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Central claims: Steinmetz (Charles Proteus Steinmetz), project folder "Steinmentz-Charles"

Source gap: none for text. All three works (Steinmetz, Electric Discharges, Waves and Impulses, 1914 ed.; Theory and Calculation of Alternating-Current Phenomena, 1916 ed.; Theory and Calculation of Transient Electric Phenomena and Oscillations, 1920 ed.) have a full OCR text layer. The OCR garbles most equations; the deep reads checked key equations on page images. Parts were deep-read: Discharges pp.111-150 (PDF); Alternating-Current pp.179-215, 379-386 and 402-404; Transient pp.104-124, 142-157, 292-316, 318-397, 431-482, 486-545, 602-648, 652-703 and the appendix 704-739. All other chapters rest on the page-by-page digests. The folder holds no document by a critic or replicator. It holds no laboratory data of Steinmetz's own, but it does record a few tests and observations that he reports himself, each in one passage of his own books with no date, place or witness: a hot-wire ammeter reading of 29 A against 28.88 A calculated (Transient p.123); mercury-arc rectifier performance curves "from tests" and oscillograms Figs. 67-77 (p.306-309); the destruction of an experimental 10,000 V, 40-cycle line by a short-circuiting arc, with the generator voltage seen to drop to about 5,000 V (p.156-157); observed V-curves of a synchronous motor (Alternating-Current p.355-356); a transformer inrush oscillogram (Transient p.226-227); and the oscillograms of arcing grounds in the 1914 lectures. None of these tests a contested claim; they show that he measured and compared. The 1917 book Theory and Calculation of Electric Circuits and the 1923 AIEE paper (abstract only) are not in the folder; what is said of them below comes from the Investigator's finds [web]. [read]

These are Steinmetz's claims as the documents state them. No verdicts here. Nothing in the folder is marked secondary.

Energy supply for sustained oscillation. A continual (steady) or cumulative (growing) electric oscillation needs a continuous supply of oscillating energy, which can only come from the power source (engine or turbine power) through an arc, converted from low-frequency or direct-current energy to the oscillation frequency; the stored energy of the line cannot supply it. (Discharges, Lectures VIII-X, pp.120, 142, 149; the lumped-circuit form with the spark gap as the switch is in Transient Section I ch. VI, p.105-123.) [read]
Mechanism of the arc's supply: a lag in 1914, a falling characteristic by 1916-1917. In the 1914 lectures, where successive oscillation trains overlap, the energy is supplied by a lag of arc voltage behind arc current, a "negative energy cycle, or reversed hysteresis loop"; his Fig. 66 (titanium-carbon arc, 0 to 4.1 A and back in 1/120 s) shows higher voltage on rising than on falling current. Steinmetz gives no equation for this and states the mechanism "is still practically unknown" for circuits (it is understood only for hunting of synchronous machines). The oscillation frequency is set by the circuit; "the electric arc has no frequency of its own". (Discharges p.146-149.) [read] Timeline of the arc account: the 1914 pages do not use the words "negative resistance" [read]. The 1916 Alternating-Current book in this folder already gives the falling arc characteristic e = e0 + c/sqrt(i) with a residual-vapour branch e = r i (hard-carbon example e0 = 30 V, c = 40, r = 70 ohm, power factor 77 per cent; metal arcs with peaks "frequently reaching values of several thousand volts"), but uses it only to explain wave distortion and arcing-ground overvoltage, not as the energy source of an oscillation (Alternating-Current p.379-386, pp.350-357 printed) [read]. The 1917 book (Ch. X secs. 96-99) and the 1923 paper (abstract only) give a negative-resistance account in which the lag limits amplitude; 1917 sec. 85 repeats "practically unknown" [web: Investigator, sites.md; arbiter.md claim 2]. Citation of the 1914 paper: Proc. AIEE 33(1), Jan. 1914, pp.13-29 [web: via arbiter.md].
General circuit equations and the energy-transfer constant. Every circuit is described by four constants per unit length (r, L, g, C), assumed constant and with no separate radiation term in Sections III-IV, giving the telegrapher's equation. Its solutions are waves with decrements u (dissipation), m (distortion) and s ("energy transfer" or wave-front constant); one component of an impulse drops energy along the line and the other picks it up; the surge impedance is sqrt(L/C); a distortionless circuit needs r/L = g/C. In a compound circuit, low-loss sections supply power to high-loss sections during a transient, each section exporting net power Ps = 2 s W, and the whole circuit rings down at a common decrement u0 (approximated by u0 = sum(lambda u)/Lambda, of which Steinmetz writes "Whether this expression (46) is more general is still unknown"); in his worked example the transformers transfer 1,110 kW to a line that dissipates 1,800 kW (Transient Section IV chs. VIII-IX, p.626-628). The constant-parameter assumption is Steinmetz's own stated scope: the 1920 preface and sec. 1 say it fails for very high frequencies and steep fronts, and Section V replaces the constants by frequency-dependent r(f), L(f), g(f), C(f) used harmonic by harmonic (see claim 4b). At a junction between sections the 1920 book gives the exact factors: voltage transmission 2c2/(c1+c2), current transmission 2c1/(c1+c2), reflection (c2-c1)/(c2+c1), at most twice the incoming voltage at an open end (Ch. X, p.631-634); the 1914 lecture's rule that voltage scales as sqrt(z2/z1) is the gradual-transition result. A deep reader's exact eigenvalue check of the p.626 example finds a different u0 for each mode (8.6 to 114.9 1/s, mean near 50, against 52.2), so eq. 46 is exact only for matched distortionless sections; the direction of power flow holds in every mode. (Transient Section IV; Discharges Lectures VIII-IX.) [read; calc]
Line resonance and surge/high-voltage effects. - 4a. A line a quarter wavelength long (f = S/4l, about 47,000/l cycles with l in miles) converts constant voltage to constant current and can yield enormous open-circuit voltage (his transformer-coil example gives 283 times the supply); a line discharging to ground has f1 = 7.5 x 10^9 / l0 cycles (l0 in cm), independent of wire size and height (in print since Electrical World, 27 Aug 1898 [web: Investigator]); large high-voltage transformer coils have the lowest damping and danger frequencies of 10,000-100,000 cycles (Section III ch. IV, no test cited there), so arc-fed cumulative oscillation is most dangerous there. (Transient book Section III chapters II-IV; Discharges Lecture X.) [read] - 4b. Variation of circuit constants (Transient Section V, the 1920 edition's new section). Steinmetz derives that a line oscillation lasts the most cycles between 20,000 and 100,000 cycles (65 cycles at 100 kHz against 9 at 1 kHz for a 6-ft line), calls this band the "danger frequencies of transmission systems", and states: "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", adding that this "accounts for the not infrequent disastrous experience with such transformers" (p.674-676). This is a claim of measurement with no experimenter, paper, date, transformer or number given; it is documented in this one place in the folder (the 1917 book says only "frequently been observed", sec. 101, per the Investigator). He also derives that the steepest gradient of a rectangular wave front falls roughly as 1/sqrt(distance travelled), out to about 30-100 km and as 1/distance^2 at great distance (G about 360/sqrt(l) V/m at 60 kV for a ground-return line, l in km), so a close return conductor carries a steep front farther and a short iron wire at a station gives "practically no protection" against nearby fronts (eqs. 27-28, 42; p.685-702). The line half of the danger-band derivation and the flattening coefficients depend on the radiation coefficient of claim 7 (a deep reader's calculation: with that coefficient reduced 340-fold the band moves to megahertz); the transformer half does not. [read; calc] - 4c. Harmonic resonance on a long line: in the 1916 book's example a harmonic near 346 Hz can raise the voltage 14.4-fold (3.76-fold at the fifth harmonic), but Steinmetz judges the danger "frequently overestimated" and harmonics below 7 per cent of the fundamental cannot double the voltage; no field measurement is given. (Alternating-Current p.402-404.) [read]
Lightning flashes in clouds as discharges in a series-capacity chain. Steinmetz judges it probable that a lightning flash in a cloud is an oscillatory discharge stepping between rain drops, modelled by a multigap-arrester chain with distributed series capacity; the gap voltages add as vectors, so the sum of local gap voltages can be many times the end voltage, and a flash of miles needs only a few hundred million volts. No cloud measurement is given. Result of the recalculations (Mathematician, Arbiter): the listed constants give a gap-voltage sum of 1.46 times the applied voltage e0, not the printed 24 (the printed alpha and beta, exchanged, give 19.3 e0), and "7.86 wavelengths" should be about 1.97; the printed alpha and beta do not follow from the listed constants (possibly from an earlier set of constants). (Transient book, Section III chapter V, PDF pp.391-397.) [read; calc]
Dielectric loss and corona. Observed loss in solid insulation has an approximately constant power factor (loss proportional to f and to D squared), true dielectric hysteresis is doubtful, and a layered dielectric with a leaky layer can imitate it; air breaks down at about 30 kV/cm maximum, corona begins at an "energy distance" rather than at the surface breakdown field, and corona power follows P = a(f+25)(e-e0)^2 (quoted from Peek). The printed corona constant A = 241 lacks Peek's factor 10^-5 [web: https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/], and the printed glass-plate gradients (8.4 and 35.7 kV/cm) do not follow from the stated formula, which gives 11.4 and 45.5 kV/cm [calc]. (Alternating-Current book, Ch. XIV.) [read]
Radiation by finite field velocity (supporting, secondary to the others). A conductor radiates because the field propagates at the velocity of light; this appears as effective resistance, computed with sine- and cosine-integral "velocity functions" (sil, col) tabulated in the appendix. Two forms must be kept apart. For a wire without return, eq. 23 gives 1.97 ohm per metre at 1 MHz (0.195 ohm per metre at 100 kHz, proportional to frequency), which is exactly omega mu0/4, the exact value for an infinitely long uniform-current wire, and not the value for a real conductor. For a two-wire line the radiation resistance grows as f^2 and in proportion to the spacing l' (eq. 40: 0.48 ohm/km at 100 kHz for 182 cm spacing), about 340 times the standard pair result at 100 kHz (the standard result goes as f^3 and spacing squared; the ratio is about 33 at 1 MHz) [calc]. Sec. 69 of the same chapter gives a cruder phase-lag estimate, 630 times the ohmic resistance at 1 MHz (12,600 with ground return), 3.4 (6.7) times above his own table value of 48 (480) ohm/km on p.444; the book does not flag the discrepancy [calc]. He also states that radiation resistance is independent of conductor material, so iron is "almost as good as copper" at extreme frequency (supported by his Tables I-III), and that lightning rods "probably" radiate most of the energy as "induced lightning stroke". Section V puts these radiation terms into r(f) and g(f) (so the constants are no longer constant) and the attenuation tables, danger band and flattening law rest on them. (Transient book, Section III chapters VIII-IX, Section V and appendix.) [read; calc]

Corrections noted by the deep readers in Steinmetz's printed figures (not in other project files): short-circuit interruption example gives 150,000 V, not the printed 300,000 V; glass-plate gradients; the corona formula's scale factor; "h^2 > LC s^2" misprint; seven misprints and several table errors in the appendix; Fig. 178 "388 watts" (probably 338); harmonic-resonance table values for the 3rd, 5th and 7th harmonics (1.36, 3.76, 2.18 against 1.37, 3.89, 2.09 from the printed formula); Table III copper-wire entry at 10^5 cycles; eq. 43 of Section IV ch. XI lacking a factor 10^-8; "10^11" for 10^10 V/s on p.678; the Section V preface says six new chapters, the copy has four.

Corrections to earlier documents (QE round, 2026-10-08): (1) claim 4 formerly read "asserted, no measurement cited"; wrong for the 1920 book, which claims experimental support for the transformer-winding band (see 4b). Likewise the source-gap sentence "no experimental data of Steinmetz's own beyond oscillograms" was incomplete. (2) QE's wording of the transition factor, "2c1/(c1+c2)" for the voltage, is the current factor; the voltage factor is 2c2/(c1+c2) [page image p.634], which equals the arbiter's 1.6 for the example. (3) The earlier statement that the constant-parameter assumption is a hidden tension with claim 7 should read: it is Steinmetz's stated scope and Section V lifts it, but the numbers then inherit claim 7's radiation coefficient. (4) The falling arc characteristic is in the 1916 book (claim 2 timeline), used for distortion only.