Peek-Frank: Quality Engineering (Step 4b)

Scope: the whole work product for one document, F. W. Peek Jr., Dielectric Phenomena in High Voltage Engineering, 2nd ed., McGraw-Hill 1920 (325-page scan, 324 pages OCR). I read the manifest, all eight digests, the full deep-read file (three sections: PDF pp.227-251, 60-92, 295-311), facts.json, claims.md, sites.md, the research notes, the three reviews, arbiter.md and primer.md, and I ran example.py. I checked load-bearing statements against the extracted text (_text/...13a0e3.txt, cited below by line number and PDF page).

Tags: [read: p.N] = PDF page of the extracted text; [read: line N] = line of the extracted text file; [calc] = my arithmetic.

Verdict: MINOR. The headline verdicts hold up (Peek's law Established; loss law Plausible, untested by a neutral party; time lag Established). But the core of the loss-law claim (claim 3) still rests on digests and partial text-layer reads. Two passages that bear directly on the "rupturing energy" verdicts (claims 2 and 5) and one out-of-range test of the loss law were missed at every step after the digests. One Paschen-branch error runs through three files, and the primer contradicts itself on it. All of this can be fixed by deep reads, a "QE revision" section in arbiter.md, and edits to facts.json, claims.md and primer.md. A full redo of Steps 2-4 is not needed.

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1. Coverage

• The manifest lists one document. It has 8 chunks covering PDF pp.1-325, and all 8 were digested, with no gaps in the page sequence. Nothing was skipped by Step 0. No coverage defect.
• Digest quality: the digests are usable but have errors that only a deep read or the raw text catches. Examples: the digest of p.92 gives water-coated wire as "17(1 + 0.301/sqrt r)" where the page image reads 9(1 + 0.815/sqrt r) [deep, page image p.92]; the digest of p.176 gives "mean g_o = 29" for Table LIX, but Table LIX (cables) averages 25.7 and 29 is the wire value [read: lines 8160-8223]; the digest of p.170 has "(r + 240.04)", an OCR form of (r + 0.04). Downstream files used the correct values in each case.

2. Shortcuts

3. Missed material

Every item below is in the digests or the extracted text. None of them appears in facts.json, claims.md, the reviews, the arbiter or the primer, unless a row says otherwise.

1. Measured minimum breakdown energies, from Hayden and Steinmetz (A.I.E.E., June 1910). Peek quotes this investigation twice. First: "the disruptive discharge through a dielectric requires not merely a sufficiently high voltage, but requires a definite minimum amount of energy ... a finite, though usually very small, time elapses ... During this time the disruptive energy is supplied to the dielectric", followed by "The disruptive energy of oil seems to be about 30 times greater than it is for air" [read: p.148, lines 6683-6695; footnote "Hayden and Steinmetz, A.I.E.E., June, 1910", line 6712]. Second: "when the energy is limited a voltage is reached where the spark distance becomes a function of the energy and practically independent of the voltage". For sphere gaps set to 30 kV at 60 cycles and hit by a 100 kV transient, the oil gap "will not spark over if the energy applied to the circuit is less than 1.04 joules (4 amp.). For air the minimum energy is 0.45 joule (1.5 amp.)" (Figs. 148-151) [read: p.202, lines 9686-9701; footnote line 9720]. - Why it matters: the Mathematician writes "no energy is ever computed and no units are attached to it" and "there is no number for the 'rupturing energy'", and primer Section 7 writes that the energy "was never defined, given units or computed". In the book, energy in joules and an oil-to-air ratio do appear. They are circuit energies from another investigation, not an energy stored in Peek's 0.301 sqrt(r) zone, so the criticism of the corona "energy distance" (claim 2) stands. But the claim 5 statement that rupture "needs a minimum energy" has a measured, testable form in the book. The verdicts "Not testable as stated" (Mathematician, Contrarian) and "Historically superseded but instructive" (arbiter) for the minimum-energy explanation of time lag must be re-weighed against it. - Interested parties: Steinmetz was GE's chief consulting engineer, so this is GE data too [memory, high]. Nobody has read the 1910 paper. It should go on the Investigator's next run.
2. Corona loss measured at 100,000 cycles (Alexanderson). Fig. 140 compares formula (34a) with loss measured on two parallel wires (spacing 67 cm, radius 0.127 cm, length 200 cm, f = 100,000) fed from an Alexanderson alternator, with power found at unity power factor from hot-wire meters. Peek: "This good check seems to show that the formula applies over a large range, but complete conclusions cannot be drawn from this small amount of data" [read: p.189, lines 8987-9008]. That is about 1000 times the fitted 25-120 Hz range of the (f + 25) term. It is the only out-of-sample test of the loss law in the book. It is also a GE measurement (Alexanderson was a GE engineer [memory, high]) and it is small. The arbiter's claim 3 verdict ("Plausible, untested by a neutral party") and the primer evidence table must mention it.
3. Corona-driven mechanical vibration of conductors. A pair of 20-mil steel conductors 500 ft long at about 10 ft spacing "vibrated, starting with a hardly perceptible movement, which in a few minutes had an amplitude of several feet at the center of the span". One wire vibrated as the fundamental and the other as the third harmonic, period about 1 s. The effect was repeated in the laboratory (Figs. 83-84). The rotating wire looked bright for half a turn, "as stroboscope", which Peek reads as rotation at the 60 Hz supply frequency [read: p.113, lines 4550-4568]. This is a striking experimental observation. The primer mentions only the d.c. table's "vibrates before spark-over".
4. Chapter V content that answers "unknowns" in the deep read. The loss below e_o is fitted to a probability curve (eq. 37) with q = number of rough spots and h = spot size, and values are given in Fig. 133 [digest p.181-183]. The deep read (section 2) and the Mathematician (claim 3a) call q and h undefined. Chapter V also gives a small-conductor law, c^2 = 20,500 sqrt((r + 0.04)/s), which Peek reads as residual ionization enlarging the effective radius, together with a separate disruptive gradient g_d for small wires (Table LX, 30.8-67.5 kV/cm) [digest p.170-179; read: lines 8069-8076]. A temperature series puts 1/e_o on a straight line through -273 C, a field-line check of the density law [read: p.183, line 8649]. Wind did not change measured loss even though laboratory tests showed loss rising with air velocity, and Steinmetz observed that fog raises striking distance [digest p.185-186; read: line 8759].
5. Split conductors and stranding (pp.95-98). Three conductors in a triangle give 20-30% higher critical voltage than one wire of the same total material, and Whitehead found 16% for three and 20% for four [digest]. This is the book's own evidence that the "decreased" on p.246 is a misprint, and it anticipates the bundled conductors the arbiter cites for EHV. facts.json has it only as an unverified digest line.
6. Other book content left out (peripheral, but listed for completeness): - corona contains a large ultraviolet component (apparent diameters 1 : 1.6 : 1.9 by eye, glass lens and quartz lens) [digest p.99-104]; - negative corona appears to throw metal or oxide off the surface [digest p.105]; - cumulative impulse damage: an insulator survives nine impulses at 3 times the 60-cycle puncture voltage and fails on the tenth, and oiled pressboard has a number-of-impulses-to-failure table [digest p.214-216]; - a time law for the strength of solid insulation [digest p.216-217]; - oil energy distance 1.2 sqrt(r), and oil with barriers above 700 kV/cm [digest p.195-196]; - wet flashover of bushings 50-90% of dry [digest p.151]; - "Case 1": adding a stronger insulation causes breakdown [digest p.252-254], which is a good worked example of series dielectrics for the reader.

4. Accuracy spot checks (against the extracted text)

1. A = 241 in Chapter V. The text prints "p = 241(f + 25) ... 10^-5 kw./km." and "c^2 = 20,500 ..." [read: lines 7980, 8069-8076]. The 241/244 inconsistency is confirmed. Pass.
2. Apparent g_o for stranded cable, 25.6-25.8 kV/cm, against 29 for wires (used by the Mathematician and primer Step 6 to show that m_o = 0.87 is a ratio of apparent strengths). The text gives "average value of g_o is 25.8 ... 25.6 kv. per centimeter maximum" for cables, Table LIX total average 25.7, and "g_o = 29 kv. per cm." for wires [read: lines 8160-8223]. 25.7/29.5 = 0.87 [calc]. Pass. The digest of p.176 is wrong on this point; downstream files are right.
3. Line A was single-phase (arbiter item 3; primer evidence table). Line 472 reads "Tests were made on single-phase lines unless otherwise noted" (p.20). Pass, with one correction to the citation: the arbiter's second source, line 13487 ("As these measurements were made on a single-phase line"), is the note to the indoor-line tables (p.277). The direct statement for the outdoor lines is on p.286: "These tests were made on comparatively long single-phase lines out of doors" [read: line 13872], followed by the Line A tests 146 and 18 on p.287. So the arbiter's residual caveat ("I found no Line A-specific statement") can be dropped.
4. Table I "Average, 99.0" is printed as stated [read: line 2676]. The column mean of 98.4 was recomputed by the deep reader. Pass.
5. Paschen branch for Peek's 0.00254 cm gap. p x = 760 torr x 0.00254 cm = 1.93 torr cm. The air minimum is near 0.57 torr cm [web: https://en.wikipedia.org/wiki/Paschen%27s_law, as cited in the primer], so this point lies on the right-hand branch, near the minimum [calc]. Primer answer 3 says this correctly. But primer Section 4's side-by-side table ("Small gaps ... The left branch of the Paschen curve: too little path for the avalanche"), the Physicist (claim 4 verdict, "qualitatively the left-hand branch") and the Mathematician (claim 4b, "a well-known feature of the left branch") all say left. Fail. The high average field V/d at small gaps at atmospheric pressure comes from V falling much more slowly than d on the right branch. It is not left-branch behaviour. The primer contradicts itself.

Also checked: example.py runs to completion (exit 0) and reproduces every number in primer Section 5. Its docstring says "Five steps" but lists and runs six (cosmetic). The water-film formula used by the Physicist, 9(1 + 0.815/sqrt r), matches the deep reader's page-image reading. The text layer is blank at that point [read: lines 3854-3858], so the digest's 17(...) has no source.

5. Retention

• I found no pertinent material that was dropped from the arbiter or primer because a reviewer judged it negatively. The Contrarian's anomalies are kept in both files: the thin-wire 100 kc impulse spark-over below the 60-cycle value, oil at 90 kc holding 0.39 of its 60-cycle strength, and "vibrates before spark-over". So are the Contrarian's "never properly tested" reading of the loss law and the Physicist's polarity exceptions for d.c. No retention defect of the kind STEP 4b names.
• The Investigator's leads are kept: Fitch 1913, Hartmann 1984, Peek 1927 Part IV, the 1911 Part I paper, the 1929 edition, Union College, the Steinmetz "Wrestling with Nature" snippet, the Stanford offer and the lightning generators all appear in the arbiter or primer. The 19 GE patents are in the primer but not the arbiter.
• Minor omissions (not caused by negative judgement): the Investigator's evidence of continued use, Electronics 1950 and Westinghouse Engineer 1951 [sites.md, worldradiohistory], and the German VDI 1932 report of Peek's 10 MV generator appear in neither the arbiter nor the primer. The arbiter's "century of use" rests on other sources. Add them as one line.
• Missed-material items 1-2 (Section 3) are not retention failures, since no reviewer saw them. But the primer's statement that the energy was "never ... given units or computed" now runs against material in the source. It must be corrected (see remediation).

6. Process

• Source tags. Present and mostly honest throughout. The fetch-tool summaries of Fitch and the search snippets on Hartmann and humidity are labelled as such in every file. Good practice.
• Web checks. Physicist used 3 of about 6 calls. He left "EHV corona is a design limit" as [memory, medium; not web-checked] even though it carries a split verdict. The arbiter later retagged it [web] through the Contrarian's eepower source, so it is resolved. The Physicist's uniform-field formula, V = 24.22 pd + 6.08 sqrt(pd) [memory, medium], was not checked, and the primer carries it into Section 3 ("about 26 kV/cm average at 10 cm [memory, medium]"). It is not load-bearing, but it should be checked or removed. The Townsend constants A = 15, B = 365 [memory, medium] drive the shape calculation in the Contrarian, arbiter and primer. The arbiter says the form is confirmed and the values are not; the primer repeats that caveat. Acceptable as disclosed. Mathematician used 2 of 6, and his K = 18-20 [memory, medium] is confirmed elsewhere [web: arxiv physics/0508109, Physicist].
• Verdict scale. Applied consistently by the arbiter. The Contrarian's claim 2 label "Internally inconsistent only in the narrow sense that it is a test that cannot fail" misuses the scale term (by his own words the theory does not contradict itself). The arbiter rightly did not adopt it. The Mathematician's "single-source (Peek, GE, 1915)" for claim 5 numbers is a description, not a scale verdict; the arbiter turned it into "Plausible, untested". Fine.
• Primer against STEP 4. All nine sections are present and in order, with answers at the end, example.py present and running, and the evidence table in the required columns. The source-gap note is repeated. Reader profile: symbols are defined, and acronyms mostly are (OCR, GE, APS, EHV). Undefined on first use: AIEE (Section 9 and Section 7), IEC (Section 3), N.E.L.A. (evidence table), kc (evidence table, claim 5). Minor.
• Source-gap note is repeated in claims.md, all reviews, arbiter and primer, as required.

7. Remediation (one round)

Deep reads (most important first; slug Dielectric-phenomena-in-high-voltage-eng-NNNEEEEWWWW-13a0e3)

1. Opus, PDF pp.154-188 (Chapter V). Question: Lines A and B and the indoor line. Give the full fitting chain for p = a(f + 25)(e - e_o)^2: Tables XLIII-LVII with the scale of the c^2 values (10^-5 or 10^-8, from the page image), the Sigma-Delta reductions, the c^2 against sqrt(r/s) fit and its scatter, and how A = 241 was reached. Also the small-conductor law c^2 = 20,500 sqrt((r + 0.04)/s) and g_d (Table LX); the probability curve eq. (37) with q and h (Fig. 133); the temperature series (Table LXII, 1/e_o through -273 C); humidity and vapour results (Table LXIII); fog, smoke, wind, sleet and snow; and the 100,000-cycle Alexanderson check (Fig. 140). Say for every test whether it is single-phase, and which data are out of sample.
2. Opus, PDF pp.196-202 (end of Chapter VI, oil impulse and energy). Question: what exactly do Hayden and Steinmetz (1910) and Figs. 148-151 show about energy-limited breakdown? Read the curves from page images. Answer: what energy is measured (circuit or gap), how 1.04 J and 0.45 J were obtained, whether "spark distance a function of the energy and practically independent of the voltage" is supported by the plotted data, and how this bears on Peek's "minimum energy" explanation of time lag. Include Table LXIX and the 60-cycle against impulse figures for oil.
3. Sonnet, PDF pp.139-151 (Chapter IV, second half). Question: impulse ratio Tables XXXV-XXXVII (needles, spheres, the parallel-gap method), the 5 x 10^-7 s impulse description, the Hayden-Steinmetz passage and "oil about 30 times air" (p.148) with its footnote, the rain ratio of about 2.5 for spheres, and the altitude tables XXXVIII-XLII with the worked examples. Quote numbers from page images.
4. Sonnet, PDF pp.277-294 (measured corona-loss data appendix). Question: transcribe the indoor tests 10B-54B and the outdoor Line A and B tests from page images (conductor, spacing, length, delta, kV, kW/km), so that the loss law can be refitted independently of Peek's reductions. Flag which tests feed Table LV.
5. Sonnet, PDF pp.93-113 (Chapter III continued). Question: stranding and irregularity factors (Table XVI, m_v 0.72/0.82), the split-conductor results (20-30% Peek, 16%/20% Whitehead) with conditions, corona photography and ultraviolet diameters (Tables XVII-XVIII), stroboscope polarity observations, the 500-ft steel-conductor vibration and Figs. 83-84, and Bennett's oscillograms. Confirm the numbers that support calling the p.246 "decreased" a misprint.
6. Sonnet, PDF pp.115-138 (Chapter IV, first half). Question: parallel-wire spark-over (Tables XIX-XX, critical ratio S/r = 30), the sphere-gap tables XXI-XXXIII and the 27.23(1 + 0.54/sqrt(delta R)) density law with its stated accuracy (2-3%, under 0.5% for grounded spheres), and the precautions on which the sphere-gap voltmeter claim rests.
7. Sonnet, PDF pp.202-227 (Chapter VII, solid insulation). Question: the rapid, one-minute and endurance tests; the time law of strength and its constants (p.216-217); the cumulative impulse damage examples (insulator failing on the tenth impulse; pressboard impulses-to-failure table); loss proportional to e^2 and to frequency; and any measurement behind the "a.c. heating" explanation used in claim 6.

What each later file must change (MINOR route)

• facts.json:
• Update how_read with the new deep reads.
• Add key claims for the Hayden-Steinmetz energy result (with the GE stake noted), the Alexanderson 100 kHz loss check, corona-driven conductor vibration, the split-conductor 20-30% (now [read]), and q/h and the small-conductor law from Chapter V.
• Mark "humidity has no effect" and "down to delta = 0.02" as assertions.
• Correct "50 to 90 percent ... digest summary" so it is clearly the bushing wet-flashover figure (p.151), separate from the Table VIII 36-40%.
• claims.md:
• Claim 3: drop "whether Line A was single- or three-phase is also unstated" (it is single-phase, p.20 and p.286), and add the 100 kHz check.
• Claim 4: 196 kV/cm is the free sphere-gap value; the entrapped-film value is 161 kV/cm (Contrarian correction).
• Claim 5: add that the minimum-energy idea has a measured form in the book (Hayden and Steinmetz 1910: 0.45 J air, 1.04 J oil; oil about 30 times air).
• arbiter.md, new "QE revision" section:
• (a) Re-weigh the claim 5 sub-verdict on "minimum energy" in light of the Hayden-Steinmetz data and deep read 2. If energy-limited breakdown is shown in Figs. 148-151, "Not testable as stated" no longer fits that sub-claim; the candidates are Established (as a circuit-energy threshold) or Plausible, untested, with the mechanism reading kept as Historically superseded.
• (b) Re-weigh claim 3 with the Alexanderson 100 kHz out-of-sample check (GE, small data set) and the deep reads of Chapter V and the loss appendix.
• (c) Correct item 3's citation (line 13487 is the indoor line; cite p.286, line 13872) and drop the residual caveat.
• (d) Correct "left-hand branch" to right-hand branch wherever the Physicist's or Mathematician's wording is relied on.
• (e) Note the Investigator's 1950-51 continued-use items, the 19 GE patents, and Hayden and Steinmetz 1910 as a record to obtain.
• primer.md:
• Section 4 table, "Small gaps" row: change "left branch" to "right-hand branch near the minimum: V falls much more slowly than d, so V/d is large", consistent with answer 3.
• Section 7, "never defined, given units or computed": correct it. Peek's corona "energy distance" energy is never computed, but the book does cite measured minimum breakdown energies for impulse circuits (0.45 J air, 1.04 J oil; Hayden and Steinmetz 1910) and an oil-to-air ratio of about 30. Explain to the reader why a circuit energy is not the same as Peek's stored rupturing energy.
• Section 6, evidence table: add a row or note for the 100 kHz Alexanderson check under claim 3, and update claim 5's mechanism verdict to match the arbiter's QE revision.
• Section 7: add corona-driven conductor vibration to the anomalies kept in the record.
• Define AIEE, IEC, N.E.L.A. and kc on first use.
• Check or remove the [memory, medium] uniform-field figure (26 kV/cm at 10 cm) in Section 3.
• example.py: change "Five steps" to "Six steps" in the docstring (cosmetic).

Recheck

Checked against the current arbiter.md, claims.md, facts.json, primer.md and example.py (grep and spot reads; I did not redo the deep reads).

Final: PASS