Tousey-Sinclair: Mathematician review (Step 2)

Reviewer: PhD mathematician. Date: 2026-10-09. Subject: Sinclair Tousey, Medical Electricity, Rontgen Rays and Radium (W. B. Saunders, 3rd ed., April 1921), the only work in the folder.

Tags: [read] from the extracted text, page images (via the deep reads) or Investigator files; [web] with URL; [memory] with confidence; [calc] my own arithmetic (SymPy/NumPy-style checks, done in the project venv).

How I worked: I read claims.md, facts.json (summaries), sites.md "Leads for review", all of deep/ (the single combined deep-read file, in the sections on dose table, radiography technique, dental method, X-ray generator, electrochemistry), and the extracted text where a number mattered (the Holzknecht passage, PDF p.1181; the Bernstein membrane passage in the second scan). I did not re-read the digest-only chapters (static and dynamic electricity, high-frequency, diathermy, radium); claim 3 therefore rests on the digest and on the deep read of its opening only. Source gap carried over: the book is a library-copy OCR; printed pp.282-283, 286-287, 290-295 were missing in the folder's scan, see "Corrections" for what the second scan supplies.

Reader note: the book is a clinical compendium, not a theory paper. Its mathematics is arithmetic (dose, power, ratios), one geometric construction (dental arch), a few borrowed physiology formulas (Weiss, Hoorweg) and many unit statements. I therefore judge (a) as "do the numbers and units hold together, and does the stated reasoning follow?".

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Claim 1. The author's x-ray dose "never causes dermatitis"; x-ray treatment cures or controls the surface cancers and skin diseases he reports

a. Mathematics. The exposure table (printed pp.1168-1171) is mostly arithmetically sound. I checked the mA x minutes products: 3 x 10 = 30, 3.5 x 10 = 35, 5 x 2 = 10, 3 x 12 = 36, 4 x 1.5 = 6, 5 x 13 = 65, 5 x 60 = 300, 5 x 70 = 350, 5 x 80 = 400 all agree [calc, from the deep-read transcription]. One exception: first row 25 mA x 20 min is 500, printed 250 (deep read agrees). The author's own dose is stated three ways (6-inch spark, 3 mA, 5 min unfiltered; 10 min through 3 mm Al; 30 mA-min in the table) and these agree with one another. Doubling the time when 3 mm of aluminium is inserted is the right order of magnitude for a broad spectrum [memory, medium; not checked on the web].

Three tensions remain. (i) The "H" unit. The text reads "Five H or an 'erythema dose'" and then "One H measured 'at skin distance' is an erythema dose equal to four H with the pastil at one-half the distance to the skin" [read: _text, PDF p.1181]. The 4:1 conversion is right for inverse square (half the distance, four times the dose). But if 5 H (half-distance pastil) is the erythema dose, the skin-distance equivalent is 1.25 H, not 1 H; the page uses "1 H" and "5 H" for the same dose. A 20 percent looseness, harmless in itself, shows the table mixes writers' units, as the author says ("most of the above x-ray dosage is quoted from other writers"). (ii) The author's row is marked "(5)" H, parenthesised, and 5 H is by his own definition the erythema dose, yet the same row says "never causes dermatitis". Both can hold only if the (5) is an estimate or if erythema is distinguished from dermatitis; the book does not reconcile this. The row "8.5-inch spark, 65 mA-min, 3 mm Al = 5 H, marked erythema" sits beside it. (iii) In the leukaemia and contact sections the same nominal pastil reading is applied at different distances; see claim 2.

Order-of-magnitude check [calc + web]. Modern filtered diagnostic tubes give roughly 0.02 to 0.035 mGy per mAs at 1 m at 70 to 80 kVp [web: https://www.rug.nl/education/courses/other-education/radiation-protection/edu/ts-mt/ts-mt-data-examen/mcts-mtfiguura?lang=en, search summary; the table's column mapping was unclear to the search tool, so treat as +/- factor 2]. The author's 10 min x 3 mA = 1800 mAs at 10 in (0.254 m) gives, with inverse square, 0.03 x 1800 x (1/0.254)^2 = about 0.84 Gy free-in-air for a 70 kV tube with no added filter, 0.43 Gy if the effective voltage were 50 kV (output scaling with V squared, which is the author's own rule on p.741), and a further factor of about 0.5 to 0.6 for 3 mm Al [memory, medium]. That is roughly 0.25 to 0.5 Gy per field, well below the roughly 2 Gy often quoted as threshold for early skin erythema [memory, medium; not verified]. A coil-driven gas tube with inverse discharge is less efficient than a modern tube, so the true figure may be lower still. So the single-session "never causes dermatitis" is numerically plausible, but this contradicts the label "(5) H = erythema dose": the arithmetic suggests his dose was far less than an erythema dose. That is a point in the book's favour for safety and against it for efficacy (a sub-erythema dose repeated only every 4 to 6 weeks).

b. Experimental consistency. Radiotherapy of superficial basal-cell and squamous skin cancers works and is accepted [memory, high]; the book's non-adherent epithelioma "almost certain to be cured" is the kind of lesion that responds. Chronic radiation injury accumulates; the Investigator's lead says Tousey himself reported "X-Ray Keratoses on Hand of Radiologist. Cured by Radium" (Arch. Radiol. Electrotherapy 20(10):344, 1916; not opened) [web: https://academic.oup.com/bjrbir/article-pdf/20/10/344/57486712/are.1916.0084.pdf, via sites.md]. That is evidence about operator dose, not patient dose, but it shows the same dermatology in the author's own hands. Tousey's own 1922 statement that "3600 units of soft x-rays will produce severe dermatitis" [web, via sites.md: Am J Electrotherapeutics and Radiology 1922 p.386] shows he knew dose, not "condenser" effects, produces dermatitis.

c. Tested? Not by controlled trial. The cases are the author's own and other writers' case reports; several of his own cases failed or were fatal and are reported in the book (claims.md, deep read section 12). The lupus case lacked microscopy, and the lupus and the nose epithelioma (both woman of 67 whose father lost a nasal ala) may be one patient counted twice [read: deep read]. No denominators.

d. If true. Nothing in mainstream radiotherapy would change; mainstream already accepts the weak form.

Verdict (split). Weak form (superficial skin cancers respond to low-kV x-rays): Established [memory, high]. Strong form ("never causes dermatitis", cure rates as reported): Never properly tested (case reports with no denominators, no controls, units mixed from several writers). Internal tension noted above (parenthesised "(5)" H against "never dermatitis"), minor, not a verdict of Internally inconsistent.

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Claim 2. X-ray dermatitis is partly a "condenser" (electrostatic) effect avoided by tube contact; the Sinclair Tousey tube is superior to the Cornell tube

a. Mathematics. Tousey's two-sided position is internally consistent: "has not been proved, but ... probably contains a certain element of truth", and "exceedingly dangerous to say that a burn cannot be produced with the tube in contact" [read: PDF p.1231]. The numbers are another matter.

Contact changes the dose a great deal. The deep read gives the anticathode only 2.5 in (printed "10 cm", about 4 in; the two disagree) from the skin in contact, against 10 in in his usual setup. Inverse square gives (10/2.5)^2 = 16 times the dose rate in contact, or (10/4)^2 = 6.25 if the 10 cm figure is right [calc]. The book itself says that in contact, pastil and skin are at the same distance, so a pastil reading "Tint B" means four times the usual 5.5 H [read: deep read section 11, p.1232]. So "5000 applications without a burn" (Geyser, as Tousey reports it) cannot be compared with distant treatment unless the doses were equal, which, as Tousey himself notes, no comparative experiment established ("no comparative experiments with the same doses", p.1230). The data cannot separate a condenser effect from a dose effect.

Can a capacitive effect produce a burn at all? Estimate [calc]: a tube end coupled to a patient by perhaps 10 pF, with the voltage swinging 70 kV in about 0.1 ms, carries i = C dV/dt = 10e-12 x 7e8 = about 7 mA. That is easily large enough to be felt (patients "pulled away", p.1230) but the heating, P = i^2 R with R about 1 kOhm for the body, is about 0.05 W, i.e. of the order of 0.07 K per minute in a few grams [calc; the 10 pF and 0.1 ms are my assumptions, stated as such]. Electrical heating cannot explain a burn; a discharge sensation is physically credible, a thermal burn from it is not.

b. Experimental consistency. The Investigator's lead: Kienböck's 1900 experiments attributed the skin effect to dose, not electric phenomena (Widder 2014, PMID 25012643) [web, via sites.md research/pubmed note]. Tousey's own admission that burns occurred "in cases in which this theory as to distance has been exclusively depended upon" (p.1218) is evidence against the condenser theory in the book itself.

c. Tested? No controlled comparison. Geyser's 5000 contact treatments are reported only through Tousey, and Geyser privately admitted "more than one burn" from imperfect contact [read: p.1230]. Both men are interested parties (Tousey designed the competing tube made by the same manufacturer; Geyser promoted contact treatment and later his Tricho hair-removal system was criticised by the AMA in 1925) [web, via sites.md: https://en.wikipedia.org/wiki/Albert_C._Geyser]. The comparison of the two tubes (durability on a Caldwell interrupter, "slight variations") is an engineering claim with no measurements.

d. If true. The strong form would require x-ray skin damage to depend on field effects of the high-voltage tube; that would overturn the dose-response picture of radiation injury. The weak form (contact lets the dose be applied with less sensation) changes nothing.

Verdict (split). Condenser theory as cause of dermatitis: Refuted by calculation in the heating sense (a few mA through the body dissipates milliwatt-to-tens-of-milliwatt, not burn levels) and Tested, not supported in the experimental sense (Kienböck 1900; the book's own burns despite distance) [calc; web]. Tousey's weaker "element of truth": Not testable as stated. Superiority of his tube over the Cornell tube: Never properly tested (interested-party engineering assertion).

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Claim 3. High-frequency currents, usually combined with x-ray or ultraviolet light, produce lasting clinical benefit

a. Mathematics. Digest-only for the chapters on d'Arsonval, Oudin and Tesla currents; I can check only the supporting arithmetic that reached the deep reads. The ozone production rule "as the square of the difference in potential" (Chany) is a quoted empirical law; the table was read only in part. The book quotes "oscillations at the rate of about 500,000 a second" for Leyden-jar discharge [read: deep read]. Tesla-current harmlessness is explained, via Boruttau, by the membrane being unable to follow rapid rhythm; this is the right idea (membrane charging time versus frequency) and the deep read notes the thresholds of order 10 to 100 kHz [memory, high]. Note a mathematical gap that the book does not address: heating, which does not vanish at high frequency, is dismissed with the stimulation argument.

b. Experimental consistency. The book itself records disagreement over blood pressure (Moutier's fall against German authors' rise). Almost every cure is a combination of x-ray and high-frequency, so the share of each cannot be separated (claims.md). The AJMS review of July 1911 on the 1910 edition says many electrotherapy cures are "not borne out by facts" though quoted "in good faith", and doubts the sciatica bath and scleroderma claims [web, via sites.md: https://archive.org/details/paper-doi-10_1097_00000441-191107000-00023]. That is a contemporary neurologist's criticism and stays in the record.

c. Tested? No controlled trial. Single reports with large effects (diabetic sugar from 2700 grains a day to a trace) are stated without the accompanying diet or insulin-era controls (insulin only arrived in 1921-22 [memory, high]).

d. If true. Mainstream would need a non-thermal mechanism for HF currents on metabolism and blood pressure; diathermy's heating effects are accepted, other effects are not.

Verdict. Never properly tested (confounded by combined therapy; digest-level reading, so low confidence).

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Claim 4. Dental infection causes systemic disease; the permanent dental arch is predictable from the x-ray width of the unerupted upper central incisor

a. Mathematics, formula. The construction is internally well defined. I verified the geometry [calc]. With w the central-incisor width and R = 2w + 0.24 in the radius of the circle through the six upper front teeth, A the midline point and C the point diametrically opposite (AC = 2R): the canine distal points J and H are found by swinging an arc of radius R from A, so chords AJ = AH = R, i.e. 60 degrees either side of A on the circle. The inscribed angle at C subtending arc AJ is 30 degrees, so the line CJ meets the tangent at A at distance AC tan 30 degrees = 2R/sqrt 3 = 1.155 R from A, and the segment ED on that tangent is 2.309 R. This reproduces the deep reader's "ED = 4R/sqrt 3 = 2.309 R" exactly, and the "equilateral triangle AFG" reading holds if F and G are two hexagon steps (120 degrees) from A. The first molar distance is 1.5 R. Worked case: Sissie R., w = 0.36 in gives R = 0.96, 1.5R = 1.44, ED = 2.22 in [calc, agreeing with the deep read].

Plausibility against anatomy [calc + web]. The six teeth span 120 degrees, so the front-six arc length is 2piR/3 = 2.094 R = 4.19 w + 0.50 in. Published mesiodistal widths of maxillary teeth: central about 8.7 mm, lateral about 7.0 mm, canine about 7.8 mm (contact-point to contact-point) [web: https://search.bvsalud.org/gim/resource/en/emr-109906, via search result; individual study, +/- 0.5 mm]. Six teeth: 2 x (8.7 + 7.0 + 7.8) = 47 mm = 1.85 in. With w = 8.7 mm = 0.343 in the formula gives an arc of 1.94 in, within 5 percent. For small w (0.30 in) the formula gives 1.76 in; for large w (0.40 in) 2.18 in. Because six teeth that scale in proportion would have arc about 5.4 w with no constant, while the formula's slope is 4.19 w plus 0.50, the constant 0.24 in effectively flattens the dependence on w. So the formula is a sensible first-order fit near a typical tooth width but its constants (0.24, 1.5) are not derived ("a modification of Hawley's and Bonwill's tables", not shown) [read: deep read F6].

Error propagation [calc]: each 0.01 in of w changes R by 0.02 in, molar distance by 0.03 in, ED by 0.046 in. His radiographic width agrees with the later erupted width within 0.01 in in 9 teeth of 7 children (mean difference 0.33 hundredths of an inch) [read: deep read table 2], so measurement error is small compared with variation between children. His own Table 1 has arithmetic slips: Cecelia L. 33/21 = 1.57 (printed 1.30), Margaret F. 33/25.5 = 1.29 (printed 1.25); "7 cases" but 9 children; and the permanent to temporary ratio runs 1.16 to 1.57 (upper) and 1.28 to 2.09 (lower), which he describes as varying "30 per cent" [calc, agrees with deep read]. The central claim, that regulating the temporary arch to the computed radius guides the permanent teeth, has no tabulated outcomes; the only follow-up is the untreated case whose permanent arch reproduced the narrow temporary curve.

Mathematics, focal infection statement. "Always found dental infection in every case of cancer" has no count and no control; with a very high prevalence of dental pathology in adults [memory, medium], an "always" is expected by chance and proves nothing. Not a computation, a base-rate point.

b. Experimental consistency. Focal infection theory (Rosenow, Billings, quoted at length in the book) was influential in 1910 to 1940 and declined; modern evidence supports associations between periodontal disease and some cardiovascular conditions, but not the sweeping claim that tooth removal cures systemic disease [memory, medium; not web-checked, pertinent to physicist]. The cancer link is not accepted.

c. Tested? The Investigator found contemporary acceptance: Int J Orthodontia 2(10):628-629 (Oct 1916) reviewed the Hoeber book as "from one of such eminence as Dr. Tousey"; recent pathology made his reports "more convincing", and Tousey cites Hartzell, Henrici and Leonard's counts (endocarditis in 23 of 31 cardiac cases) [web, via sites.md: IA sim_american-journal-of-orthodontics-and-dentofacial_1916-10_2_10]. That is contemporary endorsement, not a replication. The arch method was presented in 1906 (NY Institute of Stomatology), published J NY Inst Stomatology 1912 p.187, and read to the Angle School graduates in 1914 and the Harvard Odontological Society in 1915 [web, via sites.md]. No replication found.

d. If true. Focal-infection strong form: would require mainstream to accept that tooth foci are a principal cause of cancer; arch formula: nothing would change, orthodontics would gain a one-parameter predictor.

Verdict (split). Arch formula: Plausible, untested (geometry consistent, magnitude near anatomical widths, constants undemonstrated, no outcomes). Focal infection causing endocarditis, ulcer, cancer in the strong sense: Historically superseded but instructive (strong form); the cancer statement as given: Not testable as stated (no counts).

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Claim 5. Half of a radiographic plate's density comes from tissue secondary rays; fall-off slightly faster than inverse square; doubling primary current cuts exposure about tenfold; the "Tousey" unit

a. Mathematics. Four statements, taken separately.

(i) Secondary rays about one half. Evidence: with the Bucky grid exposure must be twice as long, and a lead cylinder (2 in diameter, 3 in long) held on the abdomen makes the plate "only half as dense inside the cylinder" [read: p.838-839]. The cylinder experiment bears the inference directly (the shielded plate sees fewer scattered rays; half the density comes from rays that do not come straight from the tube), assuming the cylinder walls absorb the oblique scatter. The doubling-of-exposure inference is weaker: a grid also absorbs some primary radiation (the modern "Bucky factor" bundles both losses) [memory, high], so a factor of 2 is an upper bound on the scatter fraction, not a proof of it. Modern values of the scatter share in thick abdomen at 70 to 90 kV are at or above one half, so the order of magnitude is right [memory, medium]. His mechanism, "fluorescence of the body" with "comparatively little penetration", labelled "the author's theory, not ... an established fact", is in modern terms mostly Compton scatter [memory, high]; the numerical claim stands independent of the mechanism.

(ii) Fall-off. The text says x-ray action "diminishes rather more rapidly than the square of the distance" and then gives an example whose number is exactly inverse square (twice the distance, one quarter). My check of his 9-inch plate example [calc]: a point 8 to 9 in off-centre is sqrt(81 + 64) = 12.0 to sqrt(81 + 81) = 12.7 in from the source, ratio 1.34 to 1.41, not "almost twice". Inverse square then gives 0.56 to 0.50; adding obliquity on a flat plate (cos^3) gives about 0.36 to 0.35. Neither is "a quarter". So the numerical example is wrong in geometry, and he applies inverse square elsewhere (the 76:1 gas-light comparison: 3 x 5^2 = 75; with his stated 60 in against 11 in, 3 x (60/11)^2 = 89, so 76 holds only with the rounded "five times" [calc, agrees with deep read]). Steeper-than-inverse-square is physically plausible for soft rays (air absorption of the soft component over 10 to 30 in) but he gives no data. So this sub-claim is Not testable as stated in his words and wrong in its worked example.

(iii) Tenfold. "Doubling the amperage of the primary current has reduced the time required ... tenfold" means exposure time proportional to I^(-3.32) (log 10 / log 2) [calc]. The deep read sets this against the linear rule "doubling tube mA halves the time" (p.824) and calls them unreconciled. I reconcile them with the author's own scaling rule on p.741: x-ray intensity varies with the milliamperage and the square of the voltage. In an induction coil the break voltage rises roughly with the primary current (stored energy L I^2/2, voltage about L dI/dt), and tube current rises with voltage, so the output scales roughly as I_tube x V^2 about I^3 when both rise with primary current; doubling the primary then gives about 8 times, close to his ten [reasoning; [memory, medium] for the coil behaviour; not derived in the book]. The two statements are about different variables (primary current of the coil vs. tube current at fixed voltage) and need not conflict.

(iv) The Tousey unit (effect on Kodak film of one candle-power carbon-filament light) is a defined operational unit: self-consistent but not transferable (depends on film batch, development). The author himself writes it "is no longer required" with modern apparatus. The Investigator found the unit abstracted in JAMA 60:1664 (1913), restated in J Florida Med Assoc 3:112 (1916), and noted by the historian R. F. Mould [web, via sites.md: research/2026-10-08-google-books.md], so it had some currency.

b. Experimental consistency. Scatter and grids are established radiology [memory, high]. The inverse-square law for a small source in vacuum is exact; the claim of a faster fall is plausible only through air attenuation.

c. Tested? The Bucky and lead-cylinder demonstrations are his own, with qualitative description. Not replicated in the record I have.

d. If true. Nothing. The steeper-than-inverse-square claim, if true beyond attenuation, would need a new law of propagation.

Verdict (split). Secondary rays carry about half the plate density: Established (scatter) with the quantitative figure Plausible, untested as measured by Tousey. Faster-than-inverse-square: Not testable as stated (no data; worked example is inverse square and its geometry is wrong). Tenfold per doubling: Plausible, untested (consistent with intensity proportional to I V^2 under a coil-physics assumption). Tousey unit: Historically superseded but instructive.

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Claim 6. Apparent output exceeding input in an x-ray coil is an illusion of peak-reading meters; the ideal generator is constant potential, which Cabot and Shaw built after reading Tousey

a. Mathematics. The numbers: 100 kV x 15 mA = 1500 W (correct), against a 500 W primary; Oudin 10 kV x 0.25 A = 2500 W (correct). Two products are wrong in the text: 100 kV x 2 mA is 200 W (printed 500); 56 kV x 10 mA is 560 W (printed "approximately 1 horse-power or 746 W", 33 percent high) [calc, agrees with deep read]. Both errors inflate the apparent power. Tousey is explicit that output above input "would be an impossibility".

I correct the explanation in the deep read (section 5.4), which says both factors are peak-like and the true power is about D x V_peak x I_peak. In an ordinary milliammeter (moving-coil) the reading is the time average of current, not its peak [memory, high]. Then the problem is not a peak current but a peak voltage: a spark gap measures the breakdown (peak) voltage, and the voltage across the tube during conduction is lower, indeed his own p.740 measurement says the voltage drops "to less than one-half" during the spark. With I_avg read correctly, the true power is P = (1/T) integral of v i dt, which is at most V_peak x I_avg and less when v falls below peak while current flows. So the overstatement arises from V_peak x I_avg, a factor that can reach 2 or more by his own measurement [calc]. Tousey's sentence ("the meters indicate the maximum ... rather than the average") is right for the voltage reading and wrong for the milliammeter if it is a moving-coil type; a hot-wire or other meter would have its own response. Either way the conclusion (no over-unity) stands; the explanation is incomplete. Further, a primary of 500 W cannot deliver more than 500 W, and one need only assume coil efficiency below 100 percent: at 15 mA and an effective mean tube voltage of 30 kV the delivered power is 450 W, which fits [calc, assumed numbers].

Also note a table inconsistency: the book gives 6-inch spark = 70 kV (p.740 transformer table) but uses "100 kV" in the paradox; 100 kV corresponds to about a 9-inch spark in the author's own equivalence table (p.1181) [read: deep read]. Different pages, different conventions.

The scaling statement "x-ray intensity varies with mA and with the square of the voltage" matches the modern rough rule for a tungsten target [memory, high].

b. Experimental consistency. Energy conservation is respected; the paradox is a classic measurement artefact. The constant-potential ideal: modern generators approach it, and the tube voltage fixes the maximum photon energy (Duane-Hunt) but still gives a continuous spectrum, so Tousey's hope of "all of the same wave-length" from constant voltage alone goes beyond what constant potential achieves [memory, high].

c. Tested / priority. The Cabot-Shaw claim rests on Tousey's text ("These pages were read by Messrs. Sewall Cabot and Joseph T. Shaw ... after some years of experimentation and many consultations with the author"). The Investigator found a dated 1913 statement by Tousey himself, NY Medical Journal 97:648-649 (29 March 1913), "An Improved X Ray Generator": directing Cabot and Shaw to an "unfluctuating direct current" of 10 to 100 kV; he names "Doctor Williams, of Boston" as the person who first sent Cabot and Shaw to x-rays [web, via sites.md: https://archive.org/details/newyorkmedicaljo9719unse]. Cabot's own 1912 converter patents (US1112436, US1191759) do not mention Tousey [web, via sites.md]. This is documented in one published source from the claimant himself, with a third party named; no independent corroboration found yet, and the patents' silence is not contradiction (patents seldom credit consultants).

d. If true. Nothing in physics; the priority is a matter of credit.

Verdict (split). No-over-unity statement: Established (energy conservation; my correction of the mechanism above). Constant potential is the ideal x-ray generator: Established in broad form (modern practice), with the single-wavelength hope Plausible, untested as stated and in fact not achieved by constant voltage alone. Tousey's priority: Never properly tested (self-reported, 1913 and 1921, no independent source).

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Claim 7. The body acts as a sodium-chloride electrolyte, so almost all physiological effects of electricity are electrolysis and electric osmosis; ionic medication acts at the surface; Leduc interrupted currents produce electric sleep

a. Mathematics. This is where I find the internal inconsistencies.

(i) Speed. The book says the body "conducts only by electrolysis and not at all by the sort of conduction ... characteristic of metals. This would mean that electricity can travel through the body at a rate not exceeding 39 meters a second, instead of ... 180,000 miles a second" [read: deep read, p.296]. Two pages earlier it says the "velocity at which the current flows, possibly 180,000 miles a second, will not be materially altered ..." and elsewhere "288,000 miles a second" for metals, which exceeds light (186,000 mi/s) [read: deep read p.261]. The 39 m/s has no derivation in the pages I have. What is physically true: ions drift slowly. For Na+ in water the mobility is 5.19e-8 m^2/(V s) [web: https://en.wikipedia.org/wiki/Electrical_mobility], so in a field of 100 V/m the drift speed is 5.2e-6 m/s [calc]; 39 m/s would need about 7.5e8 V/m [calc]. So the 39 m/s cannot be an ion drift speed under any biological field; and drift speed is anyway not signal speed. A signal in a conductor moves as the electromagnetic field, with charge relaxation time epsilon/sigma, which for saline (relative permittivity about 80, conductivity about 0.8 S/m) is about 1e-9 s [calc; conductivity [memory, medium]], so the body behaves as a conductor and fields adjust in nanoseconds. His two statements (180,000 mi/s and 39 m/s) cannot both describe the speed of electricity. The reasoning "electrolytic conduction, therefore slow" confuses the speed of ions with the speed of the disturbance, a classic error. Nerve impulses are a third thing (tens of m/s) and 39 m/s is of the right order for a nerve conduction speed [memory, medium] though the book does not say so.

(ii) "Almost all physiological effects ... due to electrolysis and electric osmosis" [read: p.297]. Test with his own stimulation formulas. The book gives Weiss's law Q = a + b t and Hoorweg's V = alpha + beta/C. These are mutually consistent: for a condenser with effective duration t = kRC, Q = CV = a + bkRC gives V = bkR + a/C, which is Hoorweg's form with alpha = bkR and beta = a [calc, agrees with deep read]. Normal threshold charge a is 0.2 to 0.5 microcoulomb (Hoorweg excitability 2 to 5 per microcoulomb; Cluzet 0.2 microcoulomb) [read: deep read]. Faraday's law: 0.2 microcoulomb corresponds to 0.2e-6 / 96,485 = 2.1e-12 gram-equivalents [calc], about 5e-11 g of sodium: far too little chemistry to be the cause of a muscle twitch, whereas the same charge changes the voltage of a nanofarad-scale membrane capacitance by hundreds of mV-scale amounts (Q/C, order 0.1 V for 2 nF) [calc, assumed capacitance]. The book's own stimulation mathematics is thus the argument against its electrolysis-only claim: the response depends on charge and duration (a charging process), in a way that is not electrolysis. Other effects he lists (burns in electrocution "doubtless due chiefly to electrolytic processes", p.292) are in modern understanding mostly Joule heating [memory, high]; he himself gives Prévost-Battelli condenser results where the lethal effect goes with joules (1/2 C V^2), not coulombs (an energy measure, not an electrolytic one) [read: deep read].

The book contains arithmetic slips in this region, noted by the deep readers and checked: "joules = microcoulombs x volts squared" (wrong; energy = (1/2) microcoulombs x volts x 1e-6); 1 J = "0.814 ft-lb" (correct 0.738) [calc]; electron charge 1.34e-19 C with 9e23 electrons per faraday (do not agree); oxygen gram-equivalent printed 1.000 (should be 8; the book's own electrochemical equivalent implies 8); "7 cases" for 9 children (claim 4); X-ray energy "proportional to the fourth power of velocity" (kinetic energy goes as v^2). I found nothing here to change the verdicts; each is a slip, not a consistent alternative system. The Weiss/Hoorweg notation reuses alpha and beta with two meanings; Hoorweg's law as printed ("E = a i e^(-beta t)") is a fragment [read: deep read].

(iii) Ionic medication. "Medicinal ions act chiefly at the surface" is consistent with the cataphoresis observations he cites (Tuffier and Maute; Latteux and Zimmern: copper "never in the deeper tissues") and with simple mobility estimates: drift speeds of order 1e-6 to 1e-5 m/s in 100 V/m fields cover only millimetres in an hour [calc]. His electrode limit of 1/2 mA/cm^2 (OCR "4 mA") is consistent with galvanic burn prevention [read: page images, via deep read].

b. Experimental consistency. Membrane theory: this is Bernstein's 1902 hypothesis; a K+ selective membrane acts as a concentration cell with the Nernst potential E = (RT/zF) ln(c_out/c_in) [memory, high]. The folder's scan lacked printed pp.282-283 and 286-287; the Investigator located a second scan (IA medicalelectrici00tousiala, UCLA copy) and I read the passages: electrotonus is defined there (catelectrotonus: "flow of an electric current away from the portion included between the electrodes"; anelectrotonus the reverse, p.282 of the 1921 edition) and the concentration-cell passage quotes Boruttau at length: "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 17042 onward and 17352-17430, OCR]. Tschagowetz is said to have calculated the electromotive force from the probable carbonic-acid concentration "and found an electromotive force corresponding quite closely with the observed" value; no formula is printed; the book says "Not much can be said here about the mathematic calculations" [read]. So no Nernst equation appears and the membrane account is qualitative. The qualitative picture (selective membrane, injured region negative) is what modern physiology kept.

Electric sleep (Leduc) rests on the author's own hedging: unestablished in man; one human self-experiment is the only human evidence [read: deep read]; Corrado's dog-brain findings unverified. Not tested in a controlled trial in the book.

c. Tested? The ion-migration experiments (Salaghi: 12 mA for 24 h; Leduc's ion transport) are laboratory demonstrations of electrolytic transport, not tests of "almost all effects". Electric sleep: Leduc and a few followers; no replication in the record.

d. If true. Electrolysis-only would need stimulation thresholds to scale with charge by Faraday's law; the book's own data (Weiss, Hoorweg, Lapicque cited) show strength-duration behaviour, so physiology would have to drop the membrane-capacitance picture. Not required.

Verdict (split). "Almost all physiological effects of electricity are electrolysis and electric osmosis": Refuted by calculation (Faraday's law on his own threshold charges; Joule heating; his own Prévost-Battelli energy law). The 39 m/s conduction statement: Internally inconsistent (against 180,000 mi/s on the preceding pages and 288,000 mi/s; and a conflation of ion drift with signal speed). Ionic medication acts chiefly at the surface: Plausible, untested (consistent with mobility estimates; the book hedges). Electric sleep/anaesthesia by interrupted current in man: Never properly tested. Membrane (concentration-cell) account of animal electricity: Historically superseded but instructive (it survived as the Bernstein/Nernst resting-potential picture).

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Corrections to Step 1

1. deep read, section 5.4 (claim 6 explanation). It says "both factors in his V x I are peak-like" and that true power is about D x V_peak x I_peak, citing an example of 250 W for a 1/6 duty cycle. A moving-coil milliammeter reads the average current [memory, high], so the current factor is not inflated; the inflation comes from using the peak (spark-gap) voltage while the tube sits at lower voltage during conduction (the book's own p.740 says "less than one-half the voltage during the passage of the spark"). The conclusion (no over-unity) stands; the 1/D factor applies only if the meter reads peak current. Not a fatal error; update the explanation before the primer uses it.
2. deep read, section 3 and 9 (claim 5), "two time-current rules ... the author does not reconcile them". They are different variables (coil primary current vs tube mA at fixed voltage); with the book's own rule (output proportional to mA x V^2, p.741) and a coil in which both voltage and tube current rise with primary current, an exponent near 3 results, and doubling gives about 8, near the quoted 10. The statements are compatible. Claims.md claim 5 should not present them as in conflict.
3. claims.md, claim 1 ("5 H" for the author's dose). The table prints the 5 H as "(5)" in parentheses (deep read) and the same row says "never causes dermatitis", while the text defines 5 H as the erythema dose. Claims.md states "about 5 H" without noting this. Add: parenthesised value; unreconciled with "never causes dermatitis". My order-of-magnitude dose (0.25 to 0.5 Gy per field) suggests the true dose was below erythema level.
4. claims.md, Source note on the missing pages and sites.md "Corrections": I confirm the Investigator's point. The second scan (research/pages/ia-1921-ucla.txt) does contain electrotonus (line 17042 onward) and the concentration-cell passage (lines 17352-17430), so claim 7's membrane account no longer rests on a gap in my review. The passage is qualitative (Boruttau, Ostwald 1890, Tschagowetz's calculated EMF "corresponding quite closely"), with no printed Nernst equation. A deep read of those pages for a Hoorweg/Cremer cable-model formula could still be ordered; I did not find one.
5. claims.md, claim 6 ("no second source"). Agree with the Investigator: add the 1913 NY Medical Journal statement as a lead. It is Tousey's own account, not independent corroboration.
6. claims.md, Source note ("The folder contains no patent"). Agree with the Investigator: Tousey held seven US x-ray and film-carrier patents (the first, US1100037, filed 1911-02-23, granted 1914-06-16) and probable Canadian and French family members, plus firearm-aiming and fire-control patents filed 1917 [web, via sites.md: research/2026-10-08-google-patents.md]. I did not read the patents myself; the Investigator's saved files are in research/pages/gp-*.html.
7. Claims.md, claim 6, "100 kV x 2 mA". Confirmed (200 W, not 500 W) and also confirmed 56 kV x 10 mA = 560 W. I add that the 100 kV figure itself disagrees with the 6-inch-spark = 70 kV table in the book.
8. Deep read, section 3 (claim 5), "9-inch plate example". Confirmed, with the added observation that the obliquity-corrected value is about 0.35; none of the cases yields 1/4 unless the distance is twice the central distance.
9. Hoorweg/Weiss. The deep reader's derivation (Hoorweg V = alpha + beta/C is Weiss's law for condenser pulses) is correct; I checked it independently. The summary in claims.md claim 7 should say that the book's own threshold-charge numbers are an argument against "electrolysis only".

Investigator findings kept in the record (whatever the verdict)

• Patents: US1100037 (x-ray tube, lead-glass wall opaque to primary and secondary rays, window for direct rays only), US1372110 (radiating cellular diaphragm, filed 1919), US1535359 (compensating filter, 1920), film-carrier patents US1370858, US1510424, US1527938, US1517767 citing his 1915 edition; bear on claims 2, 4, 5. [web, via sites.md]
• Second scan of the 1921 edition, 1910 and 1915 editions, and Roentgenographic Diagnosis of Dental Infection in Systemic Diseases (Hoeber, 1916) on the Internet Archive. [web: https://archive.org/details/medicalelectrici00tousiala; https://archive.org/details/roentgenographic00tousiala]
• NYMJ 97:648 (1913) generator account; Archives of the Roentgen Ray 17:427 (1913) unit paper; Medical Record 64:628 (1903) beaker interrupter; Kienböck 1900 (Widder 2014); Geyser and the Cornell tube; AJMS 1911 and Int J Orthodontia 1916 reviews; archives (New-York Historical Society typescript on protection in radiography; UPenn Dental Library Hellman reprints). [web, via sites.md]
• Life and record: born 1864, Columbia P&S 1888 (one snippet; second source wanted); active to 1937; late fiction (Twin Strangers 1934, Love's Little Hour 1935). The record does not go dark; the Investigator warns of name confusion with the publisher Sinclair Tousey (1815/1818-1887) and with a Sinclair Tousey found dead in Yonkers in 1915. [web, via sites.md]
• Wartime fire-control patents (1917): no mathematical content was provided to me; not assessed.

Web verification log (budget 6; used 3)

• Mesiodistal widths of maxillary anterior teeth (8.7/7.0/7.8 mm): [web: https://search.bvsalud.org/gim/resource/en/emr-109906], one study, via search summary; the Wheeler table itself was not reproduced online by the search. Medium confidence.
• Tube output 0.02 to 0.035 mGy/mAs at 1 m, 70 to 80 kVp: [web: https://www.rug.nl/education/courses/other-education/radiation-protection/edu/ts-mt/ts-mt-data-examen/mcts-mtfiguura?lang=en] via search summary; the filtration mapping was unclear. Used only for an order-of-magnitude estimate.
• Na+ mobility 5.19e-8 m^2/(V s): [web: https://en.wikipedia.org/wiki/Electrical_mobility].
• Not web-checked (marked [memory]): the 2 Gy erythema threshold; focal-infection history; moving-coil meter reading average current; Bucky factor; the Duane-Hunt limit; insulin 1921-22; Bernstein 1902 and the Nernst form.

Summary table