds the mass of the products by an amount Delta m, released as E = Delta m c^2 (Einstein, 1905; not available to Rutherford in 1904-06 in this form). In radium-226 decay the alpha particle carries 4.78 MeV (the alpha plus recoil total 4.87 MeV); the chain through polonium-214 releases about 24 MeV per radium atom in four alpha decays [memory, high]. One MeV is 1.6e-13 J, against a typical chemical bond energy of a few eV: a factor of about 10^6.

(a) Mathematics. Consistent, with a systematic bias I can explain. Rutherford computed the alpha energy from the 1/2 m v^2 of a particle with the ratio e/m and the measured velocity. The charge was taken as one ion charge e; in fact it is 2e [memory, high]. His energy per alpha, 5.9e-6 erg (3.7 MeV) is about 40 percent below the modern mean (about 6 MeV). His alpha count was good: Method 3 gave 1.4e11 alpha per second per gram against the modern 1.46e11 [read: 1904 book p.172-173; memory, high; calc, from the deep reader]. The two errors largely cancel in the product, and his alpha power came out 50 cal/h against the observed 100; he assigned the rest to "rearrangement" energy [read: 1904 book p.180]. In modern terms the alpha decays alone give about 0.143 W = 123 cal/h (my arithmetic from the deep reader's modern energies), the whole observed heat; the "missing" part was the low alpha energy, plus the recoil (about 2 percent) and beta and gamma. So there was no separate source. Check: 100 cal/h = 0.116 W; Curie-Laborde's "about 100", Rutherford and Barnes's 110 cal/h per gram of radium (65 per gram bromide x 385/225), and the 1913 "about 118 and with beta and gamma about 134" [read: 1913 book p.26206 region via deep/Radioactive-Transformations section 7] are mutually consistent. Energy store: 876,000 cal per year x mean life gives about 1.6e9 cal per gram for radium through radium C (1906 book numbers, mean life 1850 years) and 3.7e9 cal per gram for the whole chain (1913 book) [read: p.681 page image; calc]. Modern: 0.143 W x mean life (2335 yr = 7.4e10 s) = 1.05e10 J = 2.5e9 cal through the alpha decays [calc, memory high for mean life], within a factor 1.5 of Rutherford's 3.7e9. "Nearly four million times" the heat of burning hydrogen: 1 cc of emanation with products 1e7 cal against 3 cal for 1 cc of detonating gas, [calc] 3.3e6, consistent.

The comparison with chemistry is stated honestly in the 1904 book: 2400 cal per day against 3900 cal to form 1 g of water ("nearly as much"); the yearly figure is 225 times the water-formation energy, which is the real contrast [read: 1904 book p.175; calc].

(b) Experiment. Consistent: radium holds itself several degrees above its surroundings (Curie and Laborde, 1.5 C thermocouple, ice calorimeter) and heats inside liquid hydrogen (Dewar; my order check of 73 cc/min of gas agrees with 65 cal/h per gram bromide) [read: 1904 book p.174-176]. Heat follows the alpha activity: when the emanation is removed the alpha activity falls to 25 percent and the heating to 25-30 percent, recovering in a month, while beta and gamma fall to nearly zero (Rutherford and Barnes, Phil. Mag. 1904) [read]. The "external energy" alternative was tested: the gamma activity is unchanged when radium is sealed in thick lead; the separated emanation's heat rises and then decays exponentially, which on the absorption hypothesis would require an absorbing agent that is produced and dies away; and radium heats inside an ice calorimeter [read: 1904 St Louis address, Investigator via Wikisource; 1913 book p.437-438].

(c) Tests. Many measurements by independent groups (Curie, Laborde, Giesel, Runge and Precht, Rutherford and Barnes, Meyer and Hess 132 cal/h in 1913 against Rutherford's total 134) [read: deep/Radioactive-Transformations section 7]. The earth-heat claim in 1913 rests on later geochemistry. Replicated; the numbers are used today.

External-energy theories (kept in the record). Rutherford's 1913 survey names and quotes the proponents: Crookes 1899 (radio-elements abstract energy from gas molecules), Lord Kelvin at the British Association 1903 (radium absorbs unknown radiations, like black paper warming in light), the Curies 1902 ("borrowed from the surrounding air in some way not accounted for by the principle of Carnot"), Re 1903, Armstrong and Lowry 1903. His verdict: "Up to the present not the slightest experimental evidence has been adduced to show that the energy of radium is derived from external sources." [read: 1913 book p.433-438]. He is an interested party (author of the rival theory), but the arguments he gives are experimental and checkable, and they stand: the activity is unchanged under lead, the heat grows and decays with the emanation, and mass is lost (alpha particles and new elements appear). The decisive modern evidence is the mass difference between parent and products, which gives the energy released to better than a percent [memory, high].

(d) If it were false (external energy). Conservation of energy would have to be given up or a new universal medium-field postulated; nothing in 120 years of nuclear mass tables suggests it.

Verdict: Established. Split: the energy is the atom's own (nuclear, not electronic) internal energy and not drawn from the medium: Established. The quantitative figures (about 100 cal/h, 3.7e9 cal/g) are the right size (modern about 120-140 cal/h; about 2.5e9 to 4e9 cal/g). The 1903-06 picture of the store as electron-orbit "latent energy" and the radiation-loss cause of decay: Historically superseded but instructive.

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Claim 3. Alpha particles are helium atoms projected at about a tenth of the speed of light, beta rays fast electrons, gamma rays penetrating radiation; helium and lead are final products; uranium leads through ionium to radium (radium 3.4e-7 of uranium by weight)

Mainstream view. Alpha = helium-4 nucleus (charge +2e, mass about 4 u), beta = electron or positron, gamma = high-energy photon from a nuclear transition. The uranium-238 series ends at lead-206; thorium at lead-208; actinium (uranium-235) at lead-207. Radium-226 is the daughter of thorium-230 (ionium), itself from uranium-234, which comes from uranium-238 by way of thorium-234, protactinium-234 and the beta decay chain [memory, high].

(a) Mathematics. Consistent but with early numerical errors that Rutherford himself later fixed. In 1903-04 he gave the alpha mass as "about twice the hydrogen atom" and charge e (from the measured e/m about half that of the hydrogen ion) [read: Harper's 1904 pp.1-2]. With charge 2e the same e/m gives mass 4: his own caution that helium "comes next to hydrogen in lightness" fits. Speed "20,000 miles per second" (3.2e7 m/s, about 0.1 c) was high; real radium alphas run 1.5e7 to 2.0e7 m/s, 0.05 to 0.07 c [memory, medium for the Ra-chain range; the 1911 paper uses 2.09e9 cm/s = 0.07 c]. The recoil check in the 1906 book (alpha mass about 1/50 of the radium atom, speed 2e9 cm/s, so recoil 4e7 cm/s) is arithmetically fine but loose ("about 200 miles per second" for 250) [read: 1906 book p.284; calc]. Lead as end product: 238.5 - 8 x 3.994 = 206.6, "close to lead" (207) [read: 1913 book p.622; calc]; thorium 232.5 - 24 = 208.5, which the book honestly leaves unexplained (the answer is 208, branching at thorium C) [read]. Uranium ages: lead/uranium x 8e9 years (for Pb/U = 0.041, 330 million years, the book 340 [calc]). The 1913 book is also candid that "No definite proof of the formation of radium from pure uranium has yet been obtained" (the quadratic growth test R = 6e-13 t^2 g per kg of uranium, with t in years, had not been done) and that Russell and Rossi's failure to see ionium lines hinted at an unknown intermediate [read: 1913 book p.489-490]. That intermediate was real (UX2 and uranium-234) [memory, high]. The deep read of a mass check (radium 225.95 + 3 x 3.99 = 237.92 against uranium 238.5-ish) also holds.

(b) Experiment. Alpha = helium: Ramsay and Soddy (1903) saw the helium spectrum grow in the emanation tube (Rutherford: "must naturally be accepted with reserve" [read: Harper's 1904 p.5-6]); proved by Rutherford and Royds in 1909 [memory, high] (not in the project documents; I did not re-verify on the web, the identification is textbook). Beta = electron: Kaufmann's mass-velocity data on radium beta rays [read: 1906 book p.272]. Gamma as electromagnetic: Rutherford's own 1914 crystal diffraction [memory, medium]. The uranium chain and Boltwood's ratio are confirmed by modern half-lives (above). Geiger and Nuttall's range-period law (1911-12) was a new empirical rule found by Rutherford's group and remains valid [read: 1913 book p.632-634; memory, high].

(c) Tests. Independent: Boltwood (21 minerals), McCoy, Strutt, Gleditsch (a second table of ratios, partly below normal in altered minerals; her high Cornwall pitchblende value "difficult to explain" in Rutherford's words), Soddy, Marckwald and Russell (autunite ratios 0.21-0.68 of normal, ionium 0.76-0.93, which discriminates leaching from youth) [read: 1913 book p.486-488]. Rutherford reports the dissenting data. Replicated and extended.

(d) If it were false. Not applicable in the strong form; replications and the later atomic-number picture cover it.

Verdict: Established. Split: alpha, beta, gamma identities and the chain (with uranium-234 and UX2 intermediates added later): Established. The 1904 alpha mass (about 2 H) and speed: Historically superseded but instructive (the charge was taken as e rather than 2e).

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Claim 4. The atom has a small, massive, highly charged centre; alpha scattering follows cosec^4(phi/2); central charge of gold about 100e and equal to the atomic number by Chadwick's measurements; Coulomb's law holds to about 3e-12 cm

Mainstream view. The nuclear atom. For a point nucleus of charge Ze and a point alpha of charge 2e and kinetic energy K, a head-on approach stops at distance b = 2 x (Ze)(2e)/(2K)... in Rutherford's notation b = 2 N e E/(m u^2), where N is the number of unit charges in the centre, E the alpha's charge, m its mass and u its speed. The orbit is a hyperbola; the impact parameter p (the perpendicular distance between the incoming line and the centre) gives the deflection phi by cot(phi/2) = 2p/b. The fraction of alphas scattered beyond phi from a thin foil with n atoms per unit volume and thickness t is (pi/4) n t b^2 cot^2(phi/2), and the number per unit screen area at distance r is y = Q n t b^2 cosec^4(phi/2)/(16 r^2), where Q is the number of incident alphas. Nothing else is needed from quantum mechanics: the quantum cross-section for Coulomb scattering is exactly the same (a known coincidence) [memory, high].

(a) Mathematics. Consistent. This is the best-checked derivation in the project. The deep reader verified every step with SymPy and NumPy: the field and potential of a point charge in a uniform opposite sphere (V(R) = 0); b = 2p cot theta; equation (1) cot(phi/2) = 2p/b with the deflection table (all seven entries); equations (2)-(5); the recoil quadratic (rho = 0.979 for gold, 0.86 for aluminium; range 7 cm to 4.5 cm); the small-angle average deflection 3 pi b/8R, three times Thomson's; the compound-scattering estimate and the single-versus-compound comparison; and N = 97 and 114 from Geiger's data [read: deep/structureatom, summary, section 10; calc]. I repeated the key check by hand for the reader. Worked example: gold N = 79 in modern terms, alpha of 7.69 MeV (radium C'): b = 2 Z e^2 /(K) with e^2 = 1.44 MeV fm; 2 x 79 x 1.44/7.69 = 29.6 fm = 3.0e-12 cm; for p = b/2 the deflection is phi = 90 degrees [calc]. Rutherford's own (N = 100, u = 2.09e9 cm/s) gives 3.2e-12 cm with the paper's constants (the paper says 3.4e-12; about 6 percent high, harmless). A particle aimed at 1.6e-12 cm from the centre is turned back 90 degrees: about 1/10,000 of the atomic radius (1e-8 cm).

Imperfections in the 1911 paper, all small and all listed by the deep reader: the c.g.s. units (e = 4.65e-10 esu against modern 4.80e-10); the N proportional to A hypothesis (a hypothesis, tested for consistency by the z/A^1.5 table, in which three of eight quotients do not follow from the printed z and A, spread 208-283 instead of 208-250; I rely on the deep reader's recomputation); Crowther's data (one test, the small-t slope of I/I0, went against single scattering for beta rays; Rutherford answered with Marsden and asked for further experiments, an honest concession) [read: deep/structureatom sections 7(d)]. The 1911 argument is a bound in two senses: (1) the data cited are mostly Geiger's earlier rough numbers (1/8000 back from platinum, 1/20,000 through about 90 degrees from gold foil), with no numbers given for the 30-150 degree test ("substantial agreement"); (2) the claim that the central charge is 100 e for gold is stated as "about".

(b) Experiment. The decisive tests came after 1911 and are in the 1930 book: Geiger and Marsden (1913) tested cosec^4 over a 250,000-fold change in count (5 to 150 degrees, silver and gold), thickness proportionality (four metals), the dependence on atomic weight (N/A^1.5 = 0.21, 0.21, 0.18, 0.23, 0.24, roughly constant) and on speed (N V^4 = 22 to 28 over a ninefold change, ±12 percent) [read: 1930 book pp.222-228 and page images; calc]. Their absolute count gave a charge of about A e/2 within about 20 percent (modern Z over A/2 = 0.8 for gold and platinum) [calc]. Chadwick (1920) used an annular foil to measure Z directly: copper 29.3e, silver 46.3e, platinum 77.4e (Z = 29, 47, 78), 1-2 percent; Rutherford and Chadwick (1925) gold within 2 percent. I note, and the deep reader notes, that the 1930 book's angle table shows a systematic 35-50 percent excess at 15 to 30 degrees in the first set, not discussed in the text (probably beam width and plural scattering). Darwin's argument: for a force varying as 1/r^p the count scales as (1/V^2)^(2/(p-1)); the observed V^-4 fixes p = 2 [read: 1930 book p.232; calc]. Blackett's cloud-chamber tracks (281 deflections in argon, 1524 in air) agree with the inverse-square law, the 10 degree to 90 degree ratio being 4330 against 525 for an inverse cube [read: 1930 book p.242; calc 4332.7]. Rose (1926) found no K-shell effect down to 1.2 degrees, i.e. out to 1.7e-10 cm. Rutherford's 1930 co-authors state the limits plainly: for light elements departures from Coulomb scattering appear at close approach (discussed later in the book, digest-only for me) and for beta particles "an adequate test of the theory ... has not yet been carried out" [read: 1930 book p.261]. Modern: departures from point-Coulomb scattering of heavy nuclei appear only at higher energies (tens of MeV) [memory, medium].

The sign of the central charge was not established in 1911 [read: deep/structureatom section 9]. Rutherford assumed positive for convenience and suggested two routes (beta absorption laws; alpha emission energetics). In the 1913 book the nucleus is positive and carries nearly all the mass and "probably confined within a sphere of radius not greater than 1e-12 cm" [read: 1913 book p.646]. The modern evidence for positive charge includes Moseley's X-ray work, Bohr's atom and the recoil of light nuclei [memory, high].

Atomic charge: N = A/2 was an approximation; Z = 79 for gold, not 100. The 1911 paper's own finding that the same N explains alpha and beta scattering "to within the uncertainties" (97, 114 against 138 for platinum from beta rays) shows the data were rougher than the fit suggests. Van den Broek (1913) suggested charge = atomic number; Moseley (1913-14) and Chadwick (1920) established it [read: 1930 book p.229]. The "49 helium atoms times 2e" remark in 1911 is labelled by Rutherford as possibly "only a coincidence" and is not the modern composition; the neutron (Chadwick, 1932) replaced the 1930 "protons and electrons" nucleus [read: 1930 book p.235; memory, high].

(c) Tests. Geiger and Marsden (Manchester, Rutherford's own laboratory); Chadwick; Rose; Blackett; Auger and Perrin (argon, Z = 19 against true 18). The chief tests were done in or near Rutherford's group, which is a concern worth stating: the first scattering law test, the charge measurement and the recoil test were done by his own co-workers. Independent confirmation is abundant afterwards: every later scattering experiment, Rutherford backscattering spectrometry used daily in materials analysis, and the whole of nuclear physics [memory, high].

(d) If it were false. Atomic physics (Bohr, quantum mechanics of the atom), all of nuclear physics. Nothing needs to be changed because it is true.

Verdict: Established. Split: cosec^4(phi/2) law, inverse-square (Coulomb) force and a small, massive, charged centre: Established (tested to the distances stated, which are upper bounds of 3.2e-12 cm for gold). "Central charge about 100e for gold; N = A/2": Historically superseded (Z = 79, charge equals atomic number, Chadwick 1920 and Rutherford-Chadwick 1925). "Charge positive": Not established in 1911; Established by 1913-14 (assumed, then confirmed).

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Claim 5. Radioactive heat can account for the earth's internal heat, so Kelvin's cooling-earth limit on the age of the earth does not apply; and speculatively a similar release of atomic energy in ordinary matter at high temperature could lengthen the sun's life about a hundredfold

Mainstream view. Two parts.

Earth. Kelvin (1862-1899) treated the earth as a hot body cooling by conduction, with no heat sources, and got 20 to 100 million years. Radioactive heating, together with mantle convection (which Kelvin's solution omits), invalidates that age. Today the earth's heat flow is about 44 to 47 TW; geoneutrino measurements by KamLAND and Borexino indicate about 20 TW (roughly 40 to 50 percent) is radiogenic, mostly uranium-238, thorium-232 and potassium-40, concentrated in the crust and parts of the mantle [web: Gando et al., Nature Geoscience 4, 647 (2011), via search summary, 2026-10-09: https://www.geol.umd.edu/~mcdonoug/KITP%20Website%20for%20Bill/papers/Measurements/Gando_etal_(Nature_Geo_11).pdf and the 2023 combined analysis summarised in the same search]. Radioactivity alone does not date the earth; uranium-lead and similar methods give about 4.5 billion years [memory, high].

Sun. Fusion of hydrogen to helium (Eddington 1920 suggestion, Bethe 1938-39) supplies the solar energy: 0.7 percent of the mass converted, about 6.3e11 J/g = 1.5e11 cal/g [calc, 0.007 x c^2 = 6.3e11 J/g]. Solar lifetime on the main sequence is about 10 billion years [memory, high].

(a) Mathematics. Mostly sound; one ambiguity and one shaky extrapolation. Rutherford's 1905 popular article gives (i) 270 million tons of radium would supply the present conductive heat loss, which I reproduce with a conductivity k = 1.7 W/(m K) and the stated gradient 1/50 F per foot (0.0365 K/m): flux 0.062 W/m^2 x 5.1e14 m^2 = 3.2e13 W, and 3.2e13 W / 0.1162 W/g = 2.7e14 g = about 270 million (long) tons [calc, deep reader; the conductivity is mine, Kelvin's value not given in the text, so the number carries about a factor 1.5 uncertainty]. (ii) "five parts in one hundred million million per unit mass" = 5e-14: 2.7e14 g / 5.97e27 g = 4.6e-14, the mass fraction of the WHOLE earth, though the article says "crust" [calc; read: Harper's 1905 p.6]. The 1913 book repeats the whole-earth figure (4.6e-14) and then states the consequence: the crust actually holds about 2e-12 g radium per g, about 20 to 40 times more, and if that were uniform through the earth the heat would be "about 200 times greater" than the observed loss, so the activity must be confined to a thin shell about 20 km deep, or decrease with depth [read: deep/Radioactive-Substances section 3.5]. The shell worked example is right: Q = K T = 0.004 x 0.00031 = 1.24e-6 cal/cm^2/s = 39 cal/cm^2/yr; radioactive output 1.9e-5 cal/cm^3/yr gives a shell depth 2e6 cm = 20 km, and a temperature maximum theta = h D^2/2K = 300 C at the base [calc, agrees with the book]. Rutherford notes the paradox that more radioactive matter lowers the maximum temperature. The 1913 book therefore corrects the 1905 picture in the same hand, which I keep: the 1905 "uniform through the whole earth" reading was superseded by Strutt and Joly's measurements of rock radioactivity (Strutt: igneous rocks 0.31 to 4.78e-12 g Ra/g) [read: 1913 book p.670-671].

Sun: "radium in the sun to the extent of 2.5 parts per million of its mass would account for the present rate": 0.1162 W/g x 1.99e33 g x 2.5e-6 = 5.8e26 W against the solar 3.83e26 W [calc, 1.5 times; the exact fraction is 1.66e-6]. This gives power, not duration: radium with a 1600-year half-life would be exhausted in thousands of years [calc]. The central speculative step in 1905, "if ordinary matter in breaking up emits as much heat as radium ... the duration of the sun's heat would be prolonged for about one hundred times the estimate" is a scaling by 100 of Helmholtz's 40 million years, i.e. about 4 to 5 billion years; the 1913 book's version is more careful: "if the sun consisted entirely of uranium in equilibrium ... only about one-fourth" of the heat; and it gives the same speculation in the energy-density form: radium's 3.7e9 cal/g against Darwin's gravitational 2.7e7 cal/g (a factor 140), so a radium-like store in ordinary matter would stretch 12 million years to 1.6 billion [read: 1913 book p.681; calc]. These are rough but self-consistent. A surprising numerical coincidence: the energy per gram of hydrogen fusion (1.5e11 cal/g) is about 40 times Rutherford's "similar amount" (3.7e9), so the real store is larger than he guessed, and the sun's actual lifetime (10 billion years, only a few tenths of the mass participating) is within a factor 2-3 of his 5 billion [calc].

(b) Experiment. Earth: Strutt, Joly, Eve and McIntosh, Farr and Florance, Büchner all found rock radium above the minimum needed (20 times) [read: 1913 book p.670-671]. Modern geoneutrinos confirm radiogenic heating is about half the flux, not all of it [web, above]. Sun: no radium was ever found there (Rutherford: "no direct evidence"); the energy source is fusion.

(c) Tests. Kelvin's age was overturned in practice by Boltwood's uranium-lead ages (1907) and Holmes (1911; ages of 340 to 1640 million years in the 1913 book) [read: 1913 book p.622-623]. Rutherford's cosmological speculation was untested in his lifetime. It was in practice (partly) correct in spirit and wrong in mechanism: atoms at solar temperature do release "atomic energy", but by fusion of the lightest elements rather than by break-up of heavy ones, which is opposite in direction to the radioactive picture. Lockyer's stellar sequence (hottest stars: lightest elements) was the opposite of Rutherford's "converse" direction; both occur: heavy atoms decay, stars build them [memory, high].

Honest hedges in the source. In the 1905 article Rutherford says explicitly: "no definite limit can be set for the age of the earth" from heat; the internal heat "tends to be maintained"; "science offers no escape from the conclusion ... that the sun must ultimately grow cold and this earth must become a dead planet" [read: deep/RadiumTheCause, sections 2, 3G, 5]. The author is an interested party as the discoverer, but the claim here is modest.

(d) If it were false. Nothing for the earth part (it is true and standard); for the sun part, nothing: solar fusion replaced it.

Verdict: Split. (i) Radioactive heat removes the basis for Kelvin's cooling age: Established. (ii) The 1905 quantitative form (uniform 4.6e-14 g/g through the whole earth balances the heat loss): Historically superseded but instructive (the real radiogenic heat is about half the flux, concentrated in crust and mantle; 270 million tons of radium reproduces the heat flow if the conductivity is about 1.7 W/(m K)). (iii) The sun's life extended about 100 times by break-up of ordinary atoms at high temperature: Historically superseded but instructive (right in claiming a nuclear energy store in ordinary matter, wrong in mechanism; fusion supplies about 40 times more than he assumed).

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Claim 6. The nucleus can be disintegrated artificially by alpha bombardment (1919, nitrogen and other light elements giving protons), and alpha scattering from light nuclei departs from the Coulomb law at close approach

Mainstream view. Nuclear reaction N-14 + He-4 gives O-17 + H-1; discovered by Rutherford (1917-19), shown in a cloud chamber by Blackett (1925) to leave an O-17 track and a proton, with no helium track [memory, high; I did not check the Blackett date on the web]. Departures from Rutherford scattering for light targets occur because the alpha reaches the strong-interaction range (about 1e-12 cm) and, for hydrogen, because the target recoils; Rutherford and Chadwick studied these in 1921-25 [memory, medium; the 1930 Ch. IX-XI is digest-only for me].

(a) Mathematics. For the first part I read Rutherford's 1919 paper "Atomic Projectiles and their Collisions with Light Atoms" (Science 50, 467, 21 Nov 1919) in page images [read: research/files 1919 PDF, OCR]. It contains the recoil mechanics (hydrogen recoil of speed 1.6 times the alpha's speed, ranges for hydrogen atoms up to about 28 cm of air equivalent from alphas of 7 cm range) and the decisive passage: long-range scintillations "arising from nitrogen" of "about the same brightness and range as the H atoms produced from hydrogen", "presumably, charged hydrogen atoms", with the hedge: "the evidence so far obtained is not sufficient to distinguish definitely whether these are H atoms or atoms of mass 2, 3, or 4" and the conclusion "It is difficult to avoid the conclusion that these long-range atoms ... are not nitrogen atoms, but probably charged atoms of hydrogen or atoms of mass 2. If this be the case, we must conclude that the nitrogen atom is disintegrated under the intense forces developed in a close collision with swift alpha-particles." He also states "the helium nucleus was not seen to break up" in its collisions [read: page images, 1919 paper]. So the 1919 claim is made with stated limits (identity of the particle by range and brightness, not by deflection in a field; the measurement of the deflection "exceedingly difficult"). The fine print also records a control: the effect was seen in chemically prepared dry nitrogen, in numbers far too large to come from hydrogen traces or water vapour. The recoil mechanics is just conservation of momentum and energy (the 1911 recoil quadratic with K = M/m) and checks.

(b) Experiment. Blackett (1925) photographs showed the proton and O-17; Cockcroft and Walton (1932) split lithium with protons from an accelerator; Chadwick found the neutron by alpha bombardment of beryllium (1932) [memory, high]. The close-approach departures from Coulomb scattering for light elements are confirmed [memory, medium].

(c) Tests. First by Rutherford (interested party); confirmed by independent groups by 1925. The 1933 statement is also on the record: Rutherford told the British Association that the hopes of releasing atomic energy by splitting atoms were "moonshine" [web via Investigator: Levin Daily Chronicle, 13 Sept 1933, https://paperspast.natlib.govt.nz/newspapers/LDC19330913.2.68; I did not open the page myself]. Beside it stands Richardson's 1921 remark that transmutation was "an established fact" and controlled atomic energy would give "an illimitable supply of power" (Press, 13 Sept 1921). Both are on the record; fission (Hahn and Strassmann 1938) came after Rutherford's remark [memory, high].

(d) If it were false. All nuclear reaction physics.

Verdict: Established. Split: artificial disintegration of nitrogen by alpha particles with emission of a hydrogen nucleus: Established. Close-approach departure from Coulomb scattering for light nuclei: Established (my reading rests on the 1919 paper and memory; the 1930 chapters are digest-only).

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Claim 7. Ordinary matter may itself be slowly transforming; in 1906 Rutherford held open that disintegration might be triggered by an unknown external force like a detonator while the energy remains the atom's own; by 1930 no change of decay rate had been achieved

Mainstream view. Decay constants are properties of nuclei; ordinary stable nuclides do not decay; a handful of long-lived natural activities exist (potassium-40, rubidium-87, and others) [memory, high]. Triggered decay is real in special cases (neutron-induced fission, nuclear isomers triggered by photons, bound-state beta decay of fully ionised ions) [memory, medium]. The detonator picture as a general trigger for spontaneous decay is not supported.

(a) Mathematics. No equation is at stake; the logic is what Rutherford says and it is consistent. The 1906 passage in full: "It is conceivable, for example, that some unknown external force may supply the necessary disturbance to cause disintegration. In such a case, the external force supplies the place of a detonator to precipitate the atomic explosion. The energy liberated by the explosion, however, is derived mainly from the atom itself and not from the detonator. The law of transformation of radioactive matter does not throw any light on the question, for such a law is to be expected on either hypothesis." [read: 1906 book p.280 (Ch. XI)]. The same passage is in the St Louis address of September 1904 ("The energy set free is, however, not derived from the detonator, but from the substance on which it acts") [web: https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_67/May_1905/Present_Problems_in_Radioactivity] and in Radio-activity (2nd ed., 1905, section 270), where gravitation is named as the one force "which is not under our control" that might influence stability [Investigator, web: https://archive.org/details/radioactivity00ruth; not re-read by me]. Keep the Le Bon context: Le Bon quoted a sentence from the French version of the St Louis address as "Il serait desirable de voir apparaitre ... une sorte de theorie chimique ... pour savoir s'il faut considerer que l'energie est empruntee a l'atome lui-meme ou a des sources exterieures"; the English version says a chemical theory is required "whether the view is taken that the energy is derived from the atom itself or from external sources" [Investigator: archive.org 'archivesdesscien419gen', rexresearch, Wikisource]. In both versions the same address argues against the external source: "There is no direct evidence in support of the view ... while there is much indirect evidence against it. ... radium gives out heat inside an ice calorimeter ... unaltered by hermetically sealing it in a vessel of lead several inches thick." So Rutherford's position was: energy internal (stated firmly), trigger open (stated as conjecture), cause "primarily in the atom" by electromagnetic radiation loss and probability (1906 p.280-281) [read]. Le Bon's use of the "bolder physicists ... remain in doubt" sentence is therefore selective; Le Bon is an interested party in his own priority claims (the Investigator records his 1897 notes and the "universal radioactivity" claim) and his reading of Rutherford is his characterisation. Anyone quoting Rutherford on "external sources" should quote all three passages together, as the 1906 deep read recommends.

Ordinary matter. "Matter may be undergoing slow atomic transformation of a character similar to radium, which would be difficult to detect" and the sub-threshold alpha idea (alphas slower than about 8e8 cm/s would ionise nothing) [read: 1906 book p.288-289]. In 1913 Rutherford gave the answer: the residual ionisation in sealed vessels is "in all probability to be ascribed to the presence of traces of radio-active matter as impurities", and if intrinsic, it would need a half-life of 5e17 years [read: 1913 book p.620-621; calc: 1/(3600 x 2.7e4) = 1.03e-8 of uranium's rate]. Potassium and rubidium do emit beta rays (Campbell and Wood, 1907), a real effect now explained by potassium-40 and rubidium-87 [read: 1913 book p.612-615; memory, high]. Rutherford also records his own failed attempts at reversal (radium from emanation; polonium from alpha-bombarded lead) [read: 1913 book p.648]. The Geiger-Nuttall rule (1911-12) shows a slow alpha emitter would be extremely long-lived, so ordinary matter does not hide uranium-like alpha emission at low energy [memory, high; Gamow 1928].

Bumstead's 1906 X-ray result (lead hotter than zinc for equal absorbed X-ray fraction) is described by Rutherford as suggesting that X-rays caused atomic disintegration in lead: "suggestive ... needing more metals and different sources" [read: 1906 book p.287-288]. I could not verify the later explanation on the web (a search found only the citation, Am. J. Sci. 21, 1-24, 1906, DOI 10.2475/ajs.s4-21.121.1). The standard reading is that heavy elements produce more secondary and fluorescent radiation and photo-electrons, and the net heat depends on how much of that escapes; Barkla's 1906 work on secondary X-rays is the contemporary context [web: https://en.wikipedia.org/wiki/Henry_A._Bumstead and search summary]. I tag the "secondary radiation" explanation [memory, medium] and flag it for the Contrarian.

Decay-rate change. By 1913: "It has not so far been found possible to hasten or retard the rate of transformation ... by the physical or chemical forces available in the laboratory" and even bombardment of the emanation by its own radiation has "no observable effect" [read: 1913 book p.647-648]. Gravity: Rutherford and Compton (Nature 104, 412, 25 Dec 1919) report that Schuster suggested testing whether gravity changes the decay rate; a method was developed for comparing emanation decay over 100 days at different places; "The outbreak of the war interfered with this plan" [web: https://www.nature.com/articles/104412c0; abstract only, the body is behind a paywall, result not read]. So: the one force Rutherford identified as untested was gravity, and its test was planned and not carried out (as far as the abstract says). A modern gravitational-potential test is not found in the project record. The 1930 list (3000 C, 20,000 atmospheres, etc.) I could not verify (digest-only).

(b) Experiment. See the statements above. Modern: environment dependence of electron-capture rates, 0.2 to 1 percent [web, above]. Large pressure, temperature, electric and magnetic effects on alpha or beta decay have not been found in the 120 years since. Triggered decay is established in other forms: artificial transmutation (1919), induced radioactivity (Curie and Joliot 1934) and fission (1938) [memory, high], which realise Rutherford's 1906 hope of "disintegration of atoms by laboratory methods" through particle bombardment. In each the energy comes from the nucleus plus the projectile's kinetic energy, which is consistent with his detonator statement; but it is not a trigger of spontaneous decay.

(c) Tests. Temperature (liquid air to 1100 C and beyond), pressure, chemical state, intense radiation: tested repeatedly in 1902-13 by Rutherford's group, P. Curie, Becquerel, Bronson and others [read]. Gravity: planned, not done pre-war. Ordinary-matter radioactivity: examined by Campbell, Wood, Strutt and Rutherford, explained by impurity and potassium/rubidium. Among the testers, the Rutherford group was an interested party; Curie, Becquerel, Gates and Bronson are partly independent (Gates and Bronson worked in his laboratory).

(d) If it were true in the strong form. If decay rates could be varied at will by an outside trigger, the exponential law would have to carry an external parameter and the energy accounting would acquire a new term; the "ordinary matter transforms" form would imply continuing decay of stable nuclei with a testable energy and a testable (e.g. proton-decay) lifetime bound: proton lifetime lower limits exceed 1e34 years [memory, medium].

Verdict: Split. (i) Rutherford's 1906 "detonator" position as stated (energy internal, trigger conjectured): Plausible, untested as a general triggering of spontaneous decay (a conjecture he labelled "a matter of conjecture"); never properly tested for gravity (planned 1914, abstract only seen). (ii) "No change of decay rate by temperature, pressure, chemistry or radiation": Tested, and not supported as a way to change rates (the 1904 temperature effect was an artifact; modern environment effects are below 1 percent for electron capture). (iii) "Ordinary matter slowly transforming (alphas below the detection threshold)": Tested, not supported (impurity, potassium-40 and rubidium-87 explain the residue; Geiger-Nuttall rule); Historically superseded but instructive. (iv) Bumstead's X-ray atomic-disintegration suggestion: Tested, not supported in the stated form, with the later explanation not verified by me.

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Investigator's findings, and what I did with them

I kept every item below in the record whatever its verdict.

Absence of evidence (record goes quiet). The Rutherford-Compton gravity test of 1919 is the one place in this record where a test was announced and no result was found. Competing explanations: (1) the experiment was never carried out (war, then Rutherford's move to Cambridge, Compton's move to Washington University); (2) it was done and gave a null result that was not published as a paper; (3) a result is in the Compton Phil. Mag. 1920 paper cited by the Investigator but not opened. Record that decides: Compton, "Radioactivity and the gravitational field", Phil. Mag. 1920, and Cambridge MS Add.7653 notebooks. I judge (1) or (3) most likely but have no evidence for any.

Summary of verdicts