Arbiter: Kennard, "On Unipolar Induction" (1917)

Document: E. H. Kennard, Phil. Mag. (6) 33, 179-190 (1917; signed Univ. of Minnesota, August 1916). Inputs weighed: physicist.md, mathematician.md, contrarian.md, deep/, facts.json, claims.md, sites.md, research/. Tags: [read], [web] (URL), [memory] (confidence), [calc] (my recomputation in the project venv).

Source gap note. No gap for the main work. The whole paper was read: pp.1-9 deep read against page images, and pp.10-12 (sections 7-8) in the cleaner Internet Archive OCR and page 189 image. The "pp.10-12 rest on the digest alone" caveat in claims.md is closed (all three reviewers confirm). Gaps that remain, and that no verdict rests on: Pegram, Phys. Rev. 10, 591 (1917) was never obtained, so the independent replication is known only from Barnett 1919 and Chyba et al. 2025; Fehrle 1913, Kennard 1913 (Phys. Rev. 1, 355), the Phys. Zeits. replies, the 1922 NRC bulletin and the AIP papers were not read.

0. The physics in brief (reader profile)

Take a charge q moving at velocity v in a magnetic field B. It feels a force q(v x B)/c in Gaussian units (c = speed of light, x = vector cross product). Per unit charge this is Kennard's "electromotive intensity" (1/c)[v x B]. The old question was: v relative to what? Two main answers competed.

• Lorentz view (the one now standard). v is the charge's velocity in the frame where the field is described. An axially symmetric steady field looks the same whether or not its source spins about the axis, so spinning the solenoid alone does nothing.
• Moving-line view (Barnett's, 1912). The field lines are carried round with the magnet, so only relative motion counts.

The apparatus is a cylindrical condenser (two coaxial brass cylinders) inside a 22.5 cm solenoid. Either can be spun, alone or together. Predictions:

Results: both together gave charging; the solenoid alone gave about nothing. That favours Lorentz and rules out the moving-line theory.

1. Numbers recomputed [calc]

Where reviewers differed or Kennard's printing is doubtful:

• Prediction chain. B = 4π(1150/22.5)(25)/10 = 1606 gauss (printed 1600). Flux through r = 3.32 cm: 55,600 Mx (printed 55,400). V0 = 55,400 x 33 x 10^-8 = 0.0183 V. Rim speed 2π(33)(0.0332 m) = 6.9 m/s, so v/c is about 2.3 x 10^-8; the effect is first order in v/c and needs no relativity. All three reviewers agree.
• Ratio 0.231. (20.5/62.2)(0.1/0.1197)(6.22/7.42) = 0.2308. With the OCR misreading "26.5" it would be 0.298. The correct value is 20.5 (all agree).
• Both-together ratios. 0.237, 0.237, 0.236, 0.258: mean 0.2420, SD 0.0107, standard error 0.0053 (2.2%). The offset from 0.2308 is +4.9% (Kennard's "5%"), i.e. 2.1 standard errors. The mathematician is right that this is only marginally compatible with a naive stated precision. The contrarian's "under one standard error" is wrong: an offset of 0.011 against SE 0.0053 is about 2. Pooling the three groups (0.242, 0.228, 0.238) gives +2.3%.
• Half-speed. 0.228/0.2308 = -1.2%. Kennard prints "1.4%", a trivial difference.
• Solenoid alone. The contrarian's list (+0.4, +0.6, -1.1, +3.5) uses the raw printed signs. The sign-weighted values (weight by S x I as for "Rev. av.") are -0.4, +0.6, +1.1, +3.5. Mean +1.2 mm, SD 1.66, SE 0.83 mm. That is about 1.5 sigma from zero and 7.5% of the 16.1 mm mean full effect. The physicist and the deep read are right; the contrarian's mean from his own list (0.85) is not Kennard's printed 1.2. Neither changes the verdict.
• Absolute prediction. 0.114 x 18000/138 = 14.87 mm; the printed 0.117 would give 15.26 mm, so 0.117 is a misprint (all agree). 0.02 x 0.140 = 0.0028, not 0.03; 0.02 x 1.40 = 0.028, so "0.140" is a misprint for 1.40. Measured mean |E| in the both rows is 16.1 mm, 8% above the 14.9 mm prediction. Speed varied and was not logged, so Kennard rightly used the ratio.
• 13 A against 25 A. 0.25 against 0.27 is 8% apart (0.27/0.25 = +8.0%) with no comment from Kennard.
• div(v x B). For rigid rotation v = ωr φ̂ and B = B ẑ, v x B = ωrB r̂, with divergence (1/r) d(r ωrB)/dr = 2ωB, nonzero [SymPy: 2Bw]. All three agree.
• Centripetal acceleration. ω²r is linear in r. Kennard's printed "proportional to the square of the distance" (IA OCR p.190 line 635, and the page image per the mathematician) is wrong as stated. See claim 6.

2. Claim-by-claim

Claim 1. A condenser rotated in a magnetised coaxial solenoid charges as Lorentz predicts, despite a co-rotating metal screen

• Agreement. All three: Established; mathematics consistent; nothing in mainstream physics changes (it is mainstream).
• Disagreement. None on the verdict. The contrarian adds a process caveat: four sets rejected "for very obvious good reason", about as many abandoned for disturbances, a 10,000 ohm resistance "accidentally left in place" [read: pp.3, 8], none quantified.
• Stronger argument. The physicist's. A screen cannot cancel the effect, because the force acts on the electrons in the metal itself. The contrarian's own counterweight also holds: the sign reverses with both current and rotation direction in every row (+14.4, -15.6, +16.4, -18.0 mm), which a drifting spurious cause would not do.
• Evidence. Kennard 1917; Pegram (Phys. Rev. 10, 591, 1917) reported by Barnett 1919 as finding "the condenser ... to become charged in accordance with the theory" [read: Barnett 1919 AIEE report, research/files]. Barnett was Kennard's rival; his confirmation runs against his own earlier position. Chyba, Hand and Chyba (2025) call the Barnett-Kennard-Pegram result "a standard part of the electromagnetics literature" [read: research/files]. They have a stake (an Earth-rotation power proposal). Pegram's paper is unread.
• What would settle it. Nothing is in doubt. A modern repeat with this geometry, or reading Pegram's paper, would add precision.
• Final verdict: Established.

Claim 2. Ratio 0.242 against 0.231 (5%); 0.228 at half speed; computed charge -6.22 V0 +/-0.5%

• Agreement. The arithmetic is right. The effect is established.
• Disagreement. Wording of the quantitative verdict: physicist "Established ... 5%/0.5% not supported"; mathematician "Established at the ~5% level"; contrarian "effect Established; 5% agreement Plausible, limited precision".
• Weighing. All three reach the same substance. The data scatter by about +/-10-15% per set (0.195-0.271 alternative method; 0.211-0.263 half speed). Groups range from -1.2% to +4.9% about theory, and the 13 A/25 A groups differ by 8% unexplained. The "+/-0.5%" is Kennard's accuracy for the calculated charge, not for the comparison; it cannot be checked from the paper, since the Bessel-series solution is printed for the outer space only. My own check [calc]: an infinite coaxial condenser of this radius ratio gives about -5 V0 (physicist: 15.1/(2 ln 4.31) = 5.2 e.s.u.), against -6.22 V0 with end effects and guard rings; same order, not independently reproduced. The discriminating power does not rest on the 5%. The rival theories predict zero, and the observed ratio is about 0.24 against 0.23, so the test is decisive for the qualitative question and only good to a few percent for the quantitative one.
• Final verdict: Established for the effect and its magnitude to a few percent (one apparatus, "somewhat rough" in Kennard's words). The sub-claims of 5% and 0.5% precision are not supported by the paper's own scatter; that is a precision caveat, not a refutation.
• What would settle it. (1) A numerical re-solution of the two-cylinder boundary-value problem (finite-difference or series) to confirm -6.22 V0; the mathematician rates this an afternoon's work and it suits the primer's worked example. (2) A repeat with logged speed and a reported error budget.

Claim 3. Solenoid rotating alone gives no charge (reversing average +1.2 mm, against about 15 mm)

• Agreement. Established; consistent with Barnett (1912) and with the modern account that an axisymmetric field does not co-rotate with its source.
• Disagreement. Strength of the null. The physicist says the null is 8% of the full effect and 1.5 sigma. The mathematician says the bound is about 10% at best. The contrarian says "a few per cent". My recomputation puts it at 7.5% of 16.1 mm, with a 0.8 mm standard error, so it is a bound of roughly 10%, not a few percent. The mathematician and the physicist are stronger.
• Added limitation (physicist and mathematician, confirmed in the table): in the solenoid-alone rows G = 0, because the speed monitor is the Faraday disk on the condenser shaft, which is not turning. The speed is unrecorded, so the comparison with "about 15 mm" assumes similar speed. Kennard says "No means being at hand to record the instantaneous speed" [read: p.4]. The correct baseline is the 14.9 mm prediction or the 16.1 mm both-rows mean, not a number Kennard gives for these rows.
• Open modern flags, kept. Su (2005, arXiv physics/0512179) argues a short or non-uniform solenoid could leave a small residual under a modified Lorentz law. Su is the author of a "local-ether" theory, a stake to note [read: Su 2005, reference list]. Kennard's solenoid is 22.5 cm long with a 3.3 cm condenser radius, so end effects are not negligible, and a null of 1.2 +/- 0.8 mm leaves room for a small effect. Su does not address the corotation result. Baumgartel and Maher (2022, Sci. Rep.) say some authors need Ampere's force while others say classical explanations suffice, "albeit a full re-analysis ... with due regard to the influence of the closing wire might be necessary" [read: research/files]. This is unresolved among homopolar-motor theorists and does not touch the voltage-level charge measurement.
• What would settle it. A repeat with a logged speed on the rotating solenoid and a long-solenoid versus short-solenoid comparison, to bound any end-effect residual below 1%.
• Final verdict: Established, as a null of about 10% (not a precision null), on one apparatus plus Barnett 1912. Barnett and Kennard disputed the interpretation but agree on this fact, which adds weight.

Claim 4. Condenser alone, not completed (solenoid short-circuited), inferred by superposition with a partial 14 mm check

• Agreement. The inference is valid within linear theory and is a consequence of claims 1 and 3, not an independent test (all three). The 14 mm check has no galvanometer normalisation and a loosely specified speed ("under about the same conditions" [read: p.9]).
• Disagreement. The physicist labels it "Plausible, untested ... content Established via Barnett". The mathematician splits it: logic Established, direct run Never properly tested. The contrarian says Plausible, untested.
• Weighing. The mathematician's split is the cleanest. The run was not dismissed; it was abandoned for a stated apparatus failure ("not thought worth while to rewind it"), to Kennard's credit. Barnett 1919 describes the combined result as a corollary and "superposed" of his earlier condenser-rotating work [read: p.1510]. That is a statement in his text, not a measurement I can cite. The physicist's claim that Barnett "measured" condenser rotation in 1912 comes from Barnett's own 1919 account, so I mark it as second-hand.
• What would settle it. One run with only the condenser turning, with the galvanometer speed monitor active, giving E/G near 0.231.
• Final verdict: split. The logical inference: Established. The direct measurement by Kennard: Never properly tested (abandoned for apparatus failure, not dismissed). A single rough 14 mm run, against 14.9 mm predicted, is consistent with the inference but is not a test. Not load-bearing for the paper's conclusion.

Claim 5. The moving-line theory is disproved

• Agreement. The maths (div(v x B) = 2ωB) is correct. The experiments reject the moving-line theory. All three say "disproved" over-reads the Laplace argument alone.
• Disagreement. How to label it. The physicist: Refuted by calculation (vacuum-EMF form) plus Tested, not supported. The mathematician: experimental disproof Established, Laplace argument Plausible but incomplete. The contrarian: strict form Tested, not supported, with "no room left" overstated.
• Weighing. The mathematician's reading is the stronger and I adopt it. Kennard's reductio defeats one version: Barnett's pair of assumptions, namely f as an electric field in free ether with div(Kf) = 4πρ. Kennard himself concedes the escape ("the lines do not act on the ether, but only on material bodies"), and that escape is equally open to a relative-velocity theorist. So the algebra shows Barnett's extra assumption fails; the experiments do the disproving. Kennard's own sentence puts the weight on experiments ("definitely disposed of by the results obtained by Barnett, Fehrle, and the author"), so he does not claim more than that. "Refuted by calculation" on the scale means accepted laws applied correctly rule it out. That fits only the vacuum-EMF version, and I record it for that version only.
• Rejection history (kept as record). Barnett (1912, 1913) called Kennard's 1912 work "inconclusive" and "based on incorrect theory" and wrote "Mr. Kennard's fallacies are quite apparent" [read: Barnett PDFs in research/files, as quoted by the Investigator; neither the physicist nor the contrarian read these in full]. This is a direct rival's characterisation. His technical point (in 1912 only the iron core turned, so the fraction of "lines" that moved is unknown) was fair, and the 1917 design answers it. Kennard says Barnett maintained his view "with some heat" [read: p.9]. By 1919 Barnett accepted the corotation result and framed the options as "(1) the ether does not exist and the tubes of induction do not move, or (2) the ether exists" [read: Barnett 1919, p.1511]. The papers appeared in the Phil. Mag. and were abstracted in German journals in 1917 [Investigator, Google Books snippets]. I find no evidence of suppression or blocked publication. The dispute was open in the journals and was settled by experiment.
• What would settle it. Already settled experimentally for the relative-rotation-only idea. To close the logical gap in the Laplace argument, one would state a moving-line theory that applies only to material bodies and derive its predictions for the three cases; the table above shows it predicts the opposite of both results.
• Final verdict: split. The moving-line theory, in which only relative motion between magnet and conductor matters: Tested, not supported (Barnett, Kennard, Pegram). The version with an EMF of the form (1/c)[v x B] in free space together with div(Kf) = 4πρ: Internally inconsistent / refuted by calculation (div(v x B) = 2ωB). The Laplace argument alone, as a proof that no relative-velocity theory can work: not established; Kennard's claim is stronger than the algebra.

Claim 6. Induction depends partly on absolute rotation; the radial force "can only be explained" by motion relative to a stationary Lorentz aether

• Agreement. The "absolute rotation" part is established and uncontroversial (rotation relative to an inertial frame; gyrocompass, Foucault pendulum). The aether step is an interpretation, not a derived result, and the experiment cannot distinguish Lorentz's aether theory from special relativity in inertial frames. The claims.md wording "can only be explained" is stronger than Kennard's text: "Apparently the only remaining alternative ... must be" [read: p.190].
• Disagreement 1: the "square of the distance" sentence. The mathematician calls it an error. The physicist is silent. The contrarian calls it "loosely worded" and reads Kennard as meaning speed squared. The printed text is clear [read: IA OCR p.189-190]: "the radial acceleration, for that is proportional to the square of the distance". Centripetal acceleration ω²r is linear in r [calc]. The mathematician is right: as printed it is wrong, and the contrarian's charitable reading is a reconstruction. The conclusion of that step survives for a different reason. An ω² effect would not reverse sign with the sense of rotation, whereas the observed effect does (rows with S = + and S = - reverse).
• Disagreement 2: the verdict label. Physicist: 6a Established, 6b weak step, 6c Not testable as stated, and historically superseded but instructive. Mathematician: "stationary ether required" is Historically superseded but instructive. Contrarian: same.
• Weighing. The three agree on substance. The elimination list omits the electromagnetic field and the inertial frame defined by dynamics as the reference. That is the physicist's point about "the field in an inertial frame" and the mathematician's about the bucket and gyrocompass. Kennard's phrase about "rotation relative to the earth ... in some unknown way" is a statement about the Earth, not the apparatus frame. The laboratory is nearly inertial (Earth-rotation corrections of order (v/c)² ~ 10^-12 per Chyba 2025). In that frame the force is the plain Lorentz force; nothing "unknown" is needed. Chyba et al. read v as the charge velocity "relative to a frame in which the magnetic flux density is B" [read]. The physicist notes the word "aether" does not appear in that paper, so "not an aether" is an inference from silence. Kennard's closing statement that the result "seems ... to lend definite support to the existence of an electromagnetic ether" and is a "stumbling-block ... for those ultra-relativitists" [read: pp.189-190] was an overreach. Kennard's own 1912 paper said his method "is not capable of distinguishing" Lorentz from Hertz [web, per Investigator, IA OCR]. Barnett 1919 is explicit that the experiments are "not inconsistent with the principle of relativity of Einstein, which relates to translatory motion only" [read: p.1511].
• Interested parties. The relative-velocity/Weber school (Su, Wesley, Assis, Guala-Valverde) says the open-circuit results are not trivially relativistic; some mainstream sources call that school fringe, which is their characterisation. These authors have their own theories at stake. I record them as related work: their models can reproduce the corotation result as a force on charges in the lab frame, so they are alternatives to the aether reading, not refutations of Kennard's numbers. Millis (1996, NASA) cites Kennard in a Mach's-principle setting; that is a citation, not a test.
• What would settle it. Nothing in this geometry. Aether-versus-inertial-frame is not distinguishable here, because both predict the same charges. A genuine discriminator would have to detect a preferred translational frame, and Michelson-Morley and Kennedy-Thorndike type nulls [memory, high] already argue against that. For Machian rotation (inertial frame set by distant matter) the relevant tests are gyroscope/Sagnac type, not unipolar induction.
• Final verdict: split. 6a, induction depends on rotation relative to an inertial frame and not on rotation relative to the magnet: Established. 6b, "rotation relative to the earth is improbable": the Earth-frame alternative is simply the mainstream reading, so Plausible, untested for any other alternative. 6c, "only a stationary Lorentz aether can explain it": Not testable as stated (no measurable difference from the inertial-frame reading), and Historically superseded but instructive (a reasonable inference in 1916, replaced by field-in-an-inertial-frame language).

3. Corrected claim list (changes to claims.md)

1. Claim 1: unchanged. Add that Pegram (1917) is independent but unread.
2. Claim 2: "agrees ... to 5%" is true for one group of four; groups span -1.2% to +4.9%; "+/-0.5%" is the calculated charge's stated accuracy, not the comparison's; 20.5 not 26.5. QE revision: add that -6.22 V0 is not independently reproduced, and that applying Kennard's own p.5 rule (every earthed rotating conductor sits at Nn) to all surfaces gives about -4.0 to -4.4 V0 (ratio 0.148-0.164), so the 5% agreement is conditional on an unstated boundary assignment (section 9).
3. Claim 3: replace "against about 15 mm for the full effect" by "against the predicted 14.9 mm / the both-rows mean of 16.1 mm; the solenoid-alone rows have no speed record (reversing-average G = 0; per-row G = +0.5, -0.3, -0.6, +0.2 mm)". The raw sign-weighted values are -0.4, +0.6, +1.1, +3.5 (mean +1.2, SE 0.8 mm). QE revision: "G = 0 in those rows" is corrected to "G about 0 per row, reversing average 0"; add the sign observation (section 9).
4. Claim 4: the 14 mm is an electrometer deflection only, with no galvanometer ratio.
5. Claim 5: replace "does not satisfy Laplace's equation" by "is not divergence-free (div(v x B) = 2ωB)". The experiments, not the algebra, carry the disproof. QE revision: the equations were checked against the page image and the reconstruction stands; the argument already appears in Kennard 1912 (section 9).
6. Claim 6: replace "can only be explained" by Kennard's "apparently the only remaining alternative"; note the printed "square of the distance" error and the incomplete list of alternatives.
7. Details: the galvanometer swing time is 15 s on the page image (the deep read has 14 s). Two printed misprints, 0.117 for 0.114 and 0.140 for 1.40.
8. Priority discrepancy: Chyba credits corotation to Pegram, while Barnett 1919 credits both Kennard and Pegram. Unsettled without Pegram's paper.

4. Web checks (budget 8; 2 used)

• Barnett's affiliation in 1912 was Ohio State University [web: https://journals.aps.org/pri/abstract/10.1103/PhysRevSeriesI.35.323 and https://en.wikipedia.org/wiki/Samuel_Jackson_Barnett, per search results]. Confirmed. This was the physicist's medium-confidence [memory] item.
• Kennard's biography (Rhodes Scholar, Oxford B.S. 1911; Cornell Ph.D. 1913; Minnesota instructor 1914-1916) is already [web] from the AIP finding aid in research/2026-10-04-aip-niels-bohr-library.md (https://history.aip.org/ead/20010114.html). My re-fetch returned no biographical text, so I rely on the Investigator's saved note. The physicist's "Rhodes Scholar, Cornell Ph.D. 1913" is therefore supported.
• Remaining [memory] items are high confidence and none carries a verdict: Lorentz-theory/SR empirical equivalence; Michelson-Morley null results; Kennard uncertainty relation 1927 (the Springer snippet is in the Investigator note). Pegram's quantitative result: unknown, not asserted.

5. Absence-of-evidence analysis: Kennard's unipolar line ends in 1917

What goes dark. After this paper (communicated from Minnesota, signed August 1916), Kennard published nothing further on unipolar induction that the Investigator found. The record shows he returned to Cornell, co-wrote the 1922 NRC bulletin "Electrodynamics of Moving Media" (Swann, Tate, Bateman, Kennard) [web: HathiTrust record in research/], published the 1927 quantum-mechanics paper behind the uncertainty relation, and later did kinetic theory and naval hydrodynamics (David Taylor Model Basin) [web: AIP finding aid]. So the man did not disappear. Only the line of work stopped.

Silence in the sources is not contradiction. The reviewers all declined to pick; I agree. The record that would decide: Kennard's 1922 NRC chapter on unipolar induction (HathiTrust full view; the Investigator did not read it in volume), the 1926 Cornell lecture notes on electricity and magnetism (AIP AR 176, Box 4 Folder 4), and a Cornell memorial statement or obituary. Also Pegram's 1917 paper and the Phys. Zeits. 1912-13 exchange, which show how the dispute was received. Obtaining the 1922 chapter is the cheapest first step.

6. What would settle it (summary)

• Quantitative agreement (claim 2): re-solve the electrostatic boundary-value problem for -6.22 V0 and report an error budget for a repeat.
• Solenoid-alone null (claim 3): repeat with the speed logged and with solenoids of different length, bounding the residual below 1% (tests Su's end-effect proposal).
• Condenser alone (claim 4): one run with only the condenser turning, with the speed monitor on.
• Aether versus inertial frame (claim 6): no unipolar experiment can decide; the question is empirically empty here.
• The historical question: read Kennard's 1922 NRC chapter, the 1926 Cornell notes and a memorial statement.

7. Open questions

1. Is -6.22 V0 right to 0.5%? (Unverified by any reviewer; QE revision, section 9.1: not reproduced from Kennard's own stated rule, which gives about -4.0 to -4.4 V0.)
2. What was Pegram's quantitative result, and who has priority for corotation: Kennard (1917) or Pegram (1917)?
3. How large is any end-effect residual in the solenoid-alone case (Su 2005)? Kennard's 22.5 cm solenoid is short.
4. Do the Ampere-force/homopolar-motor analyses (Baumgartel and Maher 2022) need the "closing wire" re-analysis for the torque case? This does not touch the charge measurement.
5. Did Kennard keep or drop the aether reading after 1917?
6. What are the unexplained 8% differences between current groups, and the logic for rejecting sets after seeing them? Kennard gives no rule.
7. Modern downstream use (Chyba et al. 2025: power from Earth's rotation; the 2026 Comment/Reply, with a null reported by Veltkamp and Wijngaarden per the Investigator) is contested and not evidence for or against the 1917 experiment.

8. Final verdict table

Nothing in mainstream physics would have to change for claims 1-5; they are the mainstream view today. Claim 6 as an aether claim is the only departure, and it adds an entity the experiment cannot distinguish from the inertial-frame reading.

9. QE revision (Step 4b remediation)

Inputs added: qe.md (verdict MINOR, with an escalation condition on claim 2) and the new deep reads in deep/On-Unipolar-Induction-60158c.md: the Hertz/Barnett/Fehrle addendum (D4), "Deep read D3" (section 7 equations from page images), section 11 (D2: sign convention, per-row G, noise, 13 A/25 A), and "Deep read 2" (D1: the boundary-value problem behind -6.22 V0). Tags as before. The one number I recomputed myself is marked [calc].

Outcome in one line. One verdict changes: the quantitative half of claim 2 is downgraded from Established to Plausible, untested. Claims 1, 3, 4, 5 and 6 keep their verdicts; claim 3 gains a sign observation, claim 5 is confirmed against the page image. The QE escalation condition (R1) is met in the sense that the re-solved charge is not within 5% of -6.22 V0 on the assignment that follows Kennard's own stated rule, but not in the sense that Kennard is shown to be wrong. I explain below.

9.1 Claim 2: the -6.22 V0 charge (D1)

What the deep read established [read: page images pp.3-7, deep read 2]:

• Kennard's charge is the difference of two fluxes at the inner cylinder: -7.62 V0 on the outer face (outer space, printed Bessel solution) plus 1.40 V0 on the inner face (inner space, solution not printed) = -6.22 V0. V0 is the potential of the centre of the outer cylinder relative to the axis.
• Kennard states the rule himself: "any point of the apparatus metallically connected to earth comes to a potential of Nn e.m. units" (N = flux encircled per revolution, n = rev/s) [read: p.5]. That is proportional to r^2. At the inner cylinder (r = 0.77 cm against 3.32 cm) the rule gives (0.77/3.32)^2 = +0.0538 V0.
• The printed outer-space formula, evaluated, reproduces his outer-cylinder values and his -7.62 (the deep reader gets -7.58 from the formula and from a finite-difference solve; 0.5%). But on the inner boundary it prescribes about -0.53 V0 times the end fall-off, not +0.054 V0. [calc] I checked the key coincidence: the printed constant and log terms give -0.259 + 1.067 ln(0.77) = -0.5379, and the rule gives +0.05379. The digits agree, with opposite sign and a factor of ten. I also checked that the log coefficient 1.067 follows from boundary values -0.5379 (inner) and 1.021 (outer): (1.021 + 0.5379)/ln(3.32/0.77) = 1.0668.
• The deep reader's finite-difference re-solution (validated on a coaxial case: -5.162 against exact -5.167; grid halving changes results by under 0.01 V0) gives, for the thin-tube geometry with end plates and guard rings as stated or assumed:

• Not all of the sum is explained. For the inner face to be +1.40 V0 the cylinder must sit about 0.037 V0 above the shaft; the Nn rule gives only 0.017 V0 (which would yield +0.65 V0). The simple sign-and-decimal slip hypothesis (+0.0538 entered as -0.538) therefore does not account for the inner space. The deep reader says so and calls the slip an unproved hypothesis.

Weighing. Two readings are open, and I cannot choose between them from the paper.

1. Kennard's calculation used a boundary assignment I cannot reconstruct (for example a convention for the inner cylinder's potential relative to the electrometer wire that differs from "everything earthed rotates at Nn"). He had the 1912-13 Phys. Zeits. and Phys. Rev. papers (cited at pp.6 and 10) and may have defined the convention there; they were not read. The scenarios in which the inner cylinder is held at the electrometer's potential give -6.28 to -6.37 V0, within 1-2.5% of his figure, but they have a different split between the inner and outer faces (the inner face then is -1.4 V0, against his +1.40 V0), and the deep reader notes they do not follow from the Lorentz argument as the deep reader understands it. That a total this close can be reached from a different route is noted, not decisive.
2. The printed solution contains a sign/magnitude error, or applies the rule inconsistently. Then the Lorentz prediction is about -4.0 to -4.4 V0, the theoretical ratio is 0.15 to 0.16, and the measured 0.242 would exceed it by 50 to 60% (0.242/0.148 = 1.64; 0.242/0.164 = 1.48 [calc]).

Points in favour of keeping the paper's number: the author was a careful theorist who designed the guard rings to simplify this very calculation, and he checked errors in the boundary values (below 0.003 V0 except at the end plates). Points against: his stated rule gives something different, and he does not print the boundary values, so no reader can check. Neither the deep reader's re-solution nor my arithmetic settles which assignment is physically correct for the apparatus; the deep reader says a future reviewer should check "the claim that Nn applies to the insulated inner cylinder through needle H" with an independent derivation. That has not been done.

One argument I reject. The primer's remark that "the experiment itself sides with Kennard's number" is partly circular. The measured 0.242 can be used to discriminate between -6.22 V0 and -4.0 V0 only if the Lorentz theory is assumed true and the apparatus assumed free of unaccounted effects (the 10,000 ohm resistance, the ground-referenced frame, the amber rings, an electrometer calibration error). Taken alone, the measurement cannot tell a wrong calculation from an unmodelled effect. I record the argument as an inference at best.

What does not change. The qualitative result is independent of the assignment: every non-trivial assignment gives a charge of several V0 of the predicted sign when the condenser turns, while the solenoid-alone rows show about nil and the moving-line theory predicts the full effect for those rows. Claims 1, 3, 5 and the discrimination between the theories do not depend on -6.22 V0. The signs reverse with current and with rotation in every row (+14.4, -15.6, +16.4, -18.0 mm), which a spurious drift would not do.

Revised verdict, claim 2. Split. - The effect, its sign, its reversal with current and rotation, and its order of magnitude (the same order as any of the calculated charges, within a factor of 1.6): Established. This is also the Lorentz prediction, and the moving-line theory predicts zero. - The quantitative agreement with Lorentz theory "to 5%" (and "to a few percent"): Plausible, untested. It is consistent with known physics if the boundary assignment that gives -6.2 V0 is the right one, and the paper does not let a reader test that. It is not "Established", because the one reconstruction that follows Kennard's stated rule disagrees with it by about 35%, and it is not "Tested, not supported", because the alternative reading is not ruled out and the conflict could be a convention or a printing slip. The arbiter's earlier statement "magnitude to a few percent" is withdrawn. - If anything, the data present an anomaly worth reporting, not hiding: the measured ratio would exceed the Lorentz value computed with the paper's own rule by about 50-60%. I do not infer a real effect from this. The sources of unquantified error listed by the contrarian (rejected sets, the accidental resistance, unlogged speed) apply, and Pegram's paper (unread) might give an independent quantitative check.

What would settle it (supersedes the earlier list for claim 2): 1. Find Kennard's boundary convention: read Phys. Rev. (2) 1, 355 (1913) and the Phys. Zeits. 1912-13 papers on the dielectric and rotating-conductor calculation. This is the cheapest step. 2. Derive independently the equilibrium potential of the insulated inner cylinder connected to a stationary electrometer through a sliding contact on the axis, then set up the full two-shell problem with that value. The deep reader has already built the solver; it needs the correct boundary value. 3. Pegram's 1917 paper, if it reports a ratio. 4. Experimentally: a repeat that logs speed and reports an error budget, as before.

9.2 Claim 3: sign of the residual, per-row G, noise (D2)

• Per-row G. My earlier statement "G = 0 in those rows" is corrected. Page image p.8 shows G = +0.5, -0.3, -0.6, +0.2 mm for the four solenoid-alone rows, with a reversing average of 0 [read: page image p.8]. The conclusion stands (no speed record is available because the Faraday disk on the condenser shaft is not turning), but the wording must be "G about 0 per row (within 0.6 mm), reversing average 0".
• Sign of the +1.2 mm residual. Kennard never defines which physical sense "+" means for S or I [read: p.8]. Using the natural reading that S means the same sense in both blocks of the table, the "Both" rows have a positive reversing average (+16.1 mm, my weighting of the printed +14.4, -15.6, +16.4, -18.0 by sign(S) times sign(I)). Turning the solenoid alone by +ω is, for the condenser, the same as turning the condenser by -ω relative to the magnet system. So the moving-line theory, which Kennard says predicts that the solenoid alone "should charge the condenser" [read: p.2] and that the condenser "should remain uncharged" when both turn, would give about -15 to -16 mm in the same convention, with the opposite sign to the +1.2 mm found. The deep reader flags this as inference (the paper never prints the signed prediction), and it depends on one assumption. The residual is then of the wrong sign to be a partial moving-line effect, and it is about 8% of its size (1.2/14.9 = 8.1%). Consequence: the residual is not evidence for a small moving-line contribution. Whether it supports Su's end-effect proposal is not decidable here, because Su's sign is not stated in what I have; Su's idea (a short solenoid's non-uniform field) remains open and is not excluded by the sign alone.
• Noise. The raw electrometer triples quoted by Kennard swing by tens of millimetres (+8.5, +4.8, +3.7 and +22.4, +13.8, +1.8 for solenoid-alone rows; +5.1, -39.1, +3.3 and -12.6, +29.9, -21.5 for "Both" rows) and reduce to tabulated values of under 1 mm and about 14-16 mm respectively [read: page image p.8; the deep reader reproduced the tabulated values from the triples with (d1 - 2 d2 + d3)/6]. So the drift removal does most of the work; no single-reading noise figure is stated. My earlier estimate (SD 1.66 mm, SE 0.83 mm, about 1.5 sigma from zero) stands [calc]. The deep reader's slightly different SE (0.9 mm, 1.3 sigma) comes from rounding the SD; the conclusion is the same.
• 13 A and 25 A ratios. Kennard gives no reason for "not comparable with the previous values" (.25 and .27, an 8% difference, 8% and 17% above 0.231) [read: page image p.9]. Unknown. The groups are earlier and on a different footing. The result keeps its status as an unexplained scatter indicator.
• Verdict, claim 3: unchanged, Established as a null of about 10% of the full effect.

9.3 Claim 5: section 7 equations checked against the page image (D3)

• Equation (1) is printed f = (1/c)[V x B] + e + E, and equation (2) div(K f) = 4 pi rho [read: page image p.10]. Definitions as printed: f total electromotive intensity, e the electric force due to changes in the magnetic field ("vanishes in the present instance"), E the electric force due to electrostatic causes alone, rho "electric density". The reviewers' reconstruction matches in content; only term order and capital letters differ. K is not defined on these pages, so "dielectric constant" is an inference [memory, high]. The "two additional assumptions" are Kennard's account of Barnett; Barnett's own wording was not read here.
• Reductio as printed: "in free aether we know from electrostatics that div E = 0. Hence in free aether div f = (1/c) div [V x B], and may not vanish, which contradicts (2)." The words "may not vanish" are hedged, and the proof that the intensity "does not in general satisfy Laplace's equation" is described as "simple" but not given [read: page image p.10]. The conclusion is hedged too: the theory "seems therefore to be definitely disposed of by the results obtained by Barnett, Fehrle, and the author" [read: page image p.11]. This supports my earlier point that the experiments, not the algebra, carry the disproof.
• Footnote: E. H. Kennard, Phys. Rev. May 1913, p. 355 (the OCR's "113, p. 365" is wrong) [read: page image p.10].
• Origin of the argument. The Investigator found, and QE confirmed against the saved 1912 text, that the same point already appears in Kennard's 1912 paper: "E' in general fails to satisfy Laplace's Equation" [read: research/files/Kennard-1912-PhilMag-23-937-Unipolar-Induction_IA-OCR.txt]. So the argument predates the 1917 data, which is relevant to the reading that Kennard reasoned from theory first.
• Verdict, claim 5: unchanged.

9.4 Claim 6: one added passage

Section 8 of the paper says the radial effect cannot be due to radial acceleration, to the electron's own rotation, or to motion relative to other parts of the apparatus. It then says rotation relative to the earth "might in some unknown way be responsible ... but this seems improbable", and that otherwise the effect is due to "an absolute rotation in the same sense in which the operation of a gyrocompass is due to an absolute rotation of the earth" [read: page image p.11]. He also reasons that with sliding contacts nearly on the axis and an axial wire closing the circuit, rotation of the connecting wires and electrometer would, by Faraday's law, cause no deflection [read: page image p.11]. These do not change 6a-6c. The earth-rotation alternative was never tested. Verdict, claim 6: unchanged.

9.5 Retained material that the first arbiter pass left out (QE section 5, section 3)

Each item is recorded with its source and stake. None changes a verdict.

1. Hertz's theory. The paper mentions it once, in a parenthesis: "Then according to either Lorentz's or the moving-line theory (but not according to Hertz's) the two cylinders of the condenser should come to different potentials, and the inner one at least should be charged." [read: page image p.2]. So, as Kennard states it, Hertz's theory predicts no charge for a rotating short-circuited condenser in an energised solenoid. He does not say what it predicts for the other two cases. His 1912 paper said his method "is not capable of distinguishing" Lorentz from Hertz [web, per the Investigator's IA OCR]. Hertz's actual equations were not read in this review; I do not supply them from memory.
2. Kennard's answer to Barnett's 1912 objection. Barnett (Phys. Zeits. Sept. 1912, p. 803), as Kennard grants it: the 1912 null might be due to the non-rotation of the solenoid. Kennard: the objection "is valid, but seems decidedly weak", because it "assumes a radical difference to exist between induced and permanent magnetism, for which there is no other evidence; it even requires that the remanent magnetism shall not acquire the inducing properties of permanent magnetism until the magnetizing force is removed, for the remanence in the bar employed amounted to over 25 per cent" [read: page image p.2]. This is the experimenter's own characterisation of the weight of an objection to his work, and Barnett's reply is not in the folder beyond what Kennard reports. My earlier statement that Barnett's technical point "was fair" stands, but the fair record includes Kennard's rejoinder.
3. Kennard's concession. The 1912 rotating magnet "was necessarily enclosed in a second metallic screen of small diameter, and this might conceivably act so as to cut off the effect" [read: page image p.2]. This is the declared motive of the 1917 apparatus. It also means that the 1912 null, by its author's own account, could have been screening, not absence of induction.
4. Kennard on Fehrle. Fehrle (Ann. d. Phys. 42, 1169, 1913) reported confirmatory observations "with a rather different arrangement"; Kennard says the work "is marred by several results which must certainly be wrong: one of his results even contradicts Faraday's law for closed circuits!" [read: page image p.2]. No details are given, Fehrle's paper was not read, and Kennard is a party to the dispute, so this is his characterisation of a third party's work. Note that Fehrle's reported finding agrees with Kennard's conclusion on this point.
5. Against Kennard's interpretation: the unnamed abstract. A Semantic Scholar record attached to Kennard's 1912 title carries the abstract "We describe undisputable experiments that categorically disprove absolutistic Kennard-Bartlett-type interpretations of unipolar induction" [web: Google snippet, research/2026-10-04-crossref-semanticscholar.md]. It cannot be Kennard's own abstract; the paper it belongs to is not identified, probably in the Bartlett or Guala-Valverde line. This is that source's characterisation, with the source's own stake in a rival interpretation unknown. It is evidence against the absolute-rotation reading, not against the charge measurement, and I have not assessed it.
6. Kholmetskii 2003 and the "calculational error" remark. Kholmetskii, "One century later: Remarks on the Barnett experiment", Am. J. Phys. 71, 558 (2003; erratum exists) [web: research/2026-10-04-google.md]. Chyba, Hand and Chyba (2025) write that "a subsequent attempted theoretical refutation of these results was shown to be incorrect due to calculational error" (their refs 22-24) [read: research/files, via research/2026-10-04-aps-journals.md]. Which paper they mean is unverified; neither Kholmetskii nor refs 22-24 were read. Chyba et al. have an interest in Earth-rotation power. It is a modern re-analysis of the Barnett-type experiment and a disputed exchange around it. It cuts against anyone relying on a refutation of the Barnett-Kennard result, and it is not evidence on Kennard's numbers.
7. Pegram's 1917 "reminder". A Springer snippet from A. I. Miller's essays says that in 1917 Pegram reminded Barnett and Kennard of something (text truncated) [web: Google snippet, not opened; research/2026-10-04-google.md]. Miller 1981, "Unipolar induction: a case study of the interaction between science and technology" (doi 10.1007/978-1-4684-0548-4_3) was not reached. It bears on the priority question in open question 2 and on Chyba's crediting corotation to Pegram.
8. 1924 Wisconsin thesis. A 1924 University of Wisconsin College of Engineering B.S. thesis volume (Google Books id KalsAAAAMAAJ, full view) lists Kennard 1917 and a 1913 Kennard paper in its bibliography, p.70 [web: https://www.google.com/books/edition/_/KalsAAAAMAAJ?gbpv=1&bsq=unipolar]. It was not read. It is evidence of uptake of the paper in an engineering setting within seven years, and it counts against any suggestion that the line "went dark" in the literature, as opposed to in Kennard's own output.
9. Kennard's 1912 subtracted effect. In 1912 Kennard subtracted "an effect apparently due to electromagnetic induction when the magnetization was reversed" before quoting 0.0 +/- 0.24 against about 37 divisions predicted by the moving-line theory [read: research/files, 1912 IA OCR, lines 195-199, 258-260; confirmed by QE]. Su (2005) builds on this subtraction. It is part of the record on how the 1912 null was obtained.
10. Small items. The amber-ring (+0.03 V0) and connecting-wire (-0.02 V0) corrections, which Kennard says "just about cancel" [read: pp.6-7], are part of the -6.22 V0 chain. The cancellation is asserted, not shown; they were left out of finite-difference runs by the deep reader. The galvanometer swing time is 15 s on the page image, not 14 s [read: page image p.5]. Page citations to Barnett 1919 above ("p.1510", "p.1511") are journal pagination; the contrarian cites the same report by page of the extracted text ("p.735-745"). I have not reconciled the two schemes, and the primer should use one.

9.6 Updated open questions (replace item 1 of section 7)

1. What boundary potential did Kennard assign to the inner cylinder and guard rings, and is -6.22 V0 right? On Kennard's own rule it is about -4.0 to -4.4 V0, which would make the measured ratio 0.242 exceed the Lorentz value by 50-60%. Unresolved. This is the main open item in the project.

Other open questions keep their numbering. Add: (8) Which sign convention does S carry in the table, and is the +1.2 mm residual really of the opposite sign to the moving-line prediction? (9) What was the "attempted theoretical refutation" that Chyba et al. mention, and what did Kholmetskii 2003 argue?