Arbiter (Step 3): Charles Proteus Steinmetz, project "Steinmentz-Charles"

Inputs weighed: claims.md, physicist.md, mathematician.md, contrarian.md, facts.json, deep/ reads, sites.md and research/ notes. Tags: [read] project documents; [web] with URL; [memory] with confidence; [calc] my own arithmetic (project venv). Source honesty rules apply: the Investigator's finds and every reviewer's caveat stay in the record beside the verdicts.

Source gap (repeated): none for text. All three books have an OCR text layer, but only parts were deep-read (Discharges pp.111-150; Alternating-Current pp.179-215; Transient pp.318-397, 486-545, 704-739). The rest rests on digests. The 1923 paper (Trans. AIEE 42:470) and the 1914 paper (Proc. AIEE 33) were seen only as abstracts, and the Schenectady notebooks not at all: so the claim that Steinmetz's final account of the arc is the negative-resistance one rests on the 1917 book (read by the Mathematician and the Contrarian in OCR) plus a 1923 abstract. The folder holds no measurement by Steinmetz beyond oscillograms described in the text, and no critic or replicator. [read]

Overall picture

Steinmetz was an insider (GE chief consulting engineer, AIEE fellow), not a suppressed outsider. The record of his arc and surge work is continuous from 1898 to his death in 1923 [web: sites.md; Contrarian section 0]. Most of the books is standard, correct engineering. The learning value is in three places: (1) the 1914 explanation of arc energy supply, which he later corrected himself; (2) two worked numerical examples that do not close (lightning chain, radiation resistance); (3) a cloud model that mainstream lightning physics does not use. All three reviewers agree on this shape; the disagreements are about wording of verdicts and a few numbers, resolved below.

Numbers recomputed where reviewers differed

A. Lightning chain, Transient book Sec. 47 (Claim 5). Physicist: with printed alpha, beta the gap voltage is "roughly constant near 2.4 kV" so 300 x 2.4 / 30 gives 24:1. Mathematician: with printed alpha, beta the sum is 19.4, not 24; Steinmetz multiplied 300 by the mean of two end values. [calc, grounded 300-element chain, constants L = 2e-8 H, C0 = 1e-13 F, C = 4e-11 F, r = 1 ohm, g = 4e-6 mho, f = 1e8 Hz, e0 = 30 kV] - Z = 1 - 27.22j ohm, Y = 4e-6 + 62.83e-6j mho, sqrt(ZY) = 0.0414 - 0.00056j per element. Constants give pure attenuation (series arm net capacitive; series resonance 178 MHz), gap-voltage sum = 1.46 x e0 (44 kV). - With the printed alpha = 0.0021, beta = 0.0412: gap voltage runs from 3,042 V at the end to 212 V minimum (not constant), sum = 19.3 x e0. The Mathematician is right; the Physicist's "about 2.4 kV constant" was a loose reading, and the 24:1 comes from averaging two end values. The printed pair is the real and imaginary parts of the constants' result exchanged. A propagating regime exists for other constants (Mathematician 28.8 x at 178 MHz; Contrarian about 11 x at 250 MHz), so the effect is parameter-dependent, not impossible.

B. Radiation resistance (Claim 7). - Single wire, no return: r2 = 2 pi^2 l f 1e-9 ohm gives 0.197 ohm per metre at 100 kHz [read: page image PDF p.462, eq. 10; calc 0.1974]. This equals omega mu0 / 4, the standard result for an infinite wire carrying a uniform current [calc; memory: high]. The Contrarian is right that the number is exact for its idealisation. The Physicist is right that the idealisation is not a real 1 m wire: uniform-current short element 80 pi^2 (l/lambda)^2 = 8.8e-5 ohm [calc]; a centre-fed short dipole with triangular current is 197 (l/lambda)^2 = 2.2e-5 ohm [web: https://en.wikipedia.org/wiki/Dipole_antenna]. So the physicist's "about 9e-5" is the uniform-current element; the usual dipole value is 4 times smaller. Either way the ratio is 2,000 to 9,000. - Wire with return: I read page image PDF p.467 (printed p.430): r3 = 0.8 pi^2 f^2 l' / S x 1e-6 = 263 f^2 l' 1e-18 ohm, per metre; (a) l' = 182 cm gives 0.048 f^2 1e-12 ohm, (b) l' = 1820 cm gives 0.48 f^2 1e-12 ohm. At 100 kHz, case (a) is 4.8e-4 ohm per metre = 0.48 ohm per km. The Contrarian's 0.48 ohm per km is right; the Mathematician's "per cm" labelling in correction 8 should read per metre in the table form (per cm in the chapter VIII coefficient 2.63e-18). Standard antiphase pair (quadrupole-like): omega mu0 (kd)^2/8 = 1.4e-3 ohm per km [calc], so Steinmetz's table is about 340 x too large and scales as f^2 l' where theory gives f^3 l'^2. The Contrarian's far-field integration (4.9e-4 ohm for a finite 1 km pair) widens the gap further. He says himself (printed p.430) that the no-return condition has meaning only above about 10^4 cycles. [read: page image]

C. Other arithmetic, agreed by all three and re-checked. 283 = 2/(pi u) with u = 0.00225 [calc]; short-circuit example 150,000 V (750 A x 200 ohm), printed 300,000 V; glass-plate gradients 11.4 and 45.5 kV/cm from the stated formula, printed 8.4 and 35.7 (the printed pair also fails 0.6 x 8.4 + 0.4 x 35.7 = 19.3, not 25) [calc]; corona formula lacks the 10^-5 factor in the printed A = 241 (Mathematician read the page image p.195) [web: https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/]. The glass-plate geometry on page image p.192 was not re-read by any reviewer; the conclusion (air sparks over) holds either way.

Web checks (arbiter)

• Short-dipole radiation resistance: confirmed, and corrected for the triangular-current form: https://en.wikipedia.org/wiki/Dipole_antenna (retagged from [memory: high]).
• Maxwell-Wagner-Sillars interfacial polarization is a real mechanism for charge blocked at dielectric boundaries: https://en.wikipedia.org/wiki/Dielectric_spectroscopy. The page gives no date; "Wagner 1913" stays [memory: medium] and no verdict depends on the date.
• Reviewers' own web checks (Peek formula, intracloud potentials, winding resonances, Duddell) were accepted as reported; I did not reopen them. Transformer winding resonance literature (Contrarian: tens of kHz to MHz) is from search snippets of IPST 2015 and Chalmers papers, not full reads.

Corrected claim list

1. Sustained or cumulative oscillation needs continuous power from the source, through an arc

All three: Established. Agreement complete. Energy balance; Duddell, Poulsen, arcing grounds (1923 J. AIEE discussion). Settles nothing further. Final verdict: Established.

2. The arc supplies energy by a lag ("negative energy cycle, reversed hysteresis loop", 1914)

Agreement: the arc converts DC to oscillation power through its falling characteristic (negative differential resistance): all say Established; Steinmetz states this himself in 1917 and 1923. Disagreement: what to call the 1914 wording. Physicist: Historically superseded but instructive. Mathematician: Refuted by calculation (as a sufficient mechanism). Contrarian: Not testable as stated. Which argument is stronger: the shared calculation (Physicist, Mathematician, Contrarian all reach it separately) shows that in a lagged negative-resistance model, energy per cycle is in the in-phase part, pi R/(1 + tau^2), while the Fig. 66 loop area is the quadrature part, pi R tau/(1 + tau^2); the lag lowers supply. Numerical check (R = 18.5): tau = 0 gives 58.1 energy and 0 area, tau = 1 gives 29.1 and 29.1, tau = 5 gives 2.2 and 11.2 [Mathematician calc; consistent with Physicist's and Contrarian's derivations]. So "lag supplies the energy" fails as a sufficient mechanism for a negative-resistance arc. But Steinmetz wrote no equation in 1914, openly called the mechanism "practically unknown", and a phase lag does supply energy in a different system (hunting of synchronous machines, which he also treated). "Refuted by calculation" over-reaches against a statement with no equation; "Not testable as stated" ignores that the loop was measured (Fig. 66) and that the calculation shows what it means. Superseded-by-himself is the accurate label. Splits: - Arc converts DC/low-frequency power to oscillation power via negative resistance: Established. - 1914 wording, lag loop as the energy source: Historically superseded but instructive (Steinmetz's 1917 account assigns the lag the opposite role, limiting amplitude). - "Mechanism practically unknown for circuits": accurate for his 1914 book, an overstatement for arcs (Duddell 1900); he repeats it in 1917 sec. 85. What would settle it: full texts of the 1923 paper and 1914 "Instability" paper (does 1923 contain the in-phase/quadrature analysis?), and the Schenectady notebooks (1912 "tests on titanium and carbind", possibly the Fig. 66 data, unconfirmed): do they show a measured in-phase negative resistance? A bench test: a titanium-carbon or carbon arc with an LC shunt, measuring v(t), i(t) to separate in-phase and quadrature parts.

3. Four-constant line equations, decrements u, m, s, surge impedance sqrt(L/C), distortionless r/L = g/C

All three: equations Established (re-derived by SymPy by the deep reader; Lecture IX numbers and Cunningham line z = 589.5 ohm [calc] reproduced by all). Disagreement is only about s: the Mathematician says "Plausible, untested", the Contrarian and Physicist treat it as relabelled standard physics. It is a bookkeeping split of the attenuation with no extra observable (h = s sqrt(LC)); the Scale's "Not testable as stated" fits better than "Plausible, untested" because there is nothing to test. Caveat kept: the assumption of constant r, L, g, C and no radiation term is in tension with claim 7 unless r is read as r(f). The Contrarian's point about the sqrt(z2/z1) voltage rule stands for the 1914 lecture only; the 1920 book gives the abrupt-junction factor 2 c2/(c1+c2) (QE revision, section 2). US 1,230,615 (filed 1913, granted 1917, GE) applies surge resistance (Investigator, abstract; not re-read) and shows he acted on it; it is not an independent test. Final verdict (revised by QE revision, section 2): Established (equations, surge impedance, distortionless condition, matched termination). Energy flow between sections of a compound circuit, at the rate 2sW and in the direction s gives: Established. Single-valued s and common decrement u0 from eq. 46: an approximation, exact only for matched distortionless sections (Calculated). "Energy-transfer constant" for a uniform line: Not testable as stated (vocabulary for accepted physics). What would settle it: nothing needed beyond textbook transmission-line measurement; for the patent, test data from GE.

4. Line resonance and surge effects

Agreement: f = S/4l, f1 = 7.5e9/l0 (= c/4 l0, and in print since Electrical World 27 Aug 1898, not first in the 1920 book), 283x, and the quarter-wave behaviour are Established. The 283 comes from 2/(pi u) [calc]; the printed 300,000 V is a slip for 150,000 V. Disagreement: the 10,000-100,000 cycle "danger frequencies" of transformer coils and the cure. Physicist: Never properly tested. Contrarian: Plausible, untested; supported in kind by published winding resonances from tens of kHz to MHz [web, snippets: https://www.ipstconf.org/papers/Proc_IPST2015/15IPST031.pdf]. Mathematician: Never properly tested. Weighing: both are right about different things. [Corrected by QE revision, section 3: the 1920 book does claim measurement, "experimental investigations have shown", without a reference; the original sentence read "Steinmetz cites no measurement in the 1914/1920 pages".] In 1917 he says only "frequently been observed" (sec. 101). Later literature shows that real winding resonances exist across a range that includes his low end. That makes it consistent with known physics (Plausible, untested) but there is no controlled test on record of his numbers, of arc-fed excitation at these frequencies, or of his series R-C cure. I use "Plausible, untested". The 283x gain is a single-frequency, lossless-insulation upper estimate (real corona and dielectric loss cap it) and the 60,000 kW 700-mile quarter-wave scheme was a design study not shown to be built. Final verdict (revised by QE revision, section 3): Established (resonance formulas, f1 law, surge-impedance consequences, 283x as a model result, doubling at an open end, qualitative front flattening). Plausible, untested (transformer-winding natural frequencies in 20-100 kHz, claimed in 1920 as experimentally found, reference not given; the danger argument; the series R-C cure; 700-mile quarter-wave scheme). 20-100 kHz as the line band: reproduces from his tables but its position is set by the claim 7 radiation coefficient: Refuted by calculation as a statement about real lines. Quantitative front-flattening law (G about 360/sqrt(l) V/m at 60 kV): Never properly tested. What would settle it: impulse-response (frequency-response analysis) measurement of a large power transformer winding, with and without a series R-C across the line; and the 1917 / 1912 sources for any measurements behind "frequently observed".

5. Lightning flash in clouds as discharges stepping between rain drops (series-capacity chain, 24:1)

Agreement: the printed example does not close; no cloud data are given; modern lightning physics uses a stepped leader with streamer zone, not a drop chain. Disagreements: the exact failure (resolved in A above: the printed alpha, beta give 19.3, not 24, and are the exchanged result of the listed constants, which themselves give 1.46); and the Contrarian's addition that the premise (a mile-long flash cannot need breakdown field along its whole length) is Established in modern terms. Both fine to keep together. The modern estimates of intracloud potential (tens to hundreds of MV; one study about 300 MV [web: https://pure.psu.edu/en/publications/production-of-very-high-potential-differences-by-intracloud-light/]) are of the same order as Steinmetz's "few hundred million volts", but his figure is an extrapolation from a 24:1 ratio with no cloud parameters, so the agreement of magnitude is not support for the route. Also kept: his move to laboratory impulse generators (AP, NY Herald, 3 Mar 1922: "10,000 amperes at over 100,000 volts ... a hundred-thousandth part of a second" [web: https://www.loc.gov/resource/sn83045774/1922-03-03/ed-1/?sp=6]; 10^9 W peak, at most 10 kJ [calc]) tests arresters, not the cloud model. Final verdict, split: - Premise (no single breakdown field along the whole path): Established (modern leader picture). - Printed worked example (24:1): Internally inconsistent. - The qualitative effect (sum of gap voltages above the end voltage in a propagating chain): Plausible, untested as circuit theory; it needs a net-inductive or near-resonant series arm. - Cloud mechanism (oscillatory drop-to-drop discharge): Never properly tested (offered as "probable"; not dismissed by experiment, not tested; the mainstream prefers the leader picture on observation). What would settle it: measured fast electric-field and radio signatures of intracloud flashes (VHF interferometry) for a series-chain signature; or an inexpensive calculation: redo Sec. 47 in the propagating regime with realistic drop spacing and capacitance and compare with leader data.

6. Dielectric loss and corona

Agreement: Established as empirical engineering relations (constant power factor gives loss proportional to f e^2; air about 30 kV/cm peak = 21.2 kV rms; Peek-type corona law with (f + 25)(e - e0)^2; two-layer mechanism). Printed slips: corona factor 10^-5 missing; glass-plate gradients. Disagreement: layered dielectric imitating constant power factor. Mathematician: Plausible, untested, because for equal layers the power factor peaks at 1/3 at g = sqrt(2) omega C and stays within 10% only over a factor of 2.7 in frequency; Physicist: Established as a mechanism, with Steinmetz under-rating molecular (Debye) loss. Resolution: the mechanism is real (Maxwell-Wagner-Sillars [web: https://en.wikipedia.org/wiki/Dielectric_spectroscopy]), but a two-layer model cannot give a constant power factor over decades; that needs a distribution of time constants, which the book does not discuss. Steinmetz says "over a considerable range", so he is not wrong, only limited. "Energy distance" is an untested qualitative statement in these pages, like later streamer-criterion ideas [memory: medium]. Final verdict: Established (scalings, air strength, Peek-form corona law with the missing 1e-5 supplied). Layered-dielectric mechanism: Established as a mechanism; as the explanation of wide-range constant power factor: Plausible, untested (narrow range). "True dielectric hysteresis is doubtful": Historically superseded but instructive. What would settle it: loss tangent versus frequency on a two-layer sample over 4-5 decades.

7. Radiation from finite field velocity as effective resistance (0.2 ohm per metre, sil/col functions)

Agreement: the principle is mainstream (retarded fields). The sil/col mathematics is right (sil = -Ci, col = pi/2 - Si; seven misprints). Disagreement on the number and the verdict label: Physicist: Refuted by calculation. Mathematician: Never properly tested. Contrarian: Historically superseded but instructive. Weighing with recomputation B: the single-wire figure is exactly correct for what it models (infinite wire, uniform current, no return) and the Contrarian is right not to call the arithmetic wrong; it is the application to real conductors that fails. A real 1 m wire at 100 kHz radiates roughly 1e-5 to 1e-4 ohm, thousands of times less, and the two-wire table is about 340 times too large with the wrong frequency and spacing scaling (f^2 l' against f^3 l'^2). The Mathematician's "Never properly tested" is not apt because accepted antenna theory is the test (this is a calculation question, and the Scale has a verdict for it); the Contrarian's superseded label fits Steinmetz's model of 1920, but when a reader uses the table for a real line the calculation refutes the numbers. Steinmetz himself says (printed p.430) that the no-return condition has meaning only above about 10^4 cycles. No radiation measurement is cited by him. Interested parties (kept): Eric Dollard builds on Steinmetz's field symmetry and radiation components (Journal of Borderland Research 1990; later works); Dollard and his publishers hold a stake in the reading; mainstream engineering does not accept his wider claims [memory: high]. Recorded as related work. "Steinmetz Decoded" (modern, authorship unidentified) reads Steinmetz's shift from ether to "field of energy"; Steinmetz's 1912 address calls the ether both an infinitely thin gas and a solid, a contradiction by the Investigator's note. These are pointers. Final verdict, split: - (Qualified by QE revision, section 4: the factor about 340 holds at 100 kHz for 6-ft spacing and falls with frequency and spacing; the section 69 estimate disagrees with his own table.) - Principle (finite field velocity causes radiation, appearing as effective resistance): Established. - Quantitative single-wire formula: correct for its idealisation; inapplicable to real conductors: Refuted by calculation (as a prediction for real wires; factor about 2,000 or more [calc]). - Two-wire table and f^2 l' scaling: Refuted by calculation (about 340 x too large at 100 kHz for l' = 182 cm [calc]). - Single-delay sil/col model as a model: Historically superseded but instructive. What would settle it: measure the effective resistance of a single-turn loop and of a long spaced pair at 100 kHz with a Q-meter or network analyser and compare with omega mu0 (kd)^2/8 per length; or compute the far field of a finite pair numerically.

Summary table

Absence-of-evidence analysis

The record does not go dark. Steinmetz published on the arc and cumulative oscillation continuously from 1898 through 1923, GE kept him as chief consulting engineer, later engineers cited the 1923 paper (1930 AIEE, Gilkeson 1933), and the field absorbed his arc-oscillation account [web: Investigator, sites.md]. No funded research company disappears, no device vanishes. Competing explanations for "silence" do not need weighing here. The smaller gaps that do exist, with what would decide them: - Full text of the 1914 and 1923 AIEE papers and the 1913-14 discussion (paywalled; not read by anyone in this review). - Schenectady County Historical Society notebooks (Frequency transformation by third class conductor, 23 Mar 1922; Nernst glower as oscillator; 1912 tests on titanium and carbind; 1922 air-breakdown data; Transient-book record sheets): the likeliest place to see whether he measured the arc's in-phase negative resistance, the Fig. 66 data, and whether the lightning chain was ever calculated differently. Obtaining copies is an owner action. - Whether the 60,000 kW, 700-mile quarter-wave design was ever pursued: no record found in the pages or by the Investigator; this is silence, not evidence of rejection. - Carnegie Mellon, miSci/New York Heritage, Union College items ("Brief Note Regarding Lightning", 1915), Chronicling America (34 more hits), Espacenet family of US 1,230,615: not reached.

What would settle it (summary)

1. Claim 2: the 1923 paper and notebooks; a bench arc measurement separating in-phase and quadrature response.
2. Claim 4: frequency-response measurement of a large transformer winding, with and without the series R-C.
3. Claim 5: redo Sec. 47 in the propagating regime; compare with intracloud radio signatures.
4. Claim 7: measured effective resistance of a spaced pair or loop at 100 kHz against omega mu0 (kd)^2/8 per length.
5. Claim 6: loss tangent versus frequency of a two-layer sample.

Open questions

• Did Steinmetz measure the arc's in-phase negative resistance himself, and is the Ti-C Fig. 66 from the 1912 notebook?
• What measurements stand behind "frequently been observed" for 10-100 kHz transformer oscillation (1917 sec. 101)?
• Was the 1914 "lag/hysteresis cycle" wording (Proc. AIEE Jan 1914) meant for hunting-type machine instability, where a lag in the restoring force does supply energy, and then applied loosely to arcs?
• Do the printed alpha and beta in Sec. 47 come from an earlier (propagating) set of constants that were later changed? The listed constants do not give them.
• How do the Investigator's secondary sources (Steinmetz Decoded, Dollard) read the finite-velocity radiation model against the 1920 text?

Corrections to earlier documents

1. claims.md claim 2 and facts.json (Discharges entry): add that the 1917 book (Ch. X secs. 96-99, printed pp.187-197) and the 1923 paper (abstract) give a negative-resistance account; the 1914 loop is the quadrature (reactive) signature of a lagged negative resistance and the lag lowers supply. The quote "practically unknown" stands (1914; repeated 1917 sec. 85). Agreed by all three reviewers and the Investigator. (Timeline extended by the QE revision, section 5.)
2. claims.md claim 4 and facts.json: the f1 table dates from Electrical World, 27 Aug 1898; the danger frequencies carry no measurement in 1914/1917/1920 pages.
3. claims.md claim 5: state the result, not only the flag. The listed constants give a gap-voltage sum of 1.46 x e0; the printed alpha and beta (exchanged) give 19.3 x e0, not 24; "7.86 wavelengths" should be about 1.97. Correction to my own earlier file chain: the Physicist's "about 2.4 kV, constant, giving 24" (physicist.md claim 5a) is wrong; the Mathematician's 19.4 is right (my recomputation 19.3). Physicist's other numbers (1.5, 44.7 kV) agree with mine.
4. claims.md claim 7: add that 0.2 ohm per metre is the value for an infinite uniform-current wire without return (exact, omega mu0 / 4), not for a real conductor; the two-wire table (0.48 ohm per km at 100 kHz, l' = 182 cm) is about 340 x the standard pair result.
5. physicist.md claim 7a: the "80 pi^2 (l/lambda)^2 = 8.8e-5 ohm" is for a uniform-current element; a centre-fed short dipole is 197 (l/lambda)^2 = 2.2e-5 ohm [web: https://en.wikipedia.org/wiki/Dipole_antenna]. The Physicist's statement that "the number is refuted" should carry the qualifier "for a real wire". The "dependence on the square of the spacing" statement was [memory: medium]; my recomputation confirms the (kd)^2 dependence per unit length [calc].
6. mathematician.md correction 8: the two-wire coefficient 263 f^2 l' 1e-18 is ohm per metre in the printed table (page image PDF p.467); per cm it is 2.63e-18.
7. claims.md claim 6: add that printed A = 241 lacks the 1e-5 factor [web: eepower.com URL above], and that the printed glass-plate gradients do not follow from the stated formula (11.4 and 45.5 kV/cm).
8. claims.md claim 3 and claim 7: the constant-parameter assumption and the radiation resistance are consistent only if r is read as r(f). Add the note.
9. Deep read (Transient, B6): symbolic summary "E_open = E1/u" should read E_open = (2/(pi u)) E1; the 283 is right.
10. Citation: "Instability of Electric Circuits", Proc. AIEE 33(1), Jan. 1914, pp.13-29 (IEEE); Wikipedia's pp.2005-2021 is a Transactions pagination.

QE revision (Step 4b remediation, 2026-10-08)

Inputs: qe.md (verdict MINOR); the new deep reads in deep/ (Transient: Section V pp.652-703; Section IV ch. VIII-XI pp.602-648; Section III ch. VIII-IX pp.431-482; Section I ch. VIII pp.142-157 and ch. VI pp.104-124; Section II ch. IV pp.292-316; Alternating-Current pp.379-386, 402-404). Tags as above; [calc] is my arithmetic in the project venv (numpy only; no scipy). Steps 2-4 are not redone: no central verdict reverses, but claims 3, 4 and 7 change in wording and in the split, and several statements in my first arbiter text were wrong or incomplete.

Web checks (2 of 8 used; each one retags a [memory] item the new verdicts lean on): - Surge fronts on real lines are flattened and slowed mainly by corona (extra capacitance to ground, inductance unchanged, so the crest travels slower than the toe and the front slips back): confirmed in the abstracts and snippets of the corona-simulation literature [web: https://orca.cardiff.ac.uk/107185/ (Al-Tai et al., IEEE Trans. Power Delivery 1989); search snippets only, full texts not read]. A Foust-Menger result is named by one source but I could not confirm what it derived, so I attribute nothing to it. - Carson's ground-return paper exists: J. R. Carson, "Wave propagation in overhead wires with ground return", Bell System Tech. J. 5(4), Oct 1926, pp.539-554 [web: https://ieeexplore.ieee.org/document/6768096]. It post-dates Steinmetz's 1920 book, so the omission of earth-return loss is a limit of 1920 knowledge, not a fault.

1. What changed, in one table

2. Claim 3: energy transfer and compound circuits (revised)

New evidence [read: Transient PDF pp.602-648; deep read, fourth section]. For a circuit of sections with different constants Steinmetz defines u = (r/L + g/C)/2 (a section's own decay rate), u0 (the one decay rate shared by the whole circuit) and s = u0 - u (energy transfer constant). He states: "power transfer occurs from section to section during the oscillation of a compound circuit", positive s meaning export and negative s import (p.611), and gives the section power ledger Ps = 2 s W (eq. 39), where W is the energy stored in the section. This is a measurable quantity (v(t) and i(t) at a junction, integrated over a cycle, against local I^2 R loss), not only a label.

Checks by the deep reader [calc]: - The printed example (transformers send 1,110 kW to a line that dissipates 1,800 kW while its own field supplies 690 kW; p.627-628) is arithmetically correct inside the model; I accept it. - Eq. 46, u0 = sum of (section length fraction x u), is not the decrement of any particular mode when surge impedances differ (here c = 362 and 3,162 ohm, ratio 8.7). Exact modes of the same loop run from u0 about 9 to 115 per second; eq. 46 gives 52.2, a good average over many modes (49 to 53) but not a per-mode value. It is exact (8 digits) for equal surge impedance and distortionless sections. Steinmetz marked it "Whether this expression (46) is more general is still unknown" (p.626): the calculation answers him. - Direction of power flow holds in every mode computed (low-loss transformer to high-loss line); the size is mode dependent (about 240 to 1,015 kW for the first five modes at the same stored energy). So 1,110 kW is a model figure, not a property of the circuit. - Junction rules (p.633-634): voltage transmitted 2 c2/(c1 + c2), current 2 c1/(c1 + c2), reflection (c2 - c1)/(c2 + c1); the voltage at a single junction cannot exceed twice the incoming voltage (open end). His example, c1 = 346, c2 = 1,580: the wave enters the transformer at 1.64 times its voltage [calc]. He ties this to "destructive voltages when entering a station". Repeated reflections between junctions can exceed 2x; that is not in these pages [memory: high]. The "law of refraction" (tan ratios, p.638) is continuity of local wave impedance across the junction, a standard result [memory: high]; its likeness to Snell's law is formal.

Weighing. The Mathematician, Physicist and Contrarian judged "energy transfer" from the uniform-line chapters, where s is a bookkeeping split. In the compound-circuit chapters it has an observable and agrees with Poynting energy accounting [memory: high]. "Not testable as stated" therefore no longer fits the compound-circuit use; "Established" fits the existence and direction of the flow, and "approximation" fits eq. 46. QE's guess that a split was likely was right. A correction to QE's text: QE gives 2c1/(c1 + c2) as the abrupt-junction transmission factor; that is the current factor, the voltage factor is 2 c2/(c1 + c2).

The Contrarian's criticism that sqrt(z2/z1) is the gradual-transition rule is accurate for the 1914 Discharges lecture; the 1920 book gives the abrupt-junction factor. I withdraw it as a criticism of Steinmetz's whole work.

Verdict, claim 3 (final): - Line equations, surge impedance, distortionless condition, matched termination, junction coefficients: Established. - Energy flows between sections of a compound circuit, from low-loss to high-loss sections, at Ps = 2 s W: Established (within the telegrapher model; the sign and existence hold in every mode computed). - Eq. 46 as one u0 and one s per section: approximation, exact only for matched distortionless sections; a mode average otherwise (shown by calculation; Steinmetz's own caveat). - "Energy transfer constant" for a single uniform line (s vanishes in a standing wave): Not testable as stated. What would settle it: ring down a transformer winding alone (u about 1 per second), then connected to a line, and compare the new decay and the junction power with eqs. 19, 39; or evaluate the exact eigenvalue condition (eq. 43), which he wrote but did not solve. Notes on the book kept: the sec. 98 table mixes grounded-end and open-end roots and omits the open-line fundamental (30.8 degrees, 189 Hz, exact u0 about 18 against eq. 25's 56.6); c^2 = 125,300 should be 125,000; eq. number 45 is used twice [calc].

3. Claim 4: danger frequencies, line resonance, surge effects (revised)

3a. The correction. My text said Steinmetz cites no measurement in the 1914/1920 pages. QE found, and the Section V deep read confirms in full [read: Transient PDF pp.674, 676], that the 1920 book says: "It is interesting to note, that experimental investigations have shown, that the natural frequency of oscillation of the high voltage windings of large power transformers usually is within this range of danger frequencies [20,000 to 100,000]. ... This accounts for the not infrequent disastrous experience with such transformers, before this matter was realized." No experimenter, paper, date, transformer or failure is named. This is documented in one place in the folder (1920 book, by the person who was then GE's chief consulting engineer [memory: high]); the 1917 "frequently been observed" is the only other appearance. It is a claim of measurement with the reference missing, and General Electric test records are one plausible home for it (inference, not a finding). It must not be reduced to "asserted without measurement". The Investigator's lead stands: find the "experimental investigations" (AIEE Transactions and GE Review, c.1910-1920 [memory: medium]).

3b. The 20-100 kHz band for lines is a derived result, and I reproduce it. N = f/u (cycles an oscillation lasts) has its maximum at f* = (m1/(2 m2))^(2/3), where u = m1 sqrt(f) + m2 f^2 (skin effect plus radiation). With his constants I get 127 kHz (N 65.5, 6-ft spacing) and 27 kHz (N 42.1, ground return), matching Table VI (100 kHz, 20 kHz). The 18-in distribution circuit peaks at 200 kHz, outside his stated band; the band refers to transmission-line circuits. His skin-effect formulas reproduce the modern formula exactly at 100 kHz (2.743 ohm/km for No. 00 copper) [calc].

3c. The band's position depends on the radiation term m2, which is claim 7's coefficient. The deep reader moved the peak by dividing m2 by a constant 340, giving 6.2 MHz (6-ft) and 1.3 MHz (ground). That is too crude: the ratio between Steinmetz's radiation resistance (f^2 l') and the standard pair result (omega mu0 (1 - J0(kd))/4 per conductor, about (kd)^2, i.e. f^3 l'^2) is not constant; it falls as 1/(f l'). My recomputation with the frequency-dependent ratio [calc, arbiter; numpy; J0 by numerical integral; radiation term scaled for both magnetic and dielectric parts together; earth-return and corona losses left out]: - ratio Steinmetz : standard, 6-ft spacing: about 3,300 (loop convention) to 6,700 (per conductor) at 10 kHz; 330 to 670 at 100 kHz; 33 to 67 at 1 MHz. Ground return (l' = 1820 cm): 10 times smaller at the same frequency (33 to 67 at 100 kHz; 3 to 7 at 1 MHz). - duration maximum: 6-ft pair 127 kHz becomes 0.9 to 1.2 MHz; ground return 27 kHz becomes 0.14 to 0.19 MHz. Maximum N rises (65 to 210-240, and 42 to 115-130). So the band as derived does not survive the radiation correction: its location moves up by a factor of about 5 to 9, and the 20-100 kHz range no longer singles out. Two further limits, both [memory: high] and the first now [web] for the existence of the paper: Steinmetz treats the ground as a perfect image plane and has no earth-return resistance (Carson 1926, [web: https://ieeexplore.ieee.org/document/6768096]); and a perfectly uniform balanced two-wire line carries its wave without radiating at all (radiation is from ends, bends, unbalance), so a radiation attenuation proportional to f^2 along a straight matched line has no counterpart in standard line theory. This is Steinmetz's model result, not evidence about transformer windings.

3d. The transformer half does not depend on the radiation model. Later literature puts winding resonances from tens of kHz into MHz (Contrarian, IPST 2015 snippets). I keep "Plausible, untested": there is a 1920 claim of measurement, consistent in kind with later work, but no reference and no neutral test of his specific band. The danger argument (low-damped winding at the frequency where arc-fed cumulative oscillation is likeliest) stays "Plausible, untested"; it survives without the line band, as the older Section III ch. IV and Discharges Lecture X statement.

3e. Wave-front flattening law (new; Section V ch. III-IV). Steinmetz gives each Fourier harmonic its own decay u_n = u(f_n) (legitimate for a linear line, a frequency-domain method [memory: high]; propagation speed fixed at c, low-loss form), then G = (2E/S) times the integral of e^(-ut) df (eq. 12) and, in the near region, G = 0.282 E sqrt(log(l'/l_r)/(l' l)) per cm (eq. 27); in practice about 360/sqrt(l) V/m for a 60 kV front, ground return, l in km; valid to about 30 km, fair to 100 km; falling as 1/l^2 only at very great distance (eq. 42). The deep reader reproduced the algebra and the integral: exact against eq. 27/28 within 1% to 3 km, 8% at 30 km, 1.5x high at 300 km [calc]. The law's form comes from u growing as f^2, which in his model is radiation, counted twice (magnetic and dielectric). My frequency-dependent correction (same assumptions as 3c, circuit 3, 60 kV): the front stays about 1.1 to 1.7 times steeper at 0.03 km, 1.8 to 2.3 at 3 km, 2.5 to 3.1 at 30 km and 2.7 to 3.2 at 300 km than Steinmetz's numbers [calc, arbiter]. The deep reader's 10-17x used a constant 340 and is withdrawn. The form of the law is therefore not fragile to the radiation error within his model; its coefficients are good only to a factor of a few. The real mechanisms of flattening are different: corona on surges above inception [web: https://orca.cardiff.ac.uk/107185/ and the corona-simulation literature found in the search], earth-return resistance, skin effect. Qualitative conclusions, all in line with later practice [memory: high; the corona point now [web]]: steep fronts flatten with travel; they are dangerous mainly near their origin; closely spaced conductors carry a steep front farther than a ground-return circuit; a short iron section near a station gives little protection against nearby strokes. Steinmetz cites an observation for the first ("small inductances shunted by a spark gap ... show appreciable spark lengths ... only near the origin of the disturbance", p.652), with no place, date or experimenter. Verdict, flattening law: qualitative Established (corona-dominated in later practice); his formula as mathematics inside his model checked; as a quantitative prediction for real lines Never properly tested (no measurement in the folder). The decisive measurement: front steepness against distance on a real line with and without corona (impulse-generator tests of the kind he began in 1921-22 could do it; later cathode-ray oscillograph work from the later 1920s [memory: medium]).

3f. Two smaller points on Section I ch. VIII, "Low frequency surges": the formulas are the lumped L-C result (condenser voltage amplitude i0 sqrt(x xc); 282,800 V and 316,000 V are calculated amplitudes, reproduced [calc]); the conclusion that a short circuit is safely opened near zero current is standard practice [memory: high]. The only observation is the author's own: on "an experimental 10,000-volt, 40-cycle line, when a destructive e.m.f. was produced by a short-circuiting arc, the author observed a drop in generator e.m.f. to about 5000 volts" (p.156 [read]). No measurement of the surge voltage or of an 1,800 Hz oscillation is given; 316,000 V "accounts for" the damage, which is a consistency check, not a test. Single published source, informal, kept as evidence. Also from the Section V list of unnamed experience: oscillograms of transmission lines that do not show the rectangular wave; shunted-gap tests; "investigations of the last years" on cable dielectric loss (p.652, 655): leads for the Investigator.

Claim 4 verdict (final), by part: - Resonance formulas, f1 law, 283x (model), open-end doubling, junction coefficients: Established. - Qualitative flattening and "danger near the origin": Established. - Transformer windings oscillate at 20-100 kHz (claimed 1920 as "experimental investigations ... have shown", no reference): Plausible, untested. - Danger argument for cumulative oscillation in windings; the series R-C cure; 700-mile quarter-wave design: Plausible, untested. - 20-100 kHz as the band of longest-lasting oscillation on real lines: reproduces from his tables; Refuted by calculation as a statement about real lines once the radiation term is corrected (position moves up about 5-9x in my estimate; earth-return and corona not included). - Quantitative flattening law (G about 360/sqrt(l) V/m): Never properly tested; correct to a few times within the corrected radiation model. - Low-frequency surge formulas (Ch. VIII): Established as lumped-circuit theory; the 316 kV event: a calculation of a single reported destructive arc, Never properly tested. What would settle it: frequency-response measurement of a large transformer winding (with and without the series R-C), the "experimental investigations" themselves, and field front-steepness data with and without corona.

4. Claim 7: radiation resistance (restated; verdict unchanged)

New in Section III ch. VIII-IX and Section V [read; calc]: - Sec. 69 (PDF p.432-433) estimates radiation resistance at 1 MHz as 630 r0 (6-ft spacing) and 12,600 r0 (ground return) by putting the whole lag angle (2.2 and 22 degrees) on the whole reactance. That is 162 and 3,240 ohm/km. His own table (p.444) gives 48 and 480 ohm/km, 3.4 and 6.7 times lower. The cause is that the flux is spread logarithmically out to l', so the in-phase fraction is smaller by ln(l'/l_r) (6.0 and 8.1); partly offset by his low reactance assumption. The book does not flag this. Both numbers are far above the standard result (1.43 ohm/km for the loop, 0.72 per conductor, at 1 MHz, 6-ft spacing [calc]). - Convention. Earlier I called his table "about 340 x too large" using the loop value. Steinmetz's formula refers to a length of one conductor, so per conductor the ratio is about 670. I now state both (340 to 670) and add that the ratio depends on frequency and spacing: it scales as 1/(f l') because he has f^2 l' where the pair result goes as f^3 l'^2. At 1 MHz, 6 ft it is 33 to 67; for ground return at 100 kHz, 33 to 67. The earlier flat "340x" is withdrawn as a general figure; it is right for 6-ft spacing at 100 kHz in the loop convention. - The single-wire formula r2 = 2 pi^2 f l 1e-9 is exactly omega mu0/4 per metre for an infinite uniform-current wire [calc]; for a 1 m wire at 1 MHz it gives 1.97 ohm against a short dipole 0.0088 ohm (225x); it agrees with a real conductor only for length of order 0.75 wavelength [calc]. He calls it "a finite section of an infinitely long conductor" and states that no-return values have meaning only above about 10^4 cycles (sec. 90) or only at "extremely high" frequency (sec. 97, 10^4 and 10^5 "little meaning"); the two passages give different thresholds. He treats it as an upper limit (sec. 85). - Section V makes the radiation term load-bearing: it sets the high-frequency attenuation, the danger band and the flattening coefficients (claim 4), and it adds an equal dielectric radiation conductance. The earlier worry that a constant-parameter theory sits beside an r proportional to f^2 is therefore removed in logic (he states the limit himself, preface and sec. 1, and uses r(f), L(f), g(f), C(f) in four ranges), and moved to a question of numbers (are the radiation coefficients right?). - Two corollary claims drawn from the tables inherit the same weakness. "Iron is almost as good as copper at extreme frequency": the table supports it only through the large radiation term; with a smaller one, iron (skin resistance 106 times copper's at 1 MHz, Table II) stays much worse. "Radiation resistance is independent of conductor size and material": true in standard antenna theory (it follows from current distribution) [memory: high]. Lightning: his statement that "most of the energy of the lightning may be communicated by radiation to other bodies" (p.458) is hedged ("probably", "approximately", upper limit); the usual estimate is a small fraction of stroke energy and mostly at lower frequency (peak near 10 kHz) [memory: medium; not checked on the web]. I leave this as "Never properly tested" in his text (no measurement) and flag that it conflicts with the usual estimate. - Table III copper wire 10^5 Hz (r = 0.0052 ohm/m, power factor 0.69%) disagrees with Table I and sec. 91 (0.0032, 0.43%); printed exponents in the 25 and 60 cycle entries of the sec. 76 table are 10^-6 where 10^-8 is correct [calc]. Verdict unchanged: principle Established; single-wire formula correct for its idealisation, Refuted by calculation for real wires; two-wire table and f^2 l' scaling Refuted by calculation; model Historically superseded but instructive. Because the deep read of 69 shows his own two estimates disagree by 3-7x, the "instructive" point is stronger: the same chapter holds two different answers.

5. Claims 1 and 2: arc evidence in the folder (added)

• Timeline for claim 2, with what each text says:
• 1890: oscillogram of an alternating carbon arc (Tobey and Walbridge, AIEE Trans. 1890 p.376, reproduced as Fig. 177 in the 1916 book; Stanley alternate-arc dynamo).
• 1914: the lag / "reversed hysteresis loop" wording (Discharges Fig. 66 text).
• 1916 Alternating-Current Phenomena, 5th ed. [read: PDF pp.379-386, deep read]: the falling characteristic e = e0 + c/sqrt(i) with the residual-vapour branch e = r i; hard carbon e0 = 30 V, c = 40, r = 70 ohm gives 9.30 A, 47.2 V, 439 VA, power factor 77%; metal arcs "frequently reaching values of several thousand volts". It is used for wave distortion, a power factor below one at zero phase displacement, double-peaked voltage and arcing-ground overvoltage. In pp.379-386 and 402-404 the falling characteristic is not called a negative resistance and not used as a source of oscillation. This is the same functional form as the 1917 arc used in the primer.
• 1917 Electric Circuits and the 1923 paper (abstract): negative-resistance account. Check [calc, deep reader]: the model reproduces 9.30 A and the 77-78% power factor; the printed power 388 W looks like a misprint for 338 W (77% fits only 338). The Fig. 176 example (p = 0.796, P = 244) is about 3% off its own formulas. Not load-bearing.
• Arc rectifier (Section II ch. IV, Figs. 66-77): the arc is treated as a switch-like one-way conductor (cathode blast), and a ringing of "a few thousand cycles per second" follows the sudden stop of an anode current. The blow-out and "disruptive discharge" are conditional ("may"); Fig. 77 shows the ringing but I cannot tell from the print that it crosses zero. The tests are one plotted performance curve and captioned oscillograms; no operator, place, date or scale. A second, discontinuity-driven source of arc-related oscillation; it neither tests nor contradicts the lag mechanism.
• Claim 1 additions (Ch. VI): a spark gap turns a steady supply into pulses; the discharge power equals stored energy times repetition rate; the budget closes (5.6 VA input, 4.1 kW output, 1.4 kW in the 10,000 ohm charging resistor [calc]). The hot-wire reading of 29 A against 28.8 A is a check of energy bookkeeping only, with an estimated r1 = 5 ohm (I read 29 A as agreeing, not as an independent test; i1 does not depend on L1 or frequency, so it cannot confirm the 143 kHz or 562 kHz). The cable-system sentence (C = 102 microfarad, L = 6.4 mH, 25 Hz, "this phenomenon was observed") gives no place or date. Verdict stays Established.
• Long-line harmonic resonance (AC pp.402-404): a worst-case factor of 14.4 at 346 Hz, between the 5th and 7th harmonics of 60 Hz; he concludes that the danger "is frequently overestimated" (a limit of 7% harmonic for at most doubled voltage). Printed table values 1.36, 3.76, 2.18 differ from his formula (1.37, 3.89, 2.09) by up to 3.5%. Kept as Steinmetz's own downplaying of the resonance danger, beside the 283x and 14.4x figures.

6. Measurements in the folder (replaces the source-gap sentence "no measurement by Steinmetz beyond oscillograms")

The folder holds these recorded observations, all by Steinmetz himself or credited to others, none a test of a contested claim: hot-wire ammeter 29 A (Transient p.123); rectifier test curves and oscillograms (p.306-309); the destructive arc on a 10,000 V, 40 Hz experimental line with generator voltage fall to about 5,000 V (p.156); V-curves of a synchronous motor (AC p.355-356); transformer inrush 510 A calculated against 4.5 A (p.226-227); the 28-mile line oscillogram (Discharges Fig. 41); and the 1890 arc oscillogram. They show that he measured and compared. The central contested claims (danger frequencies, lightning chain, radiation numbers, dielectric explanation) have no measurement in the folder.

7. Investigator's finds kept (restored after QE retention check)

• 1919 Commonwealth Edison trouble report (alternator groups oscillating against each other; the lag of field flux treated as damping) [web: HathiTrust full view, snippets only; sites.md]: a field case of lag acting as damping, which bears on the open question of whether the 1914 wording came from machine hunting.
• Slepian and Peters, "Surges on Transmission Lines", Westinghouse, presented in the same April 1923 AIEE session as Steinmetz's paper [web: J. AIEE April 1923 program, sites.md]. Westinghouse was a competitor, so this is a contemporary treatment by an interested party; not read.
• Creighton's arcing-ground suppressors and neutral grounding, J. AIEE May and June 1923 [web: WorldRadioHistory]: evidence that arcing grounds were a real operating problem in 1923, and not a test of his mechanism.

8. New open questions

• What were the "experimental investigations" on transformer windings that the 1920 book relies on, and who ran them?
• Does the 1/sqrt(distance) flattening law match measured front steepness on real lines, with and without corona?
• Does a corrected, frequency-dependent radiation term (and earth-return loss) in Steinmetz's Section V give 20-100 kHz or higher for the duration maximum? My estimate is 0.14-0.19 MHz (ground return) and 0.9-1.2 MHz (6 ft), model-limited.
• Does the compound-circuit s match a ring-down of a real winding connected to a line?

9. Corrections to earlier documents (additions to the list above)

11. arbiter.md claim 4 text and correction 2 (above): "no measurement cited" is wrong for the 1920 book; correct wording: "claims experimental support ("experimental investigations have shown"), gives no reference; single source in the folder". Same error in claims.md claim 4, facts.json (Transient summary and key claims), primer evidence row 4b, and in the physicist, mathematician and contrarian files.
12. arbiter.md claim 3 (Contrarian's abrupt-junction point) and the "Not testable as stated" verdict: revised as in section 2. Also physicist.md (bookkeeping device), mathematician.md (no extra observable), contrarian.md (vocabulary) for the compound circuit. QE's coefficient 2c1/(c1+c2) is the current factor; voltage factor is 2c2/(c1+c2).
13. arbiter.md correction 8 (constant-parameter tension): not a hidden assumption; Steinmetz states the limit (preface p.15; sec. 1 p.652) and removes it in Section V with r(f), L(f), g(f), C(f); the tension becomes the radiation-number question.
14. arbiter.md recomputation B and claim 7: the factor "about 340" depends on frequency, spacing and convention (340 to 670 at 100 kHz, 6-ft; 33 to 67 at 100 kHz, ground return; 33 to 67 at 1 MHz, 6-ft). Deep read (Section V) line: "6.2 MHz and 1.3 MHz" and "10-17 times steeper" are replaced by the figures in section 3c and 3e above.
15. Source-gap statement and primer: replace "no measurement by Steinmetz beyond oscillograms" with section 6 above.
16. Dating: the falling arc characteristic is in the 1916 book (distortion use); extend the timeline in the primer section 4.
17. Process notes for the orchestrator (not verdict changes): primer section 3.4 field-strength tag (100-200 kV/m) to [memory: medium] or a confirmed source; primer section 5 arc equation e = 35 + 200/sqrt(i) rests on a 1917 page image not kept in research/files (save archive.org PDF p.217 or say it was read from an image not kept); the Section V preface says six new chapters, the copy has four; misprints listed in the deep reads (p.678 10^11 should be 10^10; p.659 reactance subscripts; eq. 43 factor 10^-8; Table VI maximum for the 18-in circuit at 200 kHz).
18. Deep-read file note: the Section I ch. VIII reader treated claim 4 as the Moray valve claim from a memory note; the claim numbering of this project is claims.md. His comments on Moray analogy are not used.