RankingsPrimerArbiterPhysicistMathematicianContrarianQESites logClaimsSourcesResearch notes

Peek-Frank: Science Contrarian review (Step 2)

Reviewer role: Science Contrarian (judges by experimental evidence; builds the strongest honest case; examines how claims were received; holds the inventor to the same standard as the critics). Project: F. W. Peek Jr., Dielectric Phenomena in High Voltage Engineering, 2nd ed., McGraw-Hill 1920 (one PDF, 325 pages). Peek worked for General Electric (GE), which had a commercial interest in transmission equipment and in the apparatus this book recommends. That is an interested-party fact, noted once here and applied below to every GE-sourced comparison. Tags: [read: p.N] = PDF page of the extracted text or page image (read by me, or by a deep reader and re-checked where I say so); [web: URL]; [memory: confidence]; [calc] = my own calculation.

Source gap carried forward. The text is OCR on 324 of 325 pages. Chapter V (PDF pp.154-188; the Line A / Line B experiments on which the loss law is fitted), the sphere-gap tables of Chapter IV, the oil and solid chapters, the design cases and the loss-data appendix (pp.277-294) were digested only and I did not deep-read them. Claim 3 therefore rests in part on a digest. Nothing here rests on [memory] alone; the two memory facts that matter are tagged below.

How I checked. I read the deep reads in full (pp.60-92, 227-251, 295-311), re-read the OCR of pp.65-66 and 232 (the energy-distance passage), pp.199-200 (spark lag) and the humidity statements, recomputed the Sigma-Delta fit, and ran a rough physical-criterion comparison (section "Strongest case", claim 2). I used four web calls (budget about 6).

Corrections to Step 1

  1. Claims.md claim 4, air films. It says entrapped air films "break down at the gradient of a free gap of the same thickness". The table (PDF p.300) does not say that for thin films. Entrapped-film strength g_a and free-sphere-gap strength g_s agree from about 0.01 cm upward (e.g. 0.455 cm: 35.6 vs 36.8 kV/cm) but differ at the thinnest films: 0.0025 cm gives g_a = 161 vs g_s = 196 kV/cm; 0.0053 cm gives 137 vs 139; at delta 0.74, 0.0051 cm gives 101 vs 143 [read: page image p.300]. The 196 kV/cm figure in claims.md is the free sphere-gap value, not the film value. The book prints no prose conclusion for this table (the deep reader's reading, and mine, is the "roughly the same" statement); the attribution of the table is also unclear (the note says "See Dubsky, 1914", so these may be Dubsky's data, not Peek's).
  2. Claims.md claim 1, "9 of 19 points discarded". Stated as fact. The book says only "points varying widely from the average straight line were then discarded as probably in experimental error" [read: page image p.74]. The count of 9 discarded and 10 kept is the deep reader's inference from matching values to Table IV. I re-derived the same split. Peek does not list the discarded points or give a threshold. Kept and discarded points have overlapping residuals (kept -5.5% to +4.0%, discarded -6.2% to +4.3% against the final line), so distance from the final line does not explain the selection. Unknown what preliminary line was used.
  3. Claims.md claim 5, rain. "36 to 40 percent" rests on two insulators of one type (A, B; Table VIII, PDF p.307), 112 to 72 kV and 116 to 70 kV, and a third data set (Table IX, a cask at reduced pressure, one insulator). The facts.json key claim carries a different figure ("50 to 90 percent of dry in the digest summary"); the page-image data is the authority. Two items is a thin base for a general statement.
  4. Claims.md claim 3, Au Sable. "15 kW/mile calculated vs 15-20 measured" is quoted by Peek from an N.E.L.A. article of June 1912 ("preliminary rough measurements"); Peek gives no spacing, temperature or barometer, so it cannot be recomputed [read: p.247-248]. It is not a measurement by Peek, and it is not clear who did the calculation. Leadville (Faccioli) and Hendricks (Pittsfield 1906) agreement is shown only as plotted curves with crosses; no numbers are printed. The Hendricks figure contains a printed inconsistency (48 in = 122 cm, book prints 132 cm) [read: p.248]. Peek himself says the comparison is hard because "all of the necessary data ... have not been recorded", and that the greater part of the Leadville curve is below e_v, where he elsewhere calls the loss "unstable and variable" [read: p.237, 240, 247].
  5. Facts.json: "text layer sampled" wording is absent, good, but mainstream_conflict omits the history of Peek's forecast that corona would "rarely be the limiting feature" of transmission voltage [read: p.249], which later practice contradicts (see claim 3).
  6. Confirmed, not corrected. The 100-mile worked example (e_o = 52.0 kV, visual 62.6-71.3 kV) recomputes; Table LXXX is e_o for stranded cable with m_o about 0.87 (deep read, not printed by Peek); A = 241 (p.237) vs 244 (p.242) is a genuine misprint; the Table I average printed "99.0" is 98.4 as a column mean (small).
  7. Investigator, one statement to temper. The note that Peek's 1927 paper "promises the mechanism that the 1920 book left unspecified" (sites.md, lead 1) is from the abstract only. The abstract reports oscillograph findings about loss (quadratic above e_v, sudden start on polished wire, probability law on cables, corona starting at the zero of the wave when applied voltage reaches twice e_v). It does not say whether the "rupturing energy" is ever specified. Open until the full paper is read.

Handling of the Investigator's findings (kept in the record whatever my verdict)

  • Peek 1927, Part IV (Trans. AIEE 46:1009-1024), cathode-ray-oscillograph measurements of loss to about 1 per cent at about 0.1 W; confirms quadratic loss above e_v, none below on polished wire, probability law at rough spots on cables [web: https://ieeexplore.ieee.org/document/5061442, abstract only]. This is Peek's own re-measurement 7 years after the book with a better instrument and bears on claim 3. Highest-value unread document.
  • Peek 1911, Part I (77-page preprint, free on archive.org) is the primary record of the Sigma-Delta fit and the points the book discards [web: archive.org crossref-pre-1923 collection, URL in research/2026-10-06-archive-org.md]. Not downloaded. It is the decisive record for the data-selection question in claim 1. Parts II (1912), III (1913), the 1915 transient-voltage paper and the 1916 d.c. paper hold the full data behind claims 5 and 6.
  • Fitch, Johns Hopkins Ph.D. thesis 1913 (Whitehead's laboratory) measured critical corona intensity over 5-108 cm Hg on nine conductor sizes. As returned by a summarising fetch tool (not checked by eye): Peek's original equation "didn't closely match", Fitch modified it, the modified form fitted "about as closely as the readings can be taken", and the results support Peek's empirical relationship; CO2 results point to molecular spacing rather than absolute density [web: https://archive.org/details/influenceofdensi00fitcrich]. This is an independent, non-GE pressure-range test of the density law. Note the nuance: independent support for the form, with a modification, and the modified formula is not yet read. Weighed under claim 1.
  • Whitehead (via book Table IV, 1917 compilation): a.c. critical gradients for wire diameters 0.074-0.231 cm from Whitehead, Peek, and Whitehead and Brown agree within about 1.5 per cent (Peek lowest by 0.5-0.8 kV/cm) [read: page image p.296]. This is in-book but from an independent laboratory (J. B. Whitehead, Johns Hopkins [memory: medium]); I count it as the best independent corroboration of the a.c. law.
  • Hartmann 1984 (IEEE Trans. IA-20:1647) derives the onset gradient from Meek's streamer criterion with an ionization coefficient depending on humidity, pressure and temperature, over radii 10^-7 to 10^7 m, and compares with experiments [web: https://ieeexplore.ieee.org/document/4504655, abstract; a search-engine summary describes the result as in "satisfactory" agreement with a variety of experiments, not independently verified by me]. It is a physics derivation of the thing Peek fitted, and it includes humidity, which Peek says has no effect.
  • Protsenko and Trotsenko 2014 centenary review of Peek's law [web: https://kpi.ua/nv-abstract-14-6] (abstract not read); Wikipedia Peek's law page repeats the irregularity factors (1.0 polished, 0.98-0.93 weathered, 0.87-0.83 cable) and notes Whitehead's alternative factors for 3- and 9-strand conductors; it cites no streamer comparison [web: https://en.wikipedia.org/wiki/Peek%27s_law]. Continued engineering use (Electronics 1950, Westinghouse Engineer 1951, EHV textbooks) is recorded by the Investigator [web: worldradiohistory.com notes]; that is evidence of use, not of an independent test.
  • Awards and standing: APS Fellow 1922, ASCE Rowland Prize 1923, Franklin Institute Levy Medal 1926 [web: Wikipedia, per Investigator]. Peek was not an outsider. The record shows no rejection of his corona work; see "How the claims were received".
  • Career and GE setting: 1905 test man, high-voltage laboratory in a boxcar, Pittsfield from 1916, Chief Engineer 1931, lightning generators 3.6 / 5 / 10 MV 1928-32, died 27 July 1933 (ETHW part 2 gives 1931, an internal inconsistency) [web: ethw.org, per Investigator, fetch-tool summaries not checked by eye]. The impulse work of the 1915 appendix continued into lightning research, which bears on claim 5 as a line of work that did not go silent. The Investigator found no absence-of-evidence anomaly and I agree: the record continues to 1933. The only open record question is whether anyone at GE carried the "energy distance" idea forward.
  • Not yet obtained (for the arbiter): 1915 transient-voltage paper; 3rd edition (1929), HathiTrust and archive.org; Union College's 84 items (blocked); "Wrestling with Nature" passage that Steinmetz "argued" about Peek's line experiments in 1916 (snippet only; interested-party GE context, content unknown).

How the claims were received (examination of rejection)

Nothing in the record shows Peek's corona law being rejected, suppressed or ignored. It was adopted, named after him, and is still used a century later as an inception estimate [web: Wikipedia Peek's law; Protsenko and Trotsenko 2014 title]. So the contrarian concern here is the opposite one: acceptance without anyone checking the selection and fitting that the book itself documents. What the record does show:

  • The constants are fitted by group averaging after discarding 9 of 19 points by an unstated rule [read: p.74-75]. Peek defends the method as "as reliable as, or more so, than ... least squares" [read: p.75]. My ordinary least-squares line through all 19 printed points gives g_0 = 30.4 kV/cm and coefficient 0.286, against Peek's 29.8 and 0.301 [calc, from Table III]. The difference is small (about 1.5% in g_0 and 5% in the coefficient) and does not threaten the engineering use, but it shows the quoted "0.301" is not unique to the data.
  • All wire data are Peek's and GE's except Watson (d.c.), Whitehead and Dean [read: preface and deep reads]. The independent Whitehead compilation agrees to about 1.5 per cent for a.c.
  • The "energy" explanation was never contradicted by experiment in the pages read; it was quietly overtaken: Peek's own 1927 title speaks of a "mechanism", and the 1984 literature derives onset from streamer criteria. I found no document that tests the "rupturing energy" idea as such, because as stated it cannot be tested (claim 2).
  • Whether any negative experiment was run, reanalysed or omitted: none located. The Investigator has not found a hostile test, and I cannot say the absence of one is evidence either way.

Strongest honest case for Peek, with the same rigour applied to him

For: 1. The 1/sqrt(r) dependence is tested over a 47-fold range of radius (0.0098 to 0.464 cm, 19 wires) with the spacing independence shown over a 42-fold range (Table I: g_v within 96.1-100.0 kV/cm for S from 2.54 to 106.8 cm) [read: p.70, p.74]. My recomputation of g from the printed voltages reproduces Table I to within 1.1 kV/cm. 2. The density law is tested two ways, temperature (-13 to 130 C, Tables VI-VII; calculated vs observed within about 1.6%) and pressure (5 to 76 cm Hg, Table VIII; within 2% for delta 0.146 to 0.997) [read: pp.77-80]. Fitch's independent pressure series is reported to support the form [web, unchecked]. 3. Table III of the appendix extends the check to delta 0.082 for d.c. and a.c. corona voltages [read: page image p.296], and the impulse-appendix Table IV compares measured and calculated 60-cycle corona down to delta 0.05 with close agreement [read: page image p.305]. 4. The Peek prediction in the text that a short gap should show a much higher breakdown gradient (the energy distance cut short) was followed by sphere-gap data: 196 kV/cm at 0.0025 cm, about 35 kV/cm above 1 cm, and an independently measured onset spacing X = 0.54 sqrt(R) that matches the sphere constant [read: p.82-90, Table IX]. That is a partly out-of-sample check; it is the only place where the "energy distance" does more than relabel the fit. 5. Peek hedged honestly in places: the "form of this rupturing energy has not been considered" [read: p.234 and the OCR of p.232 shown above]; Au Sable "preliminary rough measurements"; comparison data "have not been recorded"; tables are "an approximate idea" [read: p.249]. He also lists the high-frequency and impulse departures himself. 6. Impulse work (1915) is genuinely early quantitative work on volt-time behaviour with a described circuit (Fig. 147a, printed L, C, R) and with the sphere gap used as the measuring device [read: p.199, p.302].

Against (bad data and unfalsifiable steps I found in the inventor's own pages): 1. The energy-distance "bears out the theory" is not a test. Dividing eq. (21) by (22) gives a = r(g_v/g_0 - 1), so any g_v(r) curve can be written as "constant g_0 at distance a(r)" for any g_0. Peek leaves phi(r) free in eq. (23) and then reads 0.301 sqrt(r) off the fit [read: page image p.72]. The theory cannot fail; only the one-g_0, one-simple-a(r) fit and the density law carry empirical content. 2. In-sample agreement: the "generally less than 1 per cent" fit to Tables VI-VII is for data the constants were fitted to ("Sigma-Delta reduction of all of the data") [read: p.78-79]. 3. Unflagged anomalies in his own data: the two lowest-density points of Table VIII are 7.7-7.8% below the formula with no comment; Table VIII's calculated column uses 31 with 0.301 rather than 0.308; Table II and Table III disagree for the same wires (0.518 cm: 46.0 vs 44.5; 0.322: 50.5 vs 49.6) with no explanation; Fig. 39 labels the energy distance "0.27 sqrt r" against 0.301 in the text [read: pp.71, 74, 80]. 4. The two assertions "humidity has no effect" and "independent of material" are of unequal support. Material: five metals, one reading per diameter, no tungsten-vs-aluminium pair at identical diameter [read: p.71]. Humidity: asserted, with no humidity data in pp.60-92 and none in the tables I read; the sphere-gap passage repeats "Humidity has no measurable effect" [OCR p.~130, line 5171 of the text]. Hartmann's later theory puts humidity into the ionization coefficient [web: abstract]. I can say what the book does and does not show; I cannot say humidity matters. 5. Units: 0.301 carries cm^(1/2) (not stated); the letter "a" is used for both the coefficient and the distance [read: p.72]. Electron "same mass as the hydrogen ion" contradicts the 1/1800 ratio on the same page [read: p.230]; "critical voltage may also be decreased by grouping conductors" is likely a slip for "increased" (and contradicts the book's own earlier split-conductor data) [read: p.246]. 6. The impulse circuit table gives frequencies "55, 100, 350, 900 kc" that do not match the undamped LC frequency from the printed L and C (e.g. 45 kHz, 101, 285, 781; the printed 1.65 cm 900-kc needle spacing is probably 0.65 cm) [calc from printed L, C; read: p.303]. The impulse voltage is measured by the sphere gap, whose own impulse ratio is up to 1.06 at short pulses, and at sub-millimetre spacings the book itself says "accuracy best above 5 kv" while the sphere gap ratio rises to 1.5-3.3 there [read: p.306]. Needle-gap ratios are therefore measured against a reference with a few per cent systematic uncertainty. Not large enough to remove the effect.

Per-claim review

Claim 1. Peek's law of visual corona (g_v = g_0 delta (1 + 0.301 / sqrt(delta r)); independent of spacing, material, humidity)

a. Mathematics internally consistent? Yes for the formula and its reductions. Table IV's arithmetic is correct (slope 8.99, g_0 29.84, ratio 0.3013); the formula reproduces printed calculated columns to 0.1 kV/cm; the deep reads recomputed the worked example [calc]. Weaknesses: uses three different constants for three geometries (31/0.308 cylinders, 29.8-30/0.301 wires, 27.2/0.54 spheres), the difference attributed to a "balanced" field with no calculation [read: p.73, 79, 88]; ordinary least squares on all 19 points would give 30.4 and 0.286 [calc]. b. Consistent with established experimental results? Yes. The Whitehead and Whitehead-Brown a.c. data in Table IV agree within about 1.5% (0.5-0.8 kV/cm); Fitch (Johns Hopkins, pressure range) reportedly supports the form [web, unchecked]; the formula is still the standard onset estimate [web: Wikipedia]. Doubts: d.c. onset in Whitehead's compilation is 4-6% lower for a positive wire, and Watson's d.c. data fall 2-11% below a.c. (Table V, deep read); the book's d.c. section says "fair agreement" with a 6% footnote [read: p.77, p.296]. Humidity independence conflicts with the later theory which includes humidity [web: Hartmann abstract]; unresolved. c. Tested? By whom? Replicated? Peek and GE helpers (Humphrey thanked in the preface) tested polished wires indoors in a dark room; Watson, Whitehead, Fitch, Farwell and Dean are independent sources of overlapping data, partly in the book. Replicated in outline for a.c. by Whitehead (independent); density law tested by Fitch. The visual onset criterion is "first visible glow in a dark room" by observer, with number of observers and repeats per point not stated [read: p.69-70]. d. If true, what must change in mainstream physics? Nothing. It is a regularity, a compact description of onset in non-uniform fields that later streamer theory is expected to reproduce. Verdict (split). - a.c. law for polished wires and cylinders at 60 cycles, with density correction and spacing independence: Established (empirical engineering fit, independently corroborated for a.c.; constants not unique). - Independence of conductor material: Plausible, untested at the level claimed: a single series, mixed diameters; not contradicted (Table II). - Independence of humidity: Never properly tested in the pages read (asserted, no data); not dismissed without testing either: Peek says he checked, but the data are not shown here; later theory suggests a dependence. - d.c. extension: Established in the sense of the a.c. peak for Peek's own data, with contested exceptions (Whitehead and Watson 4-11% lower).

Claim 2. The energy-storage distance (finite rupturing energy requires gradient >= g_0 over 0.301 sqrt(r) cm)

a. Mathematics internally consistent? Consistent, but circular as a test: with phi(r) free, any g_v(r) curve satisfies it (a = r(g_v/g_0 - 1)) [calc, read: p.72]. Notation hazard (two meanings of a) and unstated units for 0.301. Peek writes the density form 1/sqrt(delta r) as "found experimentally" on p.67 and then as the "expected form" on p.76 [read: p.67, 76]: the logic goes in a circle between prediction and fit. b. Consistent with established experimental results? The geometrical content (the ionization region has finite thickness, thicker for larger r) matches how later onset criteria work. My own rough check: I integrated a Townsend first-coefficient alpha = A p exp(-B p/E) (A = 15 per cm Torr, B = 365 V per cm Torr: [memory, medium confidence], not verified on the web) along the 1/x wire field and found the surface field at which the integral reaches a fixed K. For K = 18 the result is 1.46 to 1.57 times Peek's g_v for r from 0.01 to 1.0 cm, a nearly constant ratio (K = 10 gives 1.26 to 1.37) [calc, crude: no attachment, no photoionization, no space charge]. So an ionization-integral criterion reproduces the 1/sqrt(r) trend of Peek's law with a roughly constant factor, and not its absolute value; a constant offset would come from the approximations, but I did not establish that. This is a consistency observation, not a derivation of 0.301. The rest of Peek's physical story (electrons as agents; ions saturating at the distance; "energy of the moving ions" as the rupture energy) is qualitative and he says so [read: p.232, 234]. c. Tested? Replicated? The postulate as stated (rupturing energy of unspecified form) has not been tested as such, because it has no measurable prediction beyond the fit. Partial test: the short-gap and sphere results of Chapter III (a prediction before data, per Peek; I cannot verify the order of events) and the delta dependence. Later onset theory (Meek criterion; Hartmann 1984) is the closest thing to a test of whether a physical criterion yields the same law. d. If true, what must change? Nothing, if read as a heuristic for ionization-region size. If the "rupturing energy" were a separate physical quantity beyond ionization growth, it would be new physics; Peek makes no such claim. Verdict (split). - Geometric statement (onset requires a finite ionization zone whose thickness scales with wire size): Plausible, untested by Peek; Established only in the weaker sense that later streamer/Townsend criteria show the same trend. - "Rupturing energy of some form" as the physical reason: Not testable as stated; Historically superseded but instructive (a pre-electron-avalanche picture, replaced by ionization-coefficient criteria). - The claim that experiment "bears out" the theory: Internally inconsistent only in the narrow sense that it is a test that cannot fail (the theory is not contradicted by its own equations; it is vacuous as a test).

Claim 3. Empirical corona-loss law, p = (244/delta)(f + 25) sqrt(r/s)(e - e_o)^2 x 10^-5 kW/km, e_o = 21.1 m_o r delta ln(s/r) kV; storm e_o x 0.8; corona an economic, not physical, limit on line voltage

a. Mathematics internally consistent? Yes, with the printed slips: A = 241 vs 244, "0.80 per cent" for 80 per cent, a cell of Table LXXIX (3,300 vs 4,300), the Hendricks spacing 48 in vs 132 cm [read: pp.237, 242, 245, 248]. e_o = 52.0 kV recomputes to 0.2%; Table LXXX reproduces with m_o = 0.87 to within 1 kV [calc, deep read]. The (f + 25) term and sqrt(r/s) are fitted forms (Line A / Line B, digest only). b. Consistent with established experimental results? Peek's own 1927 oscillograph work reports a quadratic law above e_v, a probability law below on cables, and no loss below e_v on polished wire [web: IEEE Xplore abstract]; this supports the structure but, in the cable case, indicates the formula's real domain is above e_v. Irregularity factors (0.98-0.93 weathered, 0.87-0.83 cable) are still quoted [web: Wikipedia]; alternative stranding factors (0.85, 0.92 for 3- and 9-strand, Whitehead) are noted there. The "economic not physical limit" forecast did not hold: at EHV (345 kV and up) corona loss and radio interference are design limits, handled by bundled conductors, which raise the effective radius and lower the surface gradient [web: https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/ ; https://eepower.com/technical-articles/an-introduction-to-bundled-conductors-in-transmission-lines/]. Peek's "quarter of a million volts may be used ... without excessive conductor diameter" [read: p.249] fits conductor-size growth, not bundling. c. Tested? Replicated? Fitted by Peek on his experimental lines (GE). Compared with measurements by others (Faccioli at Leadville; Hendricks 1906; N.E.L.A. Au Sable 1912) in comparisons that Peek selected and published himself (with GE a stakeholder); the book gives no numeric error statistic. Leadville's agreement is mostly below e_v where Peek calls the loss unstable. Au Sable is "preliminary rough measurements" (15 vs 15-20 kW/mile, calculator unclear). No controlled, neutral test is on record in the pages read, and the Investigator has not found one (Peek 1927 is his own). d. If true, what must change? Nothing; it is engineering interpolation. Verdict (split). - Loss formula as an engineering estimate above e_o: Never properly tested by a neutral party in the record (own fits and self-selected comparisons); it has been in use for a century [web], which is evidence of usefulness not of a controlled test; not dismissed. - Storm rule and altitude rules: Never properly tested in the record (asserted with approximate comparisons). - "Corona will rarely limit line voltage": Historically superseded but instructive (true at 1920 voltage levels, wrong at EHV, where bundling is needed). - Digest-only caveat: Chapter V (Lines A, B) not deep read; an arbiter or QE deep read of PDF pp.154-188 and 277-294 is needed before this verdict is firm.

Claim 4. Strength of air at small gaps and in thin films

a. Mathematics? Consistent: the Paschen table's delta x column equals p x / 76 (0.050/76 = 0.000658 vs 0.000660). The sphere constant 27.2 (1 + 0.54 / sqrt(R)) and the derived a = 0.27 sqrt(R) match an independently measured X = 0.54 sqrt(R); Peek says g_0 and alpha for spheres "cannot be exactly constant for a given radius" [read: p.88-90]. Fig. 39 labels the energy distance 0.27, text 0.301. b. Consistent with established results? Yes. The Paschen minimum is about 350 V at p x = 0.05 cm Hg cm in Peek's table; the modern value is about 330 V near 0.5-0.6 torr cm [memory: high confidence; Peek's table is consistent]. Small-gap strengths far above 30 kV/cm at micrometre gaps are consistent with the modern picture of gap-length scaling (Paschen; field emission at the smallest gaps [memory: medium]). Peek's attribution of this to a truncated energy distance is an interpretation; his data do not distinguish it from Paschen/Townsend. c. Tested? Data in the book: sphere gaps at 0.0025-2.54 cm (Tables IX-XII; attribution partly Peek), air films between glass plates (Dubsky 1914 cited, unclear whose data), Paschen table (no attribution). Replicated by others: Paschen's law is standard; the film results are not independently replicated in the record. d. If true, what must change? Nothing. Verdict (split). - Paschen behaviour and the high small-gap strength (the table): Established. - Thin entrapped film breaks down like a free gap of the same thickness: Plausible, untested at the thinnest spacings (g_a is 18% to 29% below g_s at 0.0025 cm and 0.0051 cm in the printed table); roughly equal from about 0.01 cm up. - "Energy distance cut short" as the explanation: Not testable as stated (see claim 2).

Claim 5. Time lag and impulse voltages

a. Mathematics? Consistent where checkable; printed frequencies differ from undamped LC values by up to about 20% except at 100 kc [calc]; some ratios differ slightly from impulse/60-cycle (oil 390/170 = 2.29 vs 2.10 printed). Wave No. 4 R = 6800 (unit not printed) gives non-oscillatory behaviour as expected [calc]. b. Consistent with established results? Yes in kind: breakdown of non-uniform gaps under fast impulses needs higher peak voltage than at 60 cycles (volt-time characteristics), sphere gaps measuring peak impulse voltage to a few per cent, and wet flashover of insulators being little affected by rain under impulse versus 60 cycles [memory: medium confidence; consistent with the book's own tables]. I did not run a web check for the modern volt-time data and do not give figures from memory. c. Tested? Replicated? Peek's own single-laboratory series, 1915 (generator Fig. 147a, described with L, C and R values), a large table set (needle ratio 1.00 at 55 kc short gaps up to 2.34 at 900 kc; sphere gaps within about 6%; oil ratios 2-3.3; solids 2.2-2.5; low density up to 5.8; polarity effect: negative point-plate spacing 3.05 vs positive 5.15 cm for the same voltage) [read: pp.302-310]. Peek's line of lightning-generator work from 1922-1932 continued the tests [web: ETHW, per Investigator], so the work was extended, not dropped. Independent replication of the numbers is not in the project documents. Anomalies to keep in the record (Peek does not comment): (i) in Table III, for the thinnest wires (r = 0.0318 and 0.0573 cm) the 100-kc impulse spark-over is below the 60-cycle spark-over (100 vs 135 kV; 100 vs 110; 33 vs 49; 35 vs 40 kV) while at 500 kc it rises above [read: page image p.304]; my untested reading is that 60-cycle corona forms a space-charge sheath that a single pulse has no time to build; (ii) the oil under continuous 90-kc voltage is 0.39 of the 60-cycle gradient (67 vs 170 kV/cm), which Peek attributes to heating without a measurement [read: p.310]; (iii) the thin-wire d.c. cases "vibrate before spark-over" [read: p.295]. d. If true, what must change? Nothing; it is an elaboration that breakdown takes finite time (formative and statistical lag), which mainstream accepts. Verdict (split). - Qualitative time lag (impulse ratio > 1, rising as the pulse shortens or density falls; sphere gaps as impulse voltmeters): Established. - The quantitative values: Plausible, untested by independent replication in the record (single lab). - "Rupturing energy" as the cause of the lag: Not testable as stated. - Rain effect on impulse flashover (2-3% vs 36-40%): Plausible, untested at the sample size of two insulators of one type plus one cask series; the direction agrees with mainstream expectations.

Claim 6. D.c. versus a.c.

a. Mathematics? Consistent. The "1.41" in the text is a d.c.-to-a.c.-effective ratio, so in the appendix (a.c. given as peak) it appears as 1.0 (the book's wording is not wrong, but invites confusion) [read: p.228; calc]. The appendix gives no thermal measurement of the heating explanation. b. Consistent with established experimental results? Air and oil: d.c. equals a.c. peak within about 5% in Peek's tables (needles in oil 0.95-1.02; corona onset equal for both polarities). Exceptions in the book: long needle gaps in air 0.92-0.93 of the peak at 12-15 cm; thin wires in cylinders spark over at 1.2-1.5 times the a.c. peak; negative wire sparks over higher than positive in every row; Whitehead's compilation has positive d.c. corona 4-6% below a.c.; Watson's d.c. 2-11% below. Solid (varnished cambric, 1-4 sheets): d.c. strength 1.27-2.59 times a.c. peak, rising with thickness and time [read: Table IX, p.299]. Modern: space charge makes d.c. corona polarity-dependent [memory: high] (a general point, I do not cite figures). c. Tested? Replicated? Peek 1916 (AIEE June) for most tables; Whitehead, Watson, Farwell for others. No independent replication of the varnished-cambric ratios in the record. Insulation type is a single material. d. If true, what must change? Nothing. Verdict (split). - Air and oil: d.c. = a.c. peak (to roughly 5%): Established for the conditions tabulated, with listed exceptions and contested polarity and thin-wire cases (Never properly tested beyond the single Peek series for the thin-wire and long-gap exceptions). - Solid insulation d.c. gain larger than 41%: Established as a measurement on one material (varnished cambric, Peek 1916) and Plausible, untested as to heating being the cause (no thermal data).

Summary for the arbiter

  • Where evidence is strongest: the a.c. onset law and the density law (claim 1), Paschen behaviour (claim 4) and the qualitative impulse time lag (claim 5).
  • Where evidence is weak: the "energy distance" as physics (vacuous as a test; its form is untestable), the loss law's neutral testing (self-selected comparisons; Chapter V not deep-read), humidity independence (asserted), and the economic-limit forecast (superseded).
  • What would settle it: (1) read Peek 1911 Part I for the discarded points and refit; (2) a Townsend/streamer integral with documented air constants against Peek's g_v(r) over 0.01-1 cm (my crude run reproduces the trend only); (3) read Peek 1927 Part IV for any statement of the rupturing energy and for loss data on the cables; (4) deep read PDF pp.154-188 (Lines A and B, single- or three-phase unknown) and 277-294.

Web sources used (4 calls): https://en.wikipedia.org/wiki/Peek%27s_law ; https://eepower.com/technical-articles/understanding-corona-discharge-in-high-voltage-transmission-lines/ ; https://eepower.com/technical-articles/an-introduction-to-bundled-conductors-in-transmission-lines/ ; a search on Hartmann 1984 (summary only; abstract at https://ieeexplore.ieee.org/document/4504655).