Tousey-Sinclair: Physicist review (Step 2)

Reviewer: PhD physicist. Project: Sinclair Tousey, Medical Electricity, Rontgen Rays and Radium (W. B. Saunders, 3rd ed., April 1921), plus the Investigator's 2026-10-08 findings. Date of review: 2026-10-09.

Tags: [read] taken from the project documents (deep reads, digests, extracted text; I re-read the source passages named); [web] with URL; [memory] with confidence. Where a number is my own calculation I say so. The reader is assumed to be an undergraduate self-learner, so each calculation is shown with its symbols.

0. What I read and what I did not

• Read in full: claims.md, sites.md (Leads for review), the single deep-read file (all sections listed in its headings; I read the sections bearing on claims 1-7 in full and skimmed the rest), research notes (Google Patents, Internet Archive, Google Books, Google search, PubMed, Wikipedia, NYT), and the saved Internet Archive text of the 1921 UCLA scan around printed pp.282 and 287 (research/pages/ia-1921-ucla.txt, lines 17030-17075 and 17340-17440, OCR noisy) [read].
• Source text read myself (extracted PDF text): the diabetes passage of the high-frequency chapter (text file lines 32575-32640, PDF p.585) [read].
• Digest only (no deep read): high-frequency chapter 544-647 except the p.585 passage, so claim 3 rests partly on digest lines. I say so in the claim.
• Nothing in research/files/ (the Investigator saved no downloads). The patent pages and IA texts are in research/pages/.
• Web checks done (7 searches): erythema dose and Holzknecht unit; focal infection theory; x-ray tube output; Leduc electrosleep. Two of them (tube output, 600 R erythema value) returned nothing I could cite, so my dose estimate in claim 1 stays [memory, low-medium] and is labelled a range, not a result.
• No source gap for the central works, but the project is one book. Everything about Tousey comes from his own text except the Investigator's finds. He compiles other workers' reports, so I judge "what the book reports" and "what Tousey himself claims" separately.

1. The mainstream view, in brief (so each verdict has a yardstick)

1. X-rays are short-wavelength electromagnetic radiation, produced when fast electrons decelerate in a target (bremsstrahlung, a continuous spectrum with a sharp maximum photon energy set by the tube voltage, the Duane-Hunt limit) plus characteristic lines [memory, high]. Röntgen found them in November 1895 (8 Nov; publication 28 Dec) [memory, high].
2. Biological damage from x-rays is set by the absorbed dose in tissue (energy per kilogram, unit gray, Gy). It is not caused by the tube's electric field. This was shown experimentally by Kienböck in 1900: "X-ray-dose, not electric phenomena, was the active agent" [web: https://pubmed.ncbi.nlm.nih.gov/25012643/, abstract of Widder 2014, via the Investigator].
3. Nerves and muscle are excited by ionic currents that change the membrane voltage; the resting voltage is a diffusion (Nernst) potential. Current in tissue is ionic, and its main bulk effect at higher frequency is Joule heating [memory, high].
4. Radiation dose in the 1900s was measured with colour-change pastilles (Holzknecht "H", Sabouraud-Noiré Tint B). Observers disagreed by up to a factor of about 4 on what a "full erythema dose" was [web: summary of RSNA papers, search result above, e.g. https://pubs.rsna.org/doi/full/10.1148/14.4.346; the 1:4 spread is from a 1927 paper by Martius and Grebe quoted there]. This matters for every dose in the book.

2. Claim-by-claim review

Claim 1: the "Tousey dose" never causes dermatitis; x-rays cure or control surface cancers and skin diseases, with only temporary benefit in leukaemia and little cure in pulmonary tuberculosis

What the book says [read: deep read section 1, p.1182]. The dose table row, printed in bold: spark 6 in, Benoist 7, 3 mA, 10 min, 30 mA-min, 10 in, 3 mm Al, "(5)" H and "(10)" X (parentheses as printed), "Author's dose for every kind of therapy. Never causes dermatitis. Not to be repeated inside of four to six weeks." Most of the other rows are "quoted from other writers".

a. Is the mathematics internally consistent? Partly not, in the book's own units. - The same table calls 5 H an "Erythema dose" (rows at 2, 3, 4, 6, 7, 7.5, 8 in spark) [read: p.1181-1184]. Erythema is reddening of the skin, the first stage of radiation dermatitis. On p.713 Tousey writes "5 Holzknecht units produce a mild and 7 a severe dermatitis" [read: p.713, per claims.md correction]. So by his own labels, the "Author's dose" of "(5) H" that "never causes dermatitis" is an erythema dose that produces mild dermatitis. The parentheses may mean the H figure was computed, not measured; the book does not say. The deep reader also records that the unit itself shifts: "One H measured 'at skin distance' is an erythema dose equal to four H with the pastil at one-half the distance" [read: p.1181], so an H copied from another author can be a factor of four off. - Arithmetic slips in the table (25 mA x 20 min printed as 250 mA-min; 5 H printed for both 7.5 and 20 mA-min) are noted by the deep reader and I confirm they are in the source, not repaired [read]. - Lupus case: 35 treatments of 2 minutes with 5 minutes = 1 H gives 70/5 = 14 H total, as the deep reader found [read: p.1197]. That is 14 H spread over 2.5 months (about 0.4 H per visit), a small-fraction schedule, consistent with "slightest degree of redness".

b. Consistent with established experiments? My own estimate of the dose actually delivered, shown so the reader can redo it. - Quantities: tube current I = 3 mA; time t = 10 min = 600 s; charge Q = I t = 0.003 x 600 = 1.8 C = 1800 mAs. Distance 10 in = 0.254 m. Filter 3 mm Al. Voltage: a "6-inch spark" is about 70 kV peak by his own table [read: p.1181]. - A modern diagnostic tube at about 70-80 kVp with 2.5-3 mm Al filtration gives roughly 30-50 microgray per mAs in air at 1 m [memory, medium; I tried to verify by web search and did not find a citable figure, so treat as unverified]. Scale to 0.254 m by the inverse-square law, factor (1/0.254)^2 = 15.5, so 0.47-0.78 mGy per mAs. Times 1800 mAs gives 0.84-1.4 Gy in air; adding skin backscatter (about x1.3 [memory, medium]) gives about 1.1-1.8 Gy at the skin. - Unfiltered 5-minute variant: 15 mA-min = 900 mAs. Without the 3 mm filter the output per mAs is about 2.5-3 times larger because soft photons are not removed [memory, medium], so about 1.4-2.3 Gy at the skin. - Compare: the threshold for early transient skin erythema is about 2 Gy in one exposure; main erythema about 6 Gy [memory, high]. The 1900s "full erythema dose" corresponded to several gray in modern terms [memory, low; the 600 R figure I wanted to cite could not be verified on the web, see section 0]. - Result: Tousey's dose sits at or somewhat below the modern erythema threshold, with a factor of about 2 of uncertainty either way (coil waveform with peak kV above the mean, gas tubes whose vacuum drifts so that mA no longer measures output, which he himself warns about: "If there is inverse discharge the milliamperes are dangerously misleading" [read: p.1181]). So "rarely causes visible reaction in one sitting" is physically plausible; "never" is not something his apparatus could guarantee. - Fractionation: x-ray therapy of superficial skin cancer and lupus (50-100 kV, filtered, repeated doses) is mainstream and effective; basal-cell carcinoma cure rates in later radiotherapy series were high (order 90 percent) [memory, medium]. So his "non-adherent epithelioma almost certain to be cured" is broadly in line. Leukaemia: temporary benefit, no cure by local x-ray, consistent with later experience [memory, high] and with his own "no case of permanent cure" [read: p.1213, 1215]. - Hazards he reports against his own headline: the hyperidrosis patient (about 10 H, 28 min) got blister, keratosis and fissures needing radium, and "would have preferred the disease to the after-effect" [read: p.1190-1191]; in hypertrichosis he deliberately induced an "x-ray burn"; psoriasis recurrence and slow-healing elbow [read: p.1186-1188]; and the Investigator found Tousey's own case report of x-ray keratoses on his own hands, cured by radium, Archives of Radiology and Electrotherapy 20(10):344 (1916) [web: https://academic.oup.com/bjrbir/article-pdf/20/10/344/57486712/are.1916.0084.pdf, snippet only, PDF not opened]. Warts and moles: he notes that a severe x-ray skin change "produces in some cases a tendency toward malignancy" [read: p.1191]. That is correct: radiation-induced skin cancer is established [memory, high].

c. Tested? By whom? Replicated? The book's own series are case reports with technique but mostly no counts and no controls; combined treatments (x-ray plus high-frequency plus drugs) blur what x-rays did alone [read: deep read section 13]. The lupus case is clinically diagnosed, not microscopically, and may be the same patient as the nose epithelioma (age 67, father lost the nasal ala) [read: p.1197, 1225]. Cited series by others are numbered (Pancoast 44 cases; Krause 5/6; Moskowicz and Stegmann 6/6) and are the stronger evidence, but I did not check them. Independent historical test: radiotherapy as a field converged on fractionated, filtered, dosimetered treatment, a different regimen from "massive doses" every 4-6 weeks [memory, medium].

d. If true, what would have to change? Nothing. Superficial x-ray therapy is mainstream. The only thing that would have to change is the dose statement: that a 5 H erythema-dose does not cause dermatitis.

Verdict (split). - "Never causes dermatitis" as stated in H units: Internally inconsistent (his own table and p.713 call 5 H an erythema or mild-dermatitis dose). On my independent estimate (1-2 Gy): Plausible, untested as "usually no visible burn", and never established as "never"; no follow-up cohort exists. - X-ray control of superficial skin cancer, lupus and ringworm of the scalp: Established in broad form; his specific cure counts are Never properly tested (no counts, no controls, combined treatments). - Temporary benefit in leukaemia and little cure in pulmonary tuberculosis: Established (and he states them himself).

Claim 2: x-ray dermatitis is partly a "condenser" (electrostatic) effect that contact treatment avoids; the Sinclair Tousey contact tube beats Geyser's Cornell tube; static charge may help ulcers heal

What the book says [read: p.1192, 1218, 1230-1233]. Geyser reports "about 5000 applications with the tube in contact without a burn" but has had burns when the patient was not in perfect contact; Tousey's objections are that Geyser used a small tube and small doses with no comparison at a distance; Tousey's own position: the theory "has not been proved" but "probably contains a certain element of truth". He also writes that burns happened in leukaemia treatment at the "safe" distance.

a. Mathematically consistent? The one calculation in the section is correct and instructive. In contact the anticathode is about 2.5 in from the skin, and the pastil normally sits at half the skin distance, so the skin gets one quarter of the pastil intensity at normal geometry; in contact pastil and skin are at the same place, so "Tint B" means four times the usual dose [read: p.1232]. By the inverse-square law, I proportional to 1/d^2, halving d multiplies I by 4, so he is right. This is a dose-distance effect, not an electrostatic one, and it is the plain explanation of why a "contact burn" and a "distance burn" do not compare unless the dose is stated. Tousey's own figures disagree on the anticathode distance (2.5 in vs "10 cm", about 4 in) [read: p.1232].

b. Consistent with experiment? No for the condenser theory. Kienböck's 1900 experiments attributed the skin effect to x-ray dose and not to electric phenomena [web: https://pubmed.ncbi.nlm.nih.gov/25012643/, via Investigator]. A tube's electrostatic field is real (patients feel static discharge, dust is attracted; Tousey notes both [read: p.1192]) but ionising radiation, not field, is what kills skin cells. Burns also occur at a distance if the dose is high, as Tousey says himself. Contact therapy later became a respectable technique (short-distance, low-voltage tubes) because it concentrates dose at the tumour, not because it removes a "condenser effect" [memory, medium]. - The lead-glass bulb with one window (his US1100037, filed 1911) cuts radiation from the glass wall and off-focus sources; that is sound physics and is how modern tube housings work [web: https://patents.google.com/patent/US1100037A/en via Investigator; the modern remark is [memory, high]]. - Static-charge stimulation of ulcer healing and the "cloud of atmospheric dust repelled from the tube" that may implant bacteria [read: p.1192]: no data given; the dust effect is physically possible (electrified air moves dust) and its bacteriology is untested.

c. Tested? The condenser theory was tested around 1900 (Kienböck) and not supported. The superiority of Tousey's tube over the Cornell tube was never tested head-to-head; both authors are interested parties (Tousey designed one, Geyser the other; the Cornell tube was made by the same manufacturer [read: p.1232]). Geyser's later "Tricho" hair-removal system was criticised by the AMA in 1925 and linked to keratoses and cancers in clients [web: https://en.wikipedia.org/wiki/Albert_C._Geyser, via Investigator], which bears on how much weight his 5000-application record deserves; I note it and do not treat it as refutation of the 1908 record.

d. If true? A direct electrical (non-ionising) mechanism of skin damage would require a new interaction. Nothing in physics or later dosimetry requires it.

Verdict (split). - Condenser (electrostatic) cause of x-ray dermatitis: Tested, not supported (Kienböck 1900; dose is the cause). - Tousey's tube superior to the Cornell tube: Not testable as stated in the book (no comparison; interested parties on both sides; the physics of a lead-glass shield is sound). - Static charge speeds ulcer healing: Never properly tested.

Claim 3: high-frequency currents (d'Arsonval, Oudin, Tesla), usually combined with x-ray or ultraviolet, give lasting benefit by raising metabolism, lowering raised blood pressure, and acting through ozone and ultraviolet from the glass vacuum electrode

Reading limit. Digest of PDF 544-647 with a deep read only of the opening plus goitre, impotence and neuritis; I read the diabetes passage (PDF p.585) myself. Judgements below rest on digest lines for blood pressure [read: digest .28, p.559-595].

What the book says. Blood pressure: Guilleminot, 15 cases, about 21 to 17 cm Hg after 15-20 treatments; Moutier and Challamel, 30-50 mm Hg fall at the first cage session, 5-9 cm in other reports; Delherm and Laquerrière: immediate fall "less constant or marked", permanent fall "less marked and less constant", benefit "perhaps more on nutrition and urinary elimination"; Cohn, Boedeker found no change in urinary sugar; the book says "German authors" found rises [read: digest p.559, 581-585, 595]. Diabetes, Tousey's own: "a reduction in the amount of sugar from 2700 grains (180 grams) per diem to a mere trace", with a vacuum electrode on the abdomen from an Oudin resonator and x-ray over pancreas and liver [read: PDF p.585, text file line 32625]. The book says the other cited authors "uniformly" reported general benefit "whether the sugar disappears from the urine or not" [read: same].

a. Mathematically consistent? Two items fail a unit check. - 2700 grains = 2700/15.43 g = 175 g, not 180 g (small; Tousey rounds) [my arithmetic]. - Doumer sets "each case at a field of 506,000 Gauss (Moutier's averages 400,000 Gauss)" inside the autoconduction cage [read: digest p.584]. A 506,000 gauss field is 50.6 tesla, the field of a pulsed laboratory magnet. Test: the cage is a solenoid carrying radio-frequency current, f about 300,000-600,000 Hz [read: digest p.553]. Faraday's law gives the induced electric field around a circular path of radius r: E = (omega B r)/2 with omega = 2 pi f. Take the more realistic B = 1 mT (10 gauss), f = 5 x 10^5 Hz, r = 0.15 m: omega = 3.14 x 10^6 s^-1; E = 3.14e6 x 1e-3 x 0.15 / 2 = 236 V/m. With tissue conductivity sigma = 0.5 S/m [memory, medium], the current density is j = sigma E = 118 A/m^2, and the heating per kilogram (specific absorption rate, SAR; tissue density about 1000 kg/m^3; peak value divided by 2 for the time average) is SAR = sigma E^2 / (2 rho) = 0.5 x 236^2 / 2000 = 14 W/kg [my calculation]. That is already strong whole-body heating (modern occupational limits are about 0.4 W/kg whole body [memory, medium]). If B were truly 50 T, E and SAR would be larger by 5 x 10^4 and 2.5 x 10^9, which is impossible. So "gauss" here is not the SI-equivalent gauss; it is an instrument reading (induced current in a loop and hot-wire ammeter) given a field name. I flag this as an unresolved unit slip in the sources; I could not check Doumer's original.

b. Consistent with established results? Mixed. - What is established: radio-frequency currents do not excite nerves and muscle at these frequencies. The book says so ("an electric discharge with alternations above 5000 to the second loses its power to excite muscular contraction" [read: p.744]) and also gives Boruttau's reason (membrane ions cannot follow a rapid rhythm) [read: p.292]. Modern: nerve stimulation falls off above about 10-100 kHz while heating remains [memory, high]. Deep heating by radio-frequency current (diathermy) and cutting and coagulating electrosurgery are mainstream [memory, high], and the book marks diathermy as such. - Blood pressure: general warming dilates blood vessels, so a transient fall is physically plausible; a lasting fall from a ten-minute session is not supported in this record, and the book's own most careful replication (Delherm and Laquerrière) found smaller, inconstant effects. Placebo, bed rest, diet and "hygiene" are named as confounders by the book itself [read: digest p.583-584]. High-frequency "d'Arsonvalisation" for hypertension is not part of modern medicine [memory, medium]. - "Ultraviolet from the glass vacuum electrode": the glow in an air-filled vacuum electrode is mostly nitrogen emission (lilac). Ordinary glass blocks ultraviolet below roughly 300 nm, so the germicidal short-wave UV (UVC) cannot leave the electrode; some near-UV at 337-390 nm can [memory, high for the glass cut-off, medium for the lines]. So "bactericidal ultraviolet from the electrode" is not supported by the physics; the visible and near-UV light plus local heating, ozone and nitrogen oxides are what act. The book's claim that ozone is absorbed through the skin "is a claim without data in the text" (facts.json). Ozone is a toxic oxidant; no benefit from skin exposure is established [memory, high]. - Diabetes: with no insulin (insulin was introduced in 1921-22 [memory, high]) glycosuria varied with diet; in the same passage Cohn and Boedeker, and Vinaj's cage cases, found no change in sugar, and Denoyés could not separate the effect of diet. Tousey's own is a single described outcome, no case count, no diet record. I report it as his observation; it is not corroborated by his cited peers.

c. Tested? Contemporary replication was inconsistent (above). No blinded or sham-controlled trial is described. The Investigator found a neurologist's review of the 1910 edition: "many statements are made of cures of diseases by different forms of electrical application which are not borne out by facts, but which the author quotes in good faith" and doubts on the sciatica bath and scleroderma claims [web: https://archive.org/details/paper-doi-10_1097_00000441-191107000-00023, via Investigator]. I keep it as a contemporary professional assessment.

d. If true? A lasting metabolic effect of non-excitatory radio-frequency current beyond heating would need a non-thermal biological interaction. None is established; the heating effect already exists in mainstream physics.

Verdict (split). - Radio-frequency deep heating and absence of nerve stimulation at these frequencies: Established. - Lasting lowering of blood pressure, raised metabolism, diabetic sugar fall, ataxia, goitre, impotence cures: Never properly tested (reports are uncontrolled, the one careful repeat found weaker and inconstant effects, the sources disagree). - Therapeutic action through UV from the electrode (germicidal UV through glass): Refuted by calculation in the strong form (glass absorbs the short-wave UV); skin absorption of ozone with benefit: Never properly tested. - "506,000 gauss" as a magnetic field: Internally inconsistent (units).

Claim 4: dental infection from blind abscesses causes systemic disease (endocarditis, ulcer, cancer); the permanent dental arch can be predicted from the x-ray width of the unerupted upper central incisor

What the book says [read: p.941-942, 967-973]. "The author makes a set of dental radiographs in every case of cancer, wherever located, and has always found dental infection usually more severe than in cases already universally recognized as due to that cause"; he also writes the cancer idea conditionally: "if cancer is ordinarily due to a germ". He cites Rosenow, Billings, Tracy, a "12 per cent" Minnesota figure and the Investigator-found cardiac count (endocarditis in 23 of 31 cardiac cases, Hartzell, Henrici and Leonard) [web: https://archive.org/details/roentgenographic00tousiala, p.60, via Investigator].

a. Mathematically consistent? The arch formula is: R = 2w + 0.24 in, where w is the x-ray width of one permanent upper central incisor; first molar at 1.5 R from the midline [read: page image p.972-973]. I re-derived the construction as described. If the canine distal points J and H lie where an arc of radius R from the midline point A meets the circle (chord AJ = R means a 60 degree arc, central angle at the circle centre), and C is the diametrically opposite point (AC = 2R), then angle ACJ = 30 degrees (inscribed angle is half the arc), the tangent at A is perpendicular to AC, so AE = 2R tan 30 degrees = 1.1547 R, and E-D = 2 x 1.1547 R = 2.309 R = (4/sqrt 3) R. This agrees with the deep reader's value. Example with his case (w = 0.36 in): R = 0.96 in; molar distance 1.44 in; large-circle radius 2.22 in [consistent with deep read F6]. Table errors in the source (ratio 1.30 for 33/21 should be 1.57; 1.25 for 33/25.5 should be 1.29; "7 cases" for nine children) are the book's [read]. Table 2 (radiograph width vs actual width within 0.01 in for 9 teeth in 7 children) tests only that a horizontally laid film does not magnify a tooth's width, which is reasonable geometry (object near the film plane); it does not test the arch prediction, and the only arch follow-up is one untreated child.

b. Consistent with established results? - Dental radiography of periapical abscess and cysts is mainstream [memory, high]. - Oral bacteria entering the blood can cause endocarditis in people with damaged heart valves; this part of the doctrine survived (later narrowed prophylaxis) [memory, high]. - Focal infection as a general cause of ulcer, arthritis, cancer and "insanity", and its cure by extraction, was widely accepted in the 1920s, and then abandoned as controlled follow-up failed: from 1930 researchers questioned the evidence and Reimann and Havens concluded that removing local infections to influence remote disease "must still be regarded as an experimental procedure not devoid of hazard" [web: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7845802/ and the search summary of the focal infection literature; the Reimann and Havens line is quoted in the search result, not read in the original]. Rosenow's "elective localization" (bacteria having an affinity for a given organ) is part of this lost doctrine [web: same]. - Ulcer: the cause of most peptic ulcers was later found to be the bacterium Helicobacter pylori and acid, not teeth (Marshall and Warren, 1980s; Nobel Prize 2005) [memory, high]. Cancer: no mainstream theory ascribes cancer in general to a dental abscess "germ"; associations between poor oral health and some cancers exist as epidemiology, not a germ-localisation mechanism [memory, medium]. Tousey himself concedes newborn children can have cancer and no counts are given. - Arch formula: modern orthodontics does estimate the widths of unerupted canines and premolars from incisor widths (mixed-dentition analyses such as Moyers and Tanaka-Johnston) [memory, medium], so the idea of predicting arch needs from incisor size has descendants, but not his constants, and "training" the baby teeth to a curve to guide the permanent teeth is not a current method [memory, medium; not web-checked]. He found that baby-tooth size does not predict permanent-tooth size (permanent/temporary width ratio ranging 1.16 to 1.57 in his own table [read]), which is a real and still valid observation.

c. Tested? Counts for the cardiac claim come from others (Minnesota group). The cancer statement has no cases, no controls and no blinding; the arch method was reported to dental societies from 1906 to 1915 and printed in J NY Inst Stomatology 1912 p.187 [web: Google Books snippet via Investigator]; no outcome data. A 1916 orthodontic review called Tousey's focal-infection reports "more convincing" in view of "recent developments in pathology" [web: https://archive.org/details/sim_american-journal-of-orthodontics-and-dentofacial_1916-10_2_10, via Investigator]. That is the climate of belief at the time, not a test.

d. If true? A tooth-abscess germ as the usual cancer cause would overturn current cancer biology (genetic and carcinogen causes). The focal-infection rule for ulcer would contradict H. pylori.

Verdict (split). - Dental x-ray diagnosis of root abscess and unerupted teeth: Established. - Oral infection causing endocarditis: Established in susceptible hearts; focal infection as a cause of ulcer, cancer, insanity, with extraction as cure: Historically superseded but instructive; the "dental infection in every cancer" statement: Never properly tested (no counts or controls, and mainstream cancer biology does not support it). - Arch formula: mathematically sound as a geometric construction; as a predictor of good orthodontic outcome: Never properly tested.

Claim 5: much of a radiographic plate's density comes from tissue secondary rays (about half, by the Bucky grid), x-ray intensity falls slightly faster than inverse square, doubling the coil primary cuts exposure about tenfold, and the "Tousey" unit measures x-ray, radium and light output

What the book says [read: deep read third section 2, 3, 5, 6; p.663, 818-864, 1173-1177].

a. Mathematically consistent? - Fall-off: his one numerical example (a plate corner twice as far as the centre receives 1/4) is exactly inverse square for a doubled distance, so it does not show a steeper law. The geometry of his 9-inch example does not give "almost twice as far": points 8-9 inches off-centre are 12.0-12.7 in away, ratios 1.34-1.41, as the deep reader found; I confirm sqrt(81+64) = 12.04 and sqrt(81+81) = 12.73. Including the obliquity of a flat plate (intensity at the plate falls as cos^3 of the angle for a point source) I get cos(theta) = 9/12.04 = 0.75 and 9/12.73 = 0.71, so 0.42 and 0.35 of the central value. Add the anode heel effect (x-rays leaving at a shallow angle are absorbed in the anode itself [memory, high]) and a corner value near 1/4 is believable. So the number is fine; the attribution to "faster than inverse square" is not needed. - Exposure vs primary current: the book has two rules, "doubling the primary amperage reduced the time tenfold" [read: p.821, 861] and "twice the milliamperes would require only one-half the exposure" [read: p.824]. The deep reader called them unreconciled. They are not in conflict. Rule 2 is at fixed voltage (spark) and fixed waveform. In an induction coil, raising the primary current raises both the secondary peak voltage and the tube current. His own scaling rule is output proportional to mA x (kV)^2 [read: p.741], which matches the modern approximate form (tungsten target, I V^2) [memory, high]. If doubling the primary doubles both the tube mA and the kV, output rises by 2 x 2^2 = 8, so time falls to 1/8; with the extra effect that a gas tube conducts at all only above a threshold voltage, "tenfold" (his measured t proportional to I^-3.3) is plausible. This corrects the deep reader's "unreconciled" and Step 1's presentation of the tenfold claim as uncertain. - Secondary rays and the Bucky grid: moving grids and cell screens do cut scattered radiation, at the cost of longer exposure. His grid needs twice the exposure for the same density [read: p.838-839]; that is a "grid factor" of 2, in the low range of modern values (about 2-5) [memory, high].

b. Consistent with established results? - Scattered radiation is real and large. For limbs the scatter-to-primary ratio is of order 1 (scatter about half the detected signal); for the trunk it is much higher, 3-5 or more [memory, high]. So "about one-half" is right for thin parts and an underestimate for the abdomen. Scatter lowers contrast, which is why the Bucky grid (invented 1913) and filters help. Tousey's measured numbers (cylinder test, plate half as dense inside a lead tube) are a qualitative demonstration, not a controlled measurement [read: p.838-839]. - Mechanism: he calls the tissue secondary rays "fluorescence of the body", and says they are "partly the source of our ability to make radiographs ... of the frontal sinus"; he labels this "the author's theory, not ... an established fact" [read: p.834]. At 60-90 kV the main process in tissue is Compton scattering and, below about 30 keV, photoelectric absorption; fluorescence in light elements is negligible [memory, high]. The image comes from differences in primary attenuation (a "chart of densities", which Tousey also says [read: p.701]); scatter blurs it and adds uniform fog. So his claim that scatter is part of the source of the picture of the sinus is not supported by modern imaging physics, and his own frontal-sinus observation (sound side darker than pus side) is consistent with the pus side absorbing more primary radiation. - The 1/75 gaslight comparison (x-ray 76 times less photographically effective than a gas jet at 5x distance) is a single measurement; the factor 76 needs the rounded "five times" distance (3 x 5^2 = 75; the stated 60 in/11 in gives 3 x 5.45^2 = 89) [read: deep read; I confirm 60/11 = 5.45 and 3 x 29.7 = 89]. It reflects the small fraction (about 1-2 percent for thin photographic emulsion [memory, medium]) of x-ray photons absorbed in a film emulsion, which is why intensifying screens were introduced; so the finding is physically ordinary. - The Tousey unit: "the effect on Kodak film of 1 candle-power of carbon-filament light" [web: Google Books snippets, via Investigator: Archives of the Roentgen Ray 17:427, 1913; J Florida Med Assoc 3:112, 1916]. This ties radiation output to a photographic reaction whose response depends on film type, development, photon energy and exposure time, so it cannot be a stable physical unit. His 1922 snippet "3600 units of soft x-rays will produce severe dermatitis" [web: Am J Electrotherapeutics and Radiology 1922 p.386, Google Books snippet via Investigator] could not be converted to gray. The book itself says the unit "is no longer required" with modern apparatus [read: claims.md]. The historical record: abstracted by JAMA 60:1664 (1913), and mentioned by the historian R. F. Mould [web: via Investigator]. - Assay of radium through its sealed tube (NYT, 7 Jan 1914): measuring a radium preparation by the penetrating gamma radiation from outside the sealed tube is a standard method [memory, high]; Tousey's statement that he did so for French shipments [web: https://www.nytimes.com/1914/01/07/archives/suggests-testing-tube-of-radium-strength-can-be-determined-without.html via Investigator] is physically credible, though his own unit is not the way it was later done. - x-ray efficiency: he cites Wien's "2.5/1000" of cathode-ray energy converted to x-rays [read: p.719]. The standard estimate is efficiency about 1.1 x 10^-9 Z V (V in volts, Z = target atomic number) [memory, medium]; for tungsten (Z = 74) at 70 kV that is 1.1e-9 x 74 x 7e4 = 0.0057, i.e. 0.57 percent. Wien's 0.25 percent for a soft-tube and period target is the same order and in the right range. - "Energy of a cathode particle proportional to the fourth power of its velocity" [read: p.719]: kinetic energy goes as v^2. Whiddington's law (1911) gives the penetration range of cathode rays proportional to v^4 [memory, medium]; I suspect Tousey's sentence has garbled that range law. This is a source slip, not a fresh physics claim. - X-ray nature: the book gives both the Stokes ether-pulse theory and the corpuscle theory (Bragg, Porter), leans to ether pulses, and explains crystal reflection by "smoothness" [read: p.700-702]. The 1912 crystal diffraction experiments (von Laue, Friedrich and Knipping; then the Braggs) showed wave interference from the atomic lattice [memory, high]. By 1921 the wave picture was settled. Also note "Sir Joseph Thomson (Lord Kelvin)" is a conflation of two men [read; memory, high].

c. Tested? Scatter and grids: extensively and independently (modern radiology). The distance law and the tenfold rule: no tabulated data in the book. The Tousey unit: published, used by others in 1913-1916, then dropped.

d. If true? Nothing changes. Scatter is already mainstream physics.

Verdict (split). - Large share of plate density from secondary (scattered) rays, and grid/diaphragm benefit: Established. - That tissue "fluorescence" contributes to forming the useful image: Refuted by calculation / modern attenuation physics in the strong form (it is part of the fog); as an interpretation he labels it a theory: Not testable as stated by the evidence given. - Faster-than-inverse-square fall-off: Not testable as stated (no data; his example is inverse square); doubling of primary current cuts exposure about tenfold: Plausible, untested (consistent with I V^2 scaling, as shown); no data table. - The Tousey unit: Historically superseded but instructive (a photographic unit that cannot be standardised, replaced by the roentgen and gray).

Claim 6: an x-ray coil's apparent output exceeding its input is an illusion because meters read peaks, not averages; the ideal generator is constant-potential, which Cabot and Shaw built after reading Tousey's 1910 proposal

What the book says [read: page images pp.740-741, 744-747]. "Based upon the calculation of 100,000 volts and 2 milliamperes the power generated by an x-ray coil would be 500 watts, and with 100,000 volts and 15 milliamperes ... 1500 watts ... there is apparently a greater output than intake ... Of course this would be an impossibility, and the explanation is found in the fact that the meters indicate the maximum of the successive currents rather than their average strength." Oudin: 10,000 V x 0.25 A = 2500 W against a 500 W primary.

This is not an over-unity claim. It is a measurement-artefact argument. The project stays within the mainstream.

a. Mathematically consistent? - Arithmetic: 100,000 x 0.002 = 200 W (printed 500 W); 56,000 V x 10 mA = 560 W (printed "1 horse-power or 746 watts"); the other products agree (1500 W, 3300 W = 3 1/3 kW, 2500 W). I confirm both slips; they exaggerate the apparent output [my arithmetic; deep read section 5.4]. - Physics: real power is the time average P = , which can differ greatly from V_peak x I_peak. For a pulse train of duty cycle D (fraction of time current flows) P is about D x V_peak x I_peak. His own pulse example: duty cycle 1/6, 100 kV peak, 15 mA peak gives 1500/6 = 250 W, below the 500 W input. The second, additional correction is that the spark gap reads the voltage at which air breaks down (a peak), and the voltage falls during the discharge "to less than one-half" [read: p.740]. - Oudin resonator: a worked example I add, because the peak/average argument alone is incomplete there. A resonator is a reactive circuit: voltage and current are nearly 90 degrees out of phase (it feeds a capacitive discharge), so the real power is P = V_rms I_rms cos(phi), where phi is the phase angle between them and cos(phi) is the power factor. Take V_peak = 10 kV, so V_rms = 10,000/sqrt 2 = 7071 V; hot-wire meters read rms current, I = 0.25 A. The apparent power is 7071 x 0.25 = 1768 VA. With a power factor of 0.1, which is ordinary for a high-Q resonant circuit [memory, medium], the real power is 177 W, below the 500 W primary. Tousey attributes the whole discrepancy to peak versus average; reactive power and the V-I phase are the bigger part for the Oudin case. This is a refinement, not a refutation: his conclusion (no over-unity) is right. - Scaling rule (output proportional to mA x kV^2) and the warning that a milliammeter without constant voltage is "dangerous guesswork" [read: p.741] hold up [memory, high].

b. Consistent with established results? Yes. Peak and rms readings differ for pulsed currents; reactive power is not real power; energy conservation holds. The constant-potential ideal is correct as engineering: with fluctuating kV the spectrum is mixed, the soft part is absorbed in the skin without contributing to the image (this is why filters and constant-potential sets lower skin dose) [memory, high], which is what the 1913 Tousey paper says [web: https://archive.org/details/newyorkmedicaljo9719unse, NYMJ 97:648, via Investigator]. His hope of single-wavelength x-rays from constant voltage goes too far: the electron slows in many steps, so the spectrum is continuous up to a maximum photon energy (Duane-Hunt limit; the law was found in 1915, five years after his 1910 text) [memory, high]; constant potential fixes the cutoff only. In fairness, his statement was a hope ("might very probably be able"), not a claim.

c. Tested? The conservation argument needs no test. The priority claim (that Cabot and Shaw built a direct-current high-voltage generator from his pages) rests on Tousey's own account in the book and, per the Investigator, on his 1913 paper, in which he says his part "consisted really in directing the attention of the inventor, Mr. Cabot, to the need for such an unfluctuating direct current" and that Cabot and Shaw, wireless engineers sent by "Doctor Williams of Boston", took his book on a hunting trip and found "three or four pages which suggested the present discovery" [web: NYMJ 97:648, via Investigator]. Tousey has a stake in the credit. Cabot's two 1912 patents (US1112436, US1191759) on "electric conversion" by synchronous commutation do not mention x-rays or Tousey in the text the Investigator checked; their dates (filed 1912-08-22) are after the 1910 edition, which is consistent with Tousey's account but does not show it [web: https://patents.google.com/patent/US1112436A/en, via Investigator]. The Coolidge hot-cathode tube (1913), which made constant potential practical, came separately [memory, high]. There is no second witness: "Doctor Williams of Boston" is the person who could corroborate, and the Investigator did not find him.

d. If true? Nothing. A constant-potential x-ray source is ordinary engineering.

Verdict (split). - Output greater than input is an artefact of peak-reading meters (with the added reactive-power point for the Oudin resonator): Established. - Constant-potential generator as the ideal source: Established (with the correction that it does not make x-rays monochromatic). - Cabot and Shaw built theirs from Tousey's pages: Never properly tested as history (dated first-person account, plausible chronology, no independent witness yet; interested party).

Claim 7: the body acts as a sodium-chloride electrolyte; almost all physiological effects of electricity are electrolysis and electric osmosis; medicinal ions act at the surface (deeper effect is the current itself); Leduc's interrupted current can produce electric sleep, though the book says this is unestablished in man and (like Corrado's dog-brain findings) unverified

What the book says [read: p.258, 292-297, 403-416, 534-543].

a. Mathematically consistent? Mostly standard physical chemistry with slips. Condenser formulas are correct in electrostatic CGS units but "volts" and the dielectric constant K is missing from the plate formulas [read: deep read section 1]. Electron charge 1.34e-19 C and 9e23 electrons per faraday disagree (the modern values are 1.602e-19 C and 6.02e23 per faraday: 1.602e-19 x 6.022e23 = 96,485 C, the faraday [memory, high]). Several constants in the electrochemistry section are mis-printed (oxygen equivalent, ferric iron valence, 288,000 mi/s "conduction speed" above light) [read]. The 39 m/s statement: "electricity can travel through the body at a rate not exceeding 39 meters a second" [read: p.296] conflicts with the book's own distinction on printed p.281 and fails a calculation.

Calculation for the 39 m/s statement. Ion drift speed v = mu E where mu is mobility. For sodium ion in water mu = 5.2 x 10^-8 m^2/(V s) [memory, high]; for E = 100 V/m (1 V per cm), v = 5.2e-6 m/s = 1.9 cm per hour, about 7 million times smaller than 39 m/s. Signals in a conductor do not wait for ions to drift; the electric field is re-established by charge rearrangement in the dielectric relaxation time tau = epsilon/sigma. With epsilon_r about 80 and sigma = 0.5 S/m: tau = 80 x 8.85e-12 / 0.5 = 1.4 x 10^-9 s [memory for the constants, medium for tissue]. So the field of a current in tissue is established in nanoseconds, not metres per second. Possibly Tousey is mixing this up with the speed of the nerve impulse (frog nerve about 27-30 m/s, Helmholtz 1850 [memory, medium]); that is my guess, not his text. Note also that the older ion-speed value printed (0.166 cm/h for silver at 1 V/cm [read: deep read]) is about twelve times smaller than my figure from modern mobility (Ag+ 6.4e-8 m^2/(V s) gives about 2.3 cm/h); the OCR and units there should be checked against the page image.

b. Consistent with established results? - Body as an ionic conductor with sodium and chloride as the main charge carriers: correct. Conduction in tissue at low frequency is by ions in extracellular and intracellular fluid [memory, high]. His remark that high-tension (static) and Tesla currents are harmless "because ions cannot keep up the rhythm" matches the modern explanation [read: p.292]. - "Almost all physiologic effects ... are due to electrolysis and electric osmosis" [read: p.297]: not correct as a general statement. Electrolysis happens at electrodes and with direct current (galvanic burns, Leduc's ion transport, cataphoresis are real electrochemistry). But the nerve and muscle response to current is excitation of the cell membrane (voltage-gated channels, Hodgkin and Huxley 1952), electrical burns at body surface are mainly Joule heating, and radio-frequency heating is dielectric/resistive heating [memory, high]. Tousey's pre-membrane-channel physiology is period-typical, not careless. - Membrane theory. The folder scan lacks the page; the Investigator located it in a second scan (UCLA copy, printed p.287). The passage (a quotation within Tousey's text) reads, in the saved OCR text: the tissue currents "can only be considered principally as produced by concentration cells since no metals are present ... the two electrolytes with different degrees of concentration are separated by a 'semipermeable' membrane. This allows one kind of ions to pass through it, but not the other ions, which consequently accumulate upon it (Ostwald, 1890)" [read: ia-1921-ucla.txt lines 17352-17400; OCR noisy]. It then argues the injured place is "negative" and cites Tschagowetz's calculated EMF from carbonic acid concentration, and the dispute between Oker-Blom ("concentration cell arises from the alteration in the tissue") and MacDonald and Bernstein (a difference "previously existent between the protoplasm and the enveloping fluid"). Bernstein's "pre-existence" view is the one modern physiology kept: the resting potential is set by ion gradients across a selectively permeable membrane. Worked example with the Nernst equation, E = (RT/F) ln(c_out/c_in): potassium 5 mmol/L outside, 140 mmol/L inside, T = 310 K; RT/F = (8.314 x 310)/96485 = 26.7 mV; ln(5/140) = -3.33; E = -89 mV, compared with typical resting potentials of -70 to -90 mV in nerve and muscle [memory, high]. So the concentration-cell mechanism is right; the identity of the trapped ion (his quoted source has carbonate/acid anions trapped and cations free) is not the modern one (potassium leaves through the membrane, large anions are trapped), so the details are superseded. The Investigator's finding closes the "source gap" for this passage. Electrotonus is also in the second scan (lines 17042-17075): extrapolar currents flowing "away from the portion included between the electrodes" at the cathode and toward it at the anode, which matches the passive spread of current in the nerve core (Hermann's core-conductor picture, an ancestor of cable theory [memory, medium]). - Ionic medication acts at the surface: correct and well supported by his own cited experiments: Iscovesco and Matza (permanganate "only a surface action" in gelatin; copper at about 1 cm in several hours), Tuffier and Maute (colour reactions only in the superficial epidermis), Gautrelet (ions form local combinations, do not enter the circulation) [read: p.415-416]. The Kohlrausch speeds he quotes (and my mobility figure above) explain this: a few millimetres to a couple of centimetres per hour per V/cm. Modern iontophoresis delivers small charged drugs through the skin to limited depth (pilocarpine for sweat tests, local anaesthetics) [memory, high]. Many ion-specific cures that follow (gout by lithium, rheumatism by salicylate, warts by magnesium) come with no controls and with his own doubts [read: deep read section A3]. - Electromagnets: "no discoverable effect" in the hands of "unbiased observers", with the possibility of suggestion [read: p.457]. Static and low-frequency magnetic fields at these strengths have no established therapeutic effect [memory, medium]. This is a literature statement without cited trials. - Electric sleep. The book gives Leduc's current (interruptions 90-110 per second, EMF rarely above 30 V, about 4 mA, cathode on head) and one human self-experiment: partial inhibition, 20-minute sessions, "awakening was instantaneous" [read: p.534-535]. Animals "for three or four hours at least" with no species or count [read]. Tousey says it "has not been tried in a sufficient number of cases to justify any general statements" [read: p.536]. Modern: Leduc's 1902 work is recognised as the origin of "electrosleep" and later cranial electrotherapy stimulation, but an independent 2014 review (Cochrane, depression) found insufficient evidence and a 2018 review found only low-strength evidence for anxiety and depression, none for anaesthesia [web: https://en.wikipedia.org/wiki/Cranial_electrotherapy_stimulation; I did not open the primary reviews]. Corrado's dog experiments (720-2175 V, "20 to 30" amperes as printed, death in every dog, cell changes by Nissl and Golgi methods) are reported with Tousey's own cautions that Golgi changes occur in normal material, vacuolation may be artefact, and "observations on man ... are still lacking" [read: p.537-540]. The fibrillation account of electrocution that he gives from Cunningham, Prevost and Battelli is the modern one [read: p.542; memory, high]. "Hundredths of volts" in his Prevost-Battelli line is almost certainly "hundreds" [read; the deep reader's inference].

c. Tested? Ion transport: yes, in the cited laboratory work (Salaghi, Leduc's two rabbits, Gautrelet, Iscovesco), and these are independent of Tousey. Membrane theory: tested and kept (Bernstein 1902/1912; Hodgkin and Huxley later). Electric sleep: one self-experiment, animal reports, no human series on record in the book.

d. If true? The electrolysis-only claim would require that nerve excitation and heating be electrolysis; that would contradict the Hodgkin-Huxley model and Joule heating. The electric-sleep claim, if true as a general anaesthetic, would be an addition to neurophysiology, not a contradiction.

Verdict (split). - Body as an ionic (NaCl-type) electrolyte, with membrane concentration-cell origin of tissue currents: Established. - Medicinal ions act at the surface; deeper effect is the current: Established (supported by the experiments he cites). - "Almost all physiologic effects of electricity" are electrolysis and electric osmosis: Tested, not supported in the general form (membrane excitation and Joule heating are the main mechanisms); the 39 m/s electrical signal speed: Refuted by calculation (and Internally inconsistent with his p.281 and 180,000 mi/s text). - Leduc's electric sleep in man: Never properly tested (one self-experiment in the book; modern low-current brain stimulation trials are inconclusive).

3. Investigator's findings: what I keep and how I weigh them

All Investigator findings below stay in the record whatever my verdict. Tags show source type; they were gathered by the Investigator unless noted.

4. Corrections to Step 1

1. claims.md claim 1 (and the deep read): the "Author's dose" row prints "(5) H" and "(10) X" in parentheses, and the same table labels 5 H as the "Erythema dose"; p.713 says 5 H produces mild dermatitis. Step 1 reports the claim without noting that conflict. My estimate (1-2 Gy at the skin, see claim 1) shows the dose is plausibly just under the modern erythema threshold, not clearly harmless. The claim should read "never causes dermatitis (his statement; his own table calls 5 H an erythema dose)".
2. claims.md claim 5 and the third deep-read section 2: the "tenfold per doubling of primary current" and "doubling milliamperes halves the time" rules are not in conflict (different variables held fixed; I V^2 scaling gives 8-fold for a coil whose kV and mA both double). Replace "the author does not reconcile them" with "they apply to different conditions; the tenfold figure is plausible".
3. Deep read third section 3 (fall-off): I confirm the geometry (12.0-12.7 in) and add the obliquity and heel effect that bring the corner value from 0.50-0.56 (inverse square) to about 0.35-0.42 (cos^3) and then near 1/4. The statement "Neither reaches 1/4" holds for these two factors alone; with the heel effect it is believable. The fall-off statement is not refuted, only unneeded.
4. Deep read, "fourth power of velocity": this is likely a garbled Whiddington range law (range proportional to v^4, 1911) [memory, medium], not a kinetic-energy claim. Step 1 reads it as a source slip; I support the slip reading and add the probable origin.
5. facts.json Part 11 mainstream_conflict: "Bragg crystal diffraction 1912-13, Moseley 1913" should add von Laue, Friedrich and Knipping (1912) as the first crystal diffraction of x-rays [memory, high].
6. sites.md "Leads for review", Geyser: it sets Tousey's 1911 patent filing against the Cornell tube's 1905 date as a conflict. Tousey's book dates his own contact tube to a demonstration at the New York Odontological Society on 17 Oct 1905 [read: deep read section 11, Fig. 832]. A 1911 filing date therefore postdates both tubes and does not decide priority; the 1905 dates are on both sides and both are the inventors' own accounts.
7. claims.md Source note, patents and second scan: the Investigator's corrections (patents exist; second scan exists) are right and I have used them.
8. claims.md claim 3: "diabetic sugar from 2700 grains a day to a trace" is correct to the text [read: PDF p.585, line 32625]. Add that on the same page Cohn, Boedeker and Vinaj report no change in sugar and Denoyés could not separate diet, and that the "506,000 gauss" statement in the cage section is a unit problem (see claim 3).
9. Digest .33 entry p.700 / front matter: my notes agree with the deep reader's corrections (Battelli "not affected"; 0.8 second of arc; 5 and 7 H; "Sir Joseph Thomson (Lord Kelvin)").
10. Deep read section A (ion speeds): the Kohlrausch value for silver (0.166 cm/h at 1 V/cm) should be rechecked against the page image; modern mobility gives about 2.3 cm/h (twelve times larger). The conclusion drawn (surface-only action) survives.

5. What the reader should take from this

• The strongest, still-correct physics in the book: the peak-versus-average explanation of apparent excess power (with a reactive-power refinement for the resonator), scatter and the Bucky grid, the I V^2 rule, the body as an ionic conductor with a membrane concentration cell, the surface-only action of ionic medication, and the fibrillation account of electrocution.
• The instructive failures: a dose labelled "never causes dermatitis" that is in his own units an erythema dose; an electrostatic "condenser" theory of burns that a 1900 experiment had already set aside; a photographic unit that cannot be standardised; focal infection as the cause of ulcer and cancer; and a 39 m/s signal speed that confuses ion drift with field propagation.
• Open (not settled by the record): the Cabot and Shaw priority; whether his contact tube or the Cornell tube came first; whether his lupus case and nose epithelioma are one patient; and the dental-arch method's outcomes.
• Web checks I could not complete: modern output of a 70 kVp tube per mAs; the roentgen equivalent of an H or Tint B erythema dose. My dose estimate in claim 1 is therefore a range from [memory] and should be replaced by a calculation from a published spectrum table if a verdict ever depends on it.