Science Contrarian review: Steinmetz (Charles Proteus Steinmetz), project "Steinmentz-Charles"

Reviewer: Science Contrarian (Step 2). Sources: facts.json, claims.md, deep/ (all three reads), the Investigator's sites.md "Leads for review", research/ notes, research/pages/ia-electric-circuits-1917.txt (read by me), and my own calculations in the project venv. Tags: [read] document or deep read; [web] with URL; [memory] with confidence; [calc] my own arithmetic from stated numbers.

Source gap (repeated from claims.md): no gap in text. The three books have an OCR text layer; only parts were deep-read (Discharges PDF pp.111-150; Alternating-Current pp.179-215; Transient pp.318-397, 486-545, 704-739). The folder holds no experimental data of Steinmetz's own beyond oscillograms described in the text, and no critic or replicator. Everything below about experiments by others rests on the Investigator's web finds or on [memory], and is tagged.

0. Stance, and what kind of case this is

This is not a suppressed-claim case. Steinmetz was chief consulting engineer of General Electric and a Fellow of the AIEE (Journal of AIEE, April 1923 programme [web: https://www.worldradiohistory.com/Archive-AIEE/Journal-Of-The-AIEE-1923-04.pdf], via research/2026-10-08-worldradiohistory.md). He published on the arc and cumulative oscillation continuously from 1912 to his death in 1923 (posthumous 1924 paper), and later engineers cited the 1923 paper (1930 AIEE citation, Gilkeson 1933) [web, Investigator: sites.md]. There is no dismissal and no gap in the record to analyse; the Investigator found none. The useful work for a contrarian is therefore different: (1) separate what Steinmetz measured from what he asserted, (2) build the strongest case for the parts that were later vindicated or are still unexplored, and (3) apply the same rigour to his printed numbers, several of which do not close. Where mainstream engineering absorbed his ideas (surge impedance, arcing ground, negative-resistance oscillation) I say so plainly; where a result is his alone and untested (the cloud model), I say that.

Anomalous experimental results in the folder: none that mainstream physics disputes. The oscillograms (arcing grounds on 22-kV and 82-kV systems, transformer oscillation at switch-off, Fig. 66 arc loop) show phenomena that engineering accepts. The only unconventional material is the lightning-in-clouds model (claim 5) and the finite-velocity radiation model (claim 7), both of which are theory, not data.

1. Claim by claim (questions a-d)

Claim 1. Sustained or cumulative oscillation needs a continuous energy supply from the power source through an arc

a. Mathematics consistent? Yes. It is an energy-balance statement (dW/dt = P_supply - P_dissipation), which Steinmetz states in words only (my restatement, Discharges p.142) [read: p.142]. Nothing to check beyond bookkeeping. b. Consistent with experiment? Yes. Arcing grounds on isolated-neutral systems, the Duddell singing arc (1900) and Poulsen arc transmitters are standard cases of dc power converted to oscillation [memory: high]. Steinmetz's oscillograms (Figs. 44-46, 59-65) record arcing grounds and a cumulative oscillation in a 2500-kW transformer [read: p.120, 143-145]. Contemporary operating practice treated arcing grounds as real and recurrent: Creighton's arcing-ground suppressors and neutral-grounding discussion in J. AIEE May/June 1923 [web: Investigator, research/2026-10-08-worldradiohistory.md]. c. Tested? Observed in service and on an artificial 130-mile line (Cunningham, Proc. AIEE Jan. 1911, via Discharges pp.128, 143) [read]; Commonwealth Edison 1919 report is a field case of machine groups oscillating [web: https://babel.hathitrust.org/cgi/pt?id=uiuo.ark:/13960/t0ks6mb3n, snippets only]. No hostile test; nobody disputes it. d. If it were true, what changes? Nothing. It is conservation of energy. His point that the energy is "not limited to the small amount of the stored magnetic and dielectric energy of the system" but comes from "engine or turbine power" [read: p.149] is why such oscillations are worse than lightning transients.

Verdict: Established.

Claim 2. The arc supplies the energy by a lag of voltage behind current ("negative energy cycle, reversed hysteresis loop")

This claim needs splitting, and the Investigator's find changes the picture (see Corrections).

a. Mathematics. In Discharges (1914) there is no equation [read: p.142-149]. The deep reader's remark that the Fig. 66 loop area has units of watts, not joules, is right, and I can sharpen it. Write the small-signal arc response to current di = a sin(wt) as dv = -R a sin(wt) + X a cos(wt), where R is the in-phase (resistive) part and X the part in phase with di/dt. Over one cycle: - Energy absorbed by the arc = integral of dv di dt = -pi R a^2 / w. Only R enters. A negative R (falling characteristic) means the arc gives energy to the oscillation. [calc] - Area of the loop in the voltage-current plane = closed integral of dv d(di) = pi X a^2. Only X enters. [calc] So a loop in the v-i plane, such as Fig. 66, measures the reactive (inductive-like) component. Higher voltage on rising current (his Fig. 66) means X > 0. That is the signature of a lag, but a lag of this kind stores and returns energy; it does not by itself deliver any. The analogy with the B-H loop fails because energy in magnetic hysteresis is the integral of H dB (conjugate variables), whereas the conjugate pair for a circuit is voltage and charge (v dq = v i dt), not voltage and current. [calc, with standard circuit theory, memory: high] Delay also works against the supply: if dv(t) = -R di(t - tau), the energy per cycle scales as -R cos(w tau), falling as the lag grows. [calc] This is the role Steinmetz himself gives the lag three years later: it flattens the transient characteristic and limits amplitude (1917, sec. 98, printed pp.191-192) [read: research/pages/ia-electric-circuits-1917.txt, lines 17280 ff.; Investigator's quote verified]. So the 1914 wording (lag supplies the energy) and the 1917 wording (negative effective resistance supplies the energy, lag limits the amplitude) are in tension. The 1917 account is the correct one in the small-signal picture. This is a point against the 1914 statement, not against the phenomenon. b. Experiment. The falling arc characteristic and the negative-resistance oscillator are experimentally established [memory: high; Duddell 1900, Ayrton's arc characteristic]. Steinmetz's own Fig. 66 shows both a falling mean curve (about 100 V at 0.1 A to about 55 V at 4-5 A, my readings from the deep read) and a loop [read: page image p.148]. Titanium-carbon arc data are a single figure with no table. c. Tested? His 1917 worked instance (3 A mean current; R = 18.5 / 20.3 / 27.5 ohm for swings of 0 / 1 / 2 A; load below 18.5 ohm self-starts; 22.5 ohm needs a kick outside 1.5-4.5 A) is a calculation from a drawn characteristic, not a test [read: ia-electric-circuits-1917.txt, sec. 97, printed pp.190-191]. His 1923 paper (Trans. AIEE 42:470) states "a negative resistance, in combination with a source of power" [web: https://ieeexplore.ieee.org/document/5060887, abstract only]. Notebooks "Frequency transformation by third class conductor" (23 March 1922) and "Nernst glower as oscillator" (1922-23) exist unseen at the Schenectady County Historical Society [web: finding aid, research/files/schenectady-historical-steinmetz-papers-finding-aid-2017.pdf]; "tests on titanium and carbind" (1912) might be the Fig. 66 data (unconfirmed). Those records would show whether he measured the energy supply. d. If true: nothing changes; the negative-resistance form is textbook.

Verdicts (split): - Negative-resistance form (1917, 1923): Established. - 1914 form, "lag supplies the energy / reversed hysteresis loop", as written: Not testable as stated (no equation, no measured in-phase component; loop area in the v-i plane measures the reactive part). Steinmetz himself says the mechanism "is still practically unknown" for circuits [read: p.147], and repeats it in 1917 sec. 85 [web: ia text].

Claim 3. Four-constant circuit equations, decrements u, m, s, surge impedance sqrt(L/C), distortionless r/L = g/C, low-loss sections feed high-loss sections

a. Mathematics. Internally consistent. The deep reader re-derived the telegrapher's equation and the decrement relations with SymPy (a^2 = rg - (rC + gL)b + LC b^2 = (bL - r)(bC - g)) and found one misprint (h^2 > LCs^2 should read <) [read: deep/Transient 10]. I re-added the Lecture IX numbers: u0 = 3.6/4.5e-3 = 800; s = -100, +700, -100, -800; open-circuit case u0 = 700 [calc, agrees]. A caution for the Mathematician: "s" is a bookkeeping split of the attenuation between two counter-travelling components; it is notation for the same physics, not a new constant. Two loose points. (i) The transition rule "voltage rises as sqrt(z2/z1)" from constant energy per wavelength (ratio 2 for 200 to 800 ohm) is the gradual-transition (Green's-law) result. For an abrupt junction the standard transmission coefficient is 2 z2/(z1+z2) = 1.6, with reflected 0.6 [calc; memory: high]. His text partly acknowledges reflection ("almost all the current is reflected") [read: p.141], so this is a looseness, not a conflict. (ii) The constant-parameter assumption excludes radiation and skin effect, which his claim 7 adds as frequency-dependent effective resistance; the two chapters are consistent only if r is read as r(f). b. Experiment. Surge impedance, reflection and distortionless-line condition are established (Heaviside 1880s-90s) [memory: high]. Steinmetz's 28-mile and 154-mile oscillograms and Cunningham's artificial line (z = 590 ohm; I checked sqrt(0.3944/1.135e-6) = 589.5 [calc]) illustrate them. c. Tested? Yes, by engineering practice. His US 1,230,615 (filed 1913, granted 1917, GE) applies surge resistance sqrt(L/C): a series inductance shunted by a resistance equal to the transformer's surge resistance [web: https://patents.google.com/patent/US1230615A/en; research/files/US1230615-Steinmetz-protective-device-1917.pdf]. The patent shows he acted on the theory; it is not an independent test. d. If true: nothing changes.

Verdict: Established (circuit theory); the "energy transfer constant" is Steinmetz's vocabulary for accepted physics.

Claim 4. Line resonance and surge effects (f = S/4l, f1 = 7.5e9/l0, 283x quarter-wave rise, danger frequencies 10-100 kHz)

a. Mathematics. Checks out: 188,000/4 = 47,000; 1880 miles at 25 Hz, 783 at 60 Hz; 150 miles gives 313 Hz; the table 4700...470 Hz from 7.5e9/l0 equals c/(4 l0) [calc; read: deep]. The constants C0 = 1.11e-6 l0/(2 ln 4h/d) uF and L0 = 2e-6 l0 ln(4h/d) mH multiply to 1/c^2, so the "independent of wire size and height" result follows [calc]. 283 = 2/(pi u) with u = 0.00225 [calc, agrees]. One printed arithmetic error: the short-circuit interruption example gives 150,000 V (750 A x 200 ohm; the square-wave series equals pi/4 not pi/2), not the printed 300,000 V [calc: 4/pi x 750 x 200 = 191,000 V is the first-harmonic-peak bound; 150,000 V is i0 sqrt(L/C)]; the deep reader's correction stands. b. Experiment. Travelling-wave resonance on lines is established; the speed on real overhead lines is a few percent below c and earth return adds loss [memory: medium; not checked]. Transformer winding resonances are real: published studies and measurements show winding resonances from tens of kHz to the MHz range with internal overvoltage amplification, for example a resonance amplification factor of 2.5 at 660 kHz on a healthy winding and resonances near 800 kHz to 1.6 MHz in wind-turbine transformer windings [web: https://www.ipstconf.org/papers/Proc_IPST2015/15IPST031.pdf; https://odr.chalmers.se/handle/20.500.12380/171671?locale=en, via search snippets]. His "10,000-100,000 cycles" lies at the low end of that range; he gives no measurement, and in 1917 says only that destruction by cumulative oscillation "has frequently been observed" [read: ia text, sec. 101, printed p.200]. The 1898 Electrical World article already contains the table (4680 at 10 miles to 475 at 100 miles) [web: tuks.nl scan, research/files/steinmetz-1898-natural-period-transmission-line-lightning.pdf, OCR]. c. Tested? The wave formulas are verified by decades of line surge work. The quarter-wave "transformer" use (constant-voltage to constant-current, 1.4 MV from 5 kV of third harmonic) is a calculation; the 60,000-kW 700-mile quarter-wave scheme was a design study and was not shown to be built [read: deep, G]. The 283x factor neglects loss growth with frequency, core effects and dielectric nonlinearity; as an upper estimate it is fair, as a prediction untested. d. If true: nothing changes.

Verdicts (split): formulas f = S/4l and 7.5e9/l0 and the surge-impedance consequences: Established. Danger frequencies 10-100 kHz in large transformers: Plausible, untested (in the folder; consistent with later published ranges). Quarter-wave 700-mile power scheme and 283x output: Plausible, untested.

Claim 5. Lightning in clouds as discharges in a series-capacity chain (rain drops); 24:1 in his example

a. Mathematics. Here the deep reader's flag is correct and I confirm it independently. With his stated constants (L = 2e-8 H, C0 = 1e-13 F, C = 4e-11 F, r = 1 ohm, g = 4e-6 mho, f = 1e8 Hz; n = 300, e0 = 30 kV) I get Z = 1 - 27.2 j ohm, Y = (4 + 62.8 j)e-6 mho, and a = sqrt(ZY) = 0.0414 - 0.0006 j per element [calc]. The series arm is net capacitive (x = 12.6 < xc = 39.8 ohm; the chain's series resonance is 1/(2 pi sqrt(LC)) = 178 MHz, above his 100 MHz), so ZY is real and positive: pure attenuation, no travelling or standing wave. A series-C, shunt-C0 ladder attenuates as sqrt(C0/C) = 0.05 per element, which is essentially the 0.041 found, and his own eq. 25 has that form. Summing the gap voltages over the grounded 300-element chain gives about 44 kV, ratio 1.46 to the 30 kV applied, not 24 [calc]. His printed alpha = 0.0021, beta = 0.0412 appear to be the result for ZY negative real, that is a net-inductive series arm: (1/2)(r/|X| + g/b) x 0.0412 = 0.0021 [calc]. So the printed numbers solve a different (propagating) problem from the constants he lists. The "7.86 wavelengths" is 24.72/pi, not 24.72/(2 pi), as the deep reader noted. The qualitative idea survives in the right regime. Repeating my calculation above series resonance with the same L, C, C0, r, g: at 250 MHz the sum of gap voltages over the 300-element grounded chain is about 11 times the applied 30 kV, at 400 MHz about 4.9, at 1 GHz about 1.8 [calc; sum of |I xc| per element, single-frequency steady state]. So "gap voltages add as vectors-around-a-wave and can exceed the end voltage" is a true property of propagating chains; the specific 24:1 and the specific 100 MHz example are not reproduced. The cloud extrapolation ("a few hundred million volts") is not computed from cloud parameters in the book [read: E4]. b. Experiment. His premise, that a flash of a mile or more cannot need the disruptive field of air (about 30 kV/cm peak, about 3 MV/m) across its whole length, agrees with modern understanding: a conducting leader channel carries potential to its head and enhances the field at its tip, so ambient cloud fields well below breakdown suffice [web: https://arxiv.org/pdf/1708.07315 and related, search snippets; the threshold figure I wanted (100-200 kV/m) was not confirmed, and the sources cite tens of kV/m in thunderclouds]. The mainstream mechanism is a stepped, conducting leader with streamer zone, not a chain of capacitively coupled rain drops [memory: medium-high; Rakov and Uman is the standard text, not opened]. Stepping of the leader is a feature he did not have data for in 1909. c. Tested? No cloud measurement is given [read]. The Investigator found his move to laboratory impulse generators: AP, NY Herald 3 March 1922, "a discharge of 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]. The figures are consistent (peak power 1e9 W; at most 10 kJ) [calc]; the report also says Steinmetz estimated the bolt at about one five-hundredth of natural lightning energy, which I have not checked. That demonstrates impulse testing of arresters (a successful engineering programme), not the rain-drop model. His 1915 "Brief Note Regarding Lightning" (Union College) and the 1907 AIEE paper were not opened [web: Investigator]. d. If true: lightning physics would need drop-to-drop oscillatory stepping with distributed series capacity as the propagation mechanism. That is a different mechanism from leader physics, not a modification of fundamental laws.

Verdicts (split): premise (no single field across the flash path): Established in modern terms [web, partial]. Rain-drop series-capacity model of the flash: Never properly tested (no cloud data; not refuted by experiment; mainstream uses another mechanism). Worked 24:1 example as printed: Internally inconsistent (printed alpha, beta do not follow from its own constants; the constants give about 1.5:1 at 100 MHz).

Claim 6. Dielectric loss with approximately constant power factor; corona at an "energy distance"; P = a(f+25)(e-e0)^2

a. Mathematics. Constant power factor implies loss proportional to f and e^2 (his reasoning, p.180) [read]. The 21 kV effective = 30 kV/sqrt(2) check is right. The glass-plate example's printed gradients (8.4 and 35.7 kV/cm) do not follow from his own formula; at 25 kV, k = 4, 0.3 cm glass x2, 0.4 cm air, the air gradient is 25/(0.15 + 0.4) = 45.5 kV/cm and glass 11.4 kV/cm [calc]; the conclusion (air breaks down) is unchanged. The corona formula as printed lacks the 10^-5 scale: the standard form is P = 241 x 10^-5 ((f+25)/delta) sqrt(r/s)(e - e0)^2 kW/km per conductor [web: https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/]. The deep reader's [memory, medium] recollection is therefore confirmed; applied literally the printed form gives megawatts per kilometre for a 100-kV line, with the factor about 19 kW/km [calc, deep read's example]. b. Experiment. Air breakdown near 3 MV/m, scaling with density, is established. Constant loss tangent over wide frequency ranges in solid dielectrics is an observed approximation; a layered dielectric with a leaky layer imitating hysteresis is the Maxwell-Wagner effect [memory: high]. Corona loss formulae came from Peek's experiments from 1911 and are empirical [web: same page, search summary]; the page also notes the formula is poor at low loss (V0/V near 1). c. Tested? Peek's formula was fitted to data; the book cites Peek, "Dielectric Phenomena in High-Voltage Engineering", p.200, without his experiments [read]. Steinmetz's "energy distance" idea (breakdown needs a finite volume of over-stressed air) is a physical statement consistent with later streamer-criterion thinking [memory: medium]. d. Nothing changes.

Verdict: Established (empirical engineering relations; printed corona formula misses the 10^-5 factor; glass-plate numbers misprinted).

Claim 7. Radiation by finite field velocity: effective resistance from sil/col functions

a. Mathematics. The appendix is sound special-function mathematics with misprints (E1-E4, T1-T5 in the deep read) and no effect on Chapter VIII results [read: deep/Transient appendix]. The Chapter VIII model uses a single delay l/S applied to the static field 2I/l of a long wire. Two checks of my own: - Wire with no return: the real part ω mu0/4 = 0.197 ohm per metre at 100 kHz equals his 0.195 ohm and is the exact result for an infinitely long wire carrying a uniform-phase current [calc; cylindrical-wave result, memory: high]. That is a property of the idealisation. A real 1-metre wire radiates far less: the short-dipole value is 80 pi^2 (l/lambda)^2 = 9e-5 ohm at 100 kHz [calc, memory: high for the formula]. Reading "0.2 ohm per metre of No. 00 wire" as applying to a real wire overstates radiation by about 3 orders of magnitude. - Wire with return at spacing l': his eq. 40 gives r = 2.63 f^2 l' l0 1e-18 ohm (proportional to f^2 and to the spacing); his table gives 0.48 ohm per km at 100 kHz for 182 cm [read]. For antiparallel currents a close pair is quadrupole-like: the exact infinite-pair result scales as f^3 l'^2 (ωmu0 (kd)^2/8 per metre = about 1.4e-3 ohm per km here) [calc; memory: high for the method]. A numerical far-field integration for a 1 km, 182 cm spaced pair gives 4.9e-4 ohm at 100 kHz, and the small-loop formula 320 pi^4 (A/lambda^2)^2 gives 1.3e-3 ohm [calc; memory: high]; his table value is about 300-1000 times larger. I recommend the Physicist confirm; the difference in scaling (f^2 l' against f^3 l'^2) is a qualitative error of the single-delay model, which the deep reader's Bessel comparison already identified for the far field. b. Experiment. Radiation resistance of antennas is established; that conductors radiate because the field propagates at c is mainstream (retarded potentials) [memory: high]. His model is a first approximation, not borne out quantitatively. c. Tested? He gives no radiation measurement. His 1923 relativity lectures and the Union College note on Einstein (1915) bear on his field picture; "Steinmetz Decoded" (secondary, unidentified authors) reports he came to treat the mechanical ether as unnecessary and replaced it with a "field of energy" [web: Investigator, research/2026-10-08-steinmetz-decoded.md; to be checked against the book]. His 1912 address says the ether is "an infinitely thin gas and a solid", a contradiction, and that present theories "represent only crude conceptions" [web: research/files/steinmetz-1912-...pdf, OCR via Investigator]. Dollard (1990, and later) builds on Steinmetz's dielectric/magnetic symmetry (Discharges pp.13-14) and on radiation as an energy component of inductance [web: https://wiki.opensourceecology.de/Introduction_to_Dielectricity_%26_Capacitance_(Eric_P._Dollard), via Investigator]. Dollard is a separate worker; mainstream engineering does not accept his wider claims [memory: high]. They are recorded here as related work, not as Steinmetz's claims. d. If true: nothing beyond classical electrodynamics changes; the question is only accuracy of the model.

Verdicts (split): qualitative statement (a conductor radiates because fields propagate at c): Established. Quantitative model and tables (single-delay sil/col): Historically superseded but instructive (right at the wire surface for an infinite uniform line; wrong scaling with spacing and in the far field).

2. The strongest honest case for Steinmetz

1. He was early and largely right on the arc. His 1914 energy-conservation argument is correct, and by 1917 he had the textbook negative-resistance treatment with numbers; by 1923 he stated it in one line.
2. The line-oscillation law was in print in 1898 and the table is still correct for a lossless line; his warning that large transformer windings are the weak point for sustained high-frequency oscillation has modern counterparts in published winding resonances.
3. His lightning premise (no mile-long breakdown field) is right; his surge-impedance protective patent (1913-1917) turned theory into hardware; his 1922 impulse generator was a real laboratory step.
4. Unexamined primary records could settle open points: the Schenectady notebooks (March 1922 third-class-conductor calculations, 1912 Ti-C tests, 1921-22 breakdown data), Union College items, the 1914 and 1923 AIEE discussions. They were not seen.

3. Where Steinmetz and the record are weak (same rigour for the inventor)

• The 1914 "reversed hysteresis loop" explanation, as above.
• Fig. 66 has no data table, and the cycle time is typeset as a small fraction (read as 1/120 s from the page image) [read: p.147-148].
• Danger frequencies for transformers are asserted without a cited measurement.
• Printed arithmetic errors: 300,000 V (should be 150,000 V), glass-plate gradients, corona scale factor, alpha and beta in the arrester example, seven misprints and several table errors in the appendix (all [read] from deep reads; I confirmed the three marked [calc]).
• The cloud model rests on "it is probable".
• Some secondary sources the Investigator cites (Steinmetz Decoded, Dollard, Rex Research) are interested or unidentified; I treat their summaries as pointers.

4. Corrections to Step 1

1. claims.md claim 2 and facts.json (Discharges entry): accurate for Discharges 1914 but incomplete. The Investigator's correction is right and I verified it against the 1917 OCR text (sec. 97, printed pp.190-191; "has an effective negative resistance"). In addition: the 1917 text assigns the lag a limiting role, which contradicts the 1914 wording that the lag supplies the energy. I suggest claims.md say so.
2. claims.md claim 4: the f1 law and table date from 1898 (Investigator); I agree. The 1898 OCR gives 4680/475; the 1920 book 4700/470 (rounding).
3. claims.md claim 5: the deep reader's flag is confirmed and explained. The printed alpha and beta correspond to a net-inductive series arm, the listed constants give a net-capacitive one (pure attenuation, about 1.5:1). Rewrite as "the example as printed does not reproduce 24:1; the effect exists in the propagating regime (about 5-11:1 for the same L, C, C0, r, g at 250-400 MHz by my calculation)". Also in claims.md: "the deep reader's recalculation" should read "recalculation by the deep reader and confirmed by the Contrarian".
4. claims.md claim 7: "about 0.2 ohm per metre of No. 00 wire at 100,000 cycles" needs the qualifier that it is the value for an infinitely long wire with uniform current and no return; a real metre of wire radiates about 1e-4 ohm.
5. claims.md claim 6: add that the corona formula as printed lacks the 10^-5 factor [web confirmed], and that the corona/dielectric statements are Peek-derived empirical relations.
6. claims.md claim 3 says "no separate radiation term" and claim 7 gives a radiation resistance; note this is consistent only if r is frequency-dependent.
7. Citation (minor): "Instability of Electric Circuits" is Proc. AIEE 33(1), Jan. 1914, pp.13-29 (Investigator); agreed.

5. Web checks (budget 6; 3 used)

• Peek's corona formula includes the 10^-5 factor: confirmed [web: https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/].
• Leader propagation at ambient fields below breakdown: supported in kind; the 100-200 kV/m figure was not confirmed [web: https://arxiv.org/pdf/1708.07315].
• Transformer winding resonances from tens of kHz into MHz: supported [web: https://www.ipstconf.org/papers/Proc_IPST2015/15IPST031.pdf].
• Not web-checked and still [memory, high]: Duddell singing arc (1900), Ayrton arc characteristic, Heaviside distortionless line, Maxwell-Wagner effect, cylindrical-wave radiation resistance, short-dipole and small-loop formulae. [memory, medium]: speed of travelling waves on real overhead lines; the "stepped leader" characterisation.

6. Summary table