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Mathematician's review: Kennard, "On Unipolar Induction" (1917)

Reviewer: PhD mathematician (Step 2). Project: Kennard. Sources: E. H. Kennard, Phil. Mag. (6) 33, 179-190 (1917), signed Univ. of Minnesota, August 1916. The PDF is the only primary document in the project folder.

Tags: [read] = from the document; [read: page image p.N] = I looked at the rendered page; [web] = from the Investigator's saved files or notes (URLs in sites.md and research/); [memory] = my recall, with confidence.

Method. I re-read the whole paper myself. That means pp.1-9 against the deep read, and pp.10-12 (the Laplace argument and the aether conclusion) from the cleaner Internet Archive OCR in research/files/. I also checked the journal page 189 against its image. I recomputed every number I could in the project venv. I did no new web searches. Nothing I rely on is a medium- or low-confidence [memory] fact. The few [memory] items are marked.

0. A short primer on the mathematics (for the reader)

What is being measured. A charged particle of charge e moving with velocity v through a magnetic field B feels, in SI units, the force F = e(E + v × B). In the CGS-Gaussian units Kennard uses, the magnetic part is (e/c)(v × B), where c is the speed of light. Kennard writes this as an "electromotive intensity" f = (1/c)[v × B], the force per unit charge. The symbol [v × B] is the cross product.

Why a spinning conductor gets a voltage. Take a uniform axial field B along z. A point at distance r from the axis, spinning at angular speed ω, has speed v = ωr in the tangential direction φ̂. Then v × B = ωrB r̂, a radial force on the charges. Integrating from the axis to radius R gives a voltage ω∫rB dr = (ω/2π)·Φ(R) = nΦ(R). Here n is revolutions per second and Φ(R) is the magnetic flux enclosed by radius R. This is Kennard's "potential of Nn e.m.u." (§4). It is the Faraday disk.

Worked numbers. [read: p.7, recomputed] - Solenoid: 1150 turns over 22.5 cm at 25 A. B = 4π·(1150/22.5)·25/10 = 1606 gauss (Kennard: 1600). - Flux through the outer cylinder, radius 3.32 cm: 1606 × π(3.32)² ≈ 55,600 maxwells (Kennard: 55,400). - At 33 rev/s, V0 = 55,400 × 33 × 10⁻⁸ V = 0.0183 V. This matches Kennard.

The two competing readings. Is the "v" in v × B the velocity relative to a fixed frame (Lorentz; Kennard says "the ether"), or relative to the magnet (the "moving-line" theory, where the magnetic field lines are imagined to be carried along with the spinning magnet)? For a uniform axial field in a rotating solenoid the field looks identical at every instant. Spinning it changes nothing visible about the field, so the field does not give a way to say which part is "rotating". That is why the question is subtle. Only open circuits (charge on an insulated condenser) can answer it. Closed circuits obey Faraday's law either way.

The condenser measurement. The condenser is two coaxial cylinders (a cylindrical capacitor) inside the solenoid. Spinning it makes the outer cylinder sit at the potential Nn relative to the axis, and an electrostatic problem then fixes the charge on the insulated inner cylinder. That is the solved boundary-value problem of §4.

1. What I checked, in order

1.1 Reduction of readings (§3) [read: page image p.5]

The three deflections per set are d1 (field on), d2 (current reversed), d3 (field off). The ideal values are x, -2x, +x, where x is the single-step deflection. So (d1 - 2d2 + d3)/6 = (x + 4x + x)/6 = x. This is correct. A constant drift δ per interval adds δ(1 - 2 + 1) = 0 and drops out. A drift that grows with time does not drop out, and a curvature term remains. The alternate method (§6), "a third of whose numerical sum", is also correct: the deflections are 2x and x in opposite directions, so the sum is 3x.

A finding not in Step 1. Kennard prints the raw triples for two sets. Line 5 is +5.1, -39.1, +3.3. With x = 14.4 the ideal pattern is 14.4, -28.8, 14.4. The residuals are about -9.3, -10.3 and -11.1, a roughly constant drift of -9 to -11 mm per interval, comparable to the signal itself. That fits the linear-drift assumption. Line 6 is -12.6, +29.9, -21.5. With x = -14.4 the residuals are +1.8, +1.1 and -7.1, so the drift changes by about 9 mm over the set. The curvature term is (δ1 - 2δ2 + δ3)/6 ≈ -1.2 mm. That is about 8% of the signal. This is my arithmetic on his two printed triples [read: p.8, recomputed], so it is a diagnostic of scatter, not an error in the paper. It explains why the sets scatter and why he averages groups of four.

1.2 The theoretical ratio, 0.231 (§5) [read: page image pp.7-8]

Recomputed: (20.5/62.2)(0.1/0.1197)(6.22/7.42) = 0.3296 × 0.8354 × 0.8382 = 0.2308. Correct.

The structure is also right: E_main/G_main = (E_cal/G_cal) × (E_main/E_cal) × (G_cal/G_main), with E_main/E_cal = 6.22V0/7.42V and G_main/G_cal = 0.1197V0/0.1V. Electrometer capacity, sensitivity and speed all cancel in the ratio. The design is sound. Speed matters only if the electrometer and the galvanometer respond to different speed histories, which is possible because the galvanometer takes 15 s and the electrometer takes 20 s to reach full swing.

The galvanometer swing time is 15 s on the page image [read: page image p.5]. The deep read has 14 s (see Corrections).

Error budget (mine; Kennard gives none for the ratio). Items he states: charge ±0.5%; electrometer calibration agreement within 2% (a spread, so about 1% on the mean); 2% on flux proportionality; wire (-0.02 V0) and amber (+0.03 V0) corrections of 0.3% and 0.5% of 6.22 V0, which he says nearly cancel. A rough combination of the stated items is about 2-3%. The measured scatter of the four "both" ratios is 0.237, 0.237, 0.236, 0.258. The mean is 0.242, the standard deviation is 0.0107, and the standard error is 0.0053, or 2.2% [recomputed]. The offset from 0.231 is 0.011, or 2.1 standard errors. A +5% offset is therefore only marginally compatible with the stated precision. Pooling his other groups gives (0.242, 0.228, 0.238) with a mean of 0.236, which is +2% from theory. The half-speed group is -1.4%. So the data are consistent with theory at the few-percent level, which is Kennard's own claim ("somewhat rough"). The data do not support a claim of a few-tenths-of-a-percent agreement, and he does not make one.

1.3 The electrostatic solution (§4) [read: page image p.6]

I did not re-solve the boundary-value problem (two cylindrical shells, Bessel-type series, charge -6.22 V0). The form is plausible: for a finite cylinder, a log r term plus products of cosh(kx) and J0/K0 in r. Here K0 as he defines it is not the modified Bessel function K0 of today but the second solution, a J0 log x + series, with the sign pattern printed. The numbers (-7.62 + 1.40) V0 add correctly to -6.22. The ±0.5% accuracy claim rests on the boundary residuals he describes and cannot be checked without redoing the solution. It is internally unverified rather than found wrong. A numerical re-solution (a finite-difference or series solve) would settle it in an afternoon, and I recommend it for the primer's worked example.

Two printed arithmetic slips, both confirmed: - §5: "6.22 × .0183 × 1/300 = 0.114 × 1/300", but the next line uses 0.117. 0.114 × 18000/138 = 14.87 mm, while 0.117 gives 15.26 mm. The 14.9 mm follows from 0.114. - §4: "0.02 × 0.140 V0 = 0.03 V0". 0.02 × 0.140 = 0.0028. The 0.03 matches 0.02 × 1.40 (the inner-flux term), so 0.140 is a misprint for 1.40.

Neither affects the 0.231 ratio.

The amber argument. Kennard says a shell of amber over the whole length would raise the flux by "something like 40 per cent", and that the actual rings (one eighth of the length, flattened) give an effect that "could hardly exceed 2 per cent". A crude linear scaling gives 40% × 1/8 = 5% for rings of that length, times a fraction below 1 for the flattening, so "2%" is a defensible but not demonstrated upper bound. The claim that filling all space with a dielectric has no effect on the distribution of electrification is a statement about a moving dielectric (Minkowski-type relation). It is delegated to his Phys. Zeits. 1912/13 and Phys. Rev. 1913 papers, which the Investigator could not obtain. I cannot verify it from the project's documents.

1.4 The Faraday-disk speed monitor [read: p.4]

The galvanometer EMF is 0.1197 V0 (the flux ratio), so G is proportional to (field × speed), the same as the electrometer signal. Good. In the solenoid-alone runs the galvanometer shows 0 (the Faraday disk is on the condenser shaft, which is not turning). So the solenoid-alone runs have no speed record at all. Their electrometer deflection (+1.2 mm reversing average; earlier group +0.2 mm) can only be compared with the full effect (about 16 mm, mean |E| of the "both" rows) if speed and current were the same, which he does not document. The sets also scatter widely (individual values -1.1 to +3.5 mm). This is a real limitation of claim 3: the null is an absolute-deflection null with an undocumented speed, bounded by about 1.2 mm ± 1.5 against ~16 mm, so below ~10% at best. Barnett's own solenoid-alone work reported the null before Kennard's, and Chyba et al. (2025) state that these null results "proved that the field of a rotating axially symmetric electromagnet does not 'rotate with the magnet'" [web: research/files/Chyba-Hand-Chyba-2025-PRResearch-7-013285.pdf, p.2].

1.5 Superposition for the unfinished condenser-alone run

The argument (condenser alone = both together - solenoid alone) holds under both theories because the induced charge is linear in the two angular velocities: ω_cond for Lorentz, ω_cond - ω_sol for the moving-line theory. So the condenser-alone case is a consequence of claims 1 and 3 and is not an independent test. Direct evidence is one group of "about 14 mm", an electrometer deflection only, with no galvanometer ratio and a prediction of 14.9 mm. Note that mean |E| in the "both" rows is 16.1 mm against the same 14.9 mm prediction: about +8%, with the speed uncertain. Kennard does not make that comparison.

1.6 The current-proportionality test

13 A gave ratio 0.25 and 25 A gave 0.27, "not comparable with the previous values", a difference of 8% with no explanation. If E and G are both proportional to current, the ratio should not change, so the test should be ratio-constant. A difference of 8% on groups of four with a stated scatter of 4% per set is about 1.5 standard errors, so it is not alarming, but he gives no data. Both numbers also differ from 0.242 and 0.231, which he waves off as "not comparable". An unexplained condition difference is a minor gap in the record.

1.7 The "moving-line is disproved" argument (§7) [read: IA OCR pp.188-189 and page image 189]

His argument. If the moving-line theory is right, a rotating magnet system sets up in the free ether the electromotive intensity f = (1/c)[v × B] + e + E (his eq. 1), and Gauss's law div(Kf) = 4πρ (eq. 2) must hold for f. In free ether div E = 0, so div f = (1/c) div[v × B].

Check of the key step. For solid rotation, v = ωr φ̂ and B = B(r) ẑ (axial). Then v × B = ωrB r̂, and div = (1/r) d(r · ωrB)/dr = 2ωB when B is uniform. This does not vanish (SymPy check: 2Bω). So his statement is correct. The mathematics here is right: (1/c)[v × B] is not solenoidal, so it cannot be a pure electrostatic field in free space.

What it proves, and what it does not. The inference "so the moving-line theory is disproved" has a gap: - The step shows that a theory which both (a) identifies f with an electric field in the ether and (b) imposes div(Kf) = 4πρ on it is inconsistent. That is Barnett's assumption pair, as Kennard says. - Kennard's own escape is that "the lines do not act on the ether, but only on material bodies", with Lorentz's div(KE) = 4πρ in place of eq. 2. But that is an equally available move for a relative-velocity theory. The Lorentz force is a force on moving charges, not an electric field in the ether, so a non-solenoidal f is not a contradiction. - So the Laplace argument rejects one version of the moving-line theory (Barnett's, with f as an ether field). It does not reject the moving-line idea that v is relative to the magnet. What actually rejects that idea is the experiment: the corotating condenser charges (0.242 vs 0.231) and the solenoid-alone null.

This is a hidden assumption in claim 5 as Kennard states it. The correct reading is "Barnett's extra assumption fails; the experiments do the disproving". Kennard's own sentence "the moving-line theory seems therefore to be definitely disposed of by the results obtained by Barnett, Fehrle, and the author" puts the weight on the experiments, so he is not claiming more than that. The same Laplace argument is already in his 1912 paper (the Investigator's note) [web: research/files/Kennard-1912-...].

1.8 The "only the ether" argument (§8) [read: page image p.189, IA OCR p.190]

The sequence is: 1. Rotating condenser, connecting wires, electrometer: closed-circuit Faraday's law says relative rotation of the wires cannot matter. 2. "Rotation relative to the earth might in some unknown way be responsible ... but this seems improbable." 3. Therefore the effect is due to "absolute rotation", like a gyrocompass. 4. Each electron must feel a radial force proportional to r. It cannot be the radial acceleration "for that is proportional to the square of the distance", nor the electron's own spin, nor motion relative to other parts of the apparatus. 5. "Apparently the only remaining alternative is to ascribe the force to motion ... relative to something which is not matter ... this something must be the stationary aether of Lorentz."

Problems: - Error in step 4 (new in this review). The radial (centripetal) acceleration of a point on a rigid rotating body is ω²r, proportional to the first power of r, not the square. The page image prints "square of the distance" [read: page image p.189]. What probably should have been said is that it goes as the square of the angular speed, whereas the observed effect is linear in ω (it reverses with the direction of rotation, as the table shows). The conclusion of the step survives: an acceleration effect would not reverse with the sense of rotation and would go as ω². The reason given is wrong. - The list of alternatives is not exhaustive. It leaves out the magnetic field itself as the agent. v × B is a force on a charge in a field B that is axially symmetric and constant in the laboratory frame, so B does not "rotate with the magnet" (that is the experimental finding). The velocity that enters is the charge's velocity relative to the frame in which that B is defined: the laboratory frame, which is, to a very good approximation, an inertial frame. A fixed ether is one way to supply a preferred frame. An inertial frame defined by the dynamics (Newton's rotating-bucket argument, and the gyrocompass he cites) does the same job without any ether. Kennard's "rotation relative to the earth ... improbable" is a statement about the earth's rotation, not about the apparatus frame, and the question is not relative to what the ω is measured. - The gyrocompass analogy. A gyrocompass responds to rotation relative to inertial frames, a well-defined physical fact in Newtonian mechanics and in relativity. So the analogy does support "absolute rotation", but in the sense of "relative to inertial frames", and it does not single out a luminiferous ether. The step from "absolute rotation" to "the stationary ether of Lorentz" is a further, interpretive step. - Step 5 is therefore an inference by elimination from an incomplete list. Kennard hedges it ("Apparently ... must be"); the claims.md wording "can only be explained" is stronger than his text.

Verdict on 1.8: the internal logic is sound if the list is exhaustive, which it is not. The step to a stationary ether is an interpretation, not a mathematical consequence.

2. Corrections to Step 1

  1. Galvanometer swing time. The deep read (§3) says 14 s. The page image of p.183 prints "15 seconds" [read: page image p.5]. The Internet Archive OCR also says 15.
  2. Source gap closed. claims.md says pp.10-12 (the moving-line rebuttal and aether argument) rest on the digest alone and "should be confirmed". They are now confirmed against the Investigator's IA OCR text (pp.188-190) and the page image of p.189. The equations in §7 match the digest; the digest was accurate.
  3. Claim 6 wording. claims.md says the radial force "can only be explained by motion relative to a stationary Lorentz aether". Kennard's text is "Apparently the only remaining alternative". It is an elimination argument that he hedges, and I show it is incomplete (1.8).
  4. Claim 3 comparison. claims.md quotes "+1.2 mm against about 15 mm for the full effect". The "about 15 mm" is not Kennard's number for those rows. It is the predicted 14.9 mm, or the mean |E| of 16.1 mm in the "both" rows. The solenoid-alone rows have no recorded speed (G = 0), so the comparison is indicative only.
  5. Claim 2. "Agrees to 5%" is accurate as the full-speed group result. The accompanying data (half-speed -1.4%, alternative method 0.238/0.241, current test 0.25 vs 0.27) show a spread of -1.4% to +5% (and +8% between the 13 A and 25 A groups, which are said to be non-comparable). The 5% is 2.1 standard errors of that group.
  6. Missing Step 1 point. The deep read notes the 0.117/0.114 and 0.140/1.40 slips and I confirm both. Neither changes any claim. The deep read states "no R is given" for solenoid-alone rows; that is correct.
  7. Investigator's Su (2005) note. Su's reexamination is not a refutation of Kennard's 1917 conclusions; it is an alternative force law. Su's own abstract says his law reproduces Barnett's null for a long solenoid with the capacitor inside, and predicts a nonzero effect when the capacitor is outside the solenoid or the solenoid is short. His law is a "modified Lorentz force law" based on a "local-ether model" that he derives himself [web: research/files/Su-2005-arXiv-physics-0512179-Barnett-reexamination.pdf, abstract and intro]. It is relative-velocity (Galilean) electrodynamics, which is a revival of a form of the moving-line idea. He does not address Kennard's corotation result, only the solenoid-alone null. Kennard's solenoid is 22.5 cm long with the condenser at 3.3 cm radius, so the end-effect nonuniformity he points to is not negligible and the 1.2 mm null leaves room for a small effect. It does not touch the corotation measurement. The Investigator's note that Chyba says "an attempted theoretical refutation was shown incorrect" is not tied to a specific paper, and I did not identify it.

3. Per-claim review

Each claim is answered under (a) mathematics, (b) consistency with established experiment, (c) testing, (d) what mainstream physics would have to change. The claim numbers are those of claims.md.

Claim 1. The rotating condenser inside a solenoid charges as Lorentz's theory predicts, even with a metallic screen rotating with it.

  • (a) Mathematically consistent. The prediction chain (flux, V0 = nΦ, charge -6.22 V0, capacity 138 e.s.u., 14.9 mm) recomputes correctly, except for two misprints that do not propagate. The electrostatic solution is unverified by me but plausible.
  • (b) Consistent with all established experimental results I know of. It is the same effect as the Faraday disk, and the standard textbook account (Lorentz force in the lab frame) predicts it. Independent support: Barnett (1919, AIEE report) says the corollary "has been confirmed in each of two recent investigations; one by Kennard ... and one by Pegram ... The condenser was found to become charged" [web: research/files/AIEE-1919-report-electromagnetic-induction.pdf, §23]; Pegram, Phys. Rev. 10, 591 (1917) [web: via Barnett 1919 and Chyba 2025; Pegram's paper itself not obtained].
  • (c) Tested by Kennard (one apparatus, groups of four sets, "somewhat rough"), and by Pegram with a corotating condenser and coil. Barnett, Kennard's critic in the dispute, acknowledged the charging. Not yet found: a modern repeat with this exact geometry. Baumgärtel & Maher (2022) and Müller (2014) test related unipolar geometries [web: Investigator notes]; I have not read them in depth.
  • (d) Nothing. It is textbook electrodynamics (Lorentz force with v measured in the lab).
  • Verdict: Established. Qualitatively replicated by an independent worker (Pegram); quantitatively good to a few percent, one apparatus.

Claim 2. Measured ratio 0.242 (full speed) against calculated 0.231; 0.228 at half speed; charge -6.22 V0 ±0.5%.

  • (a) Consistent. 0.2308 recomputed. The error budget is partly unstated (see 1.2). The ±0.5% charge accuracy is claimed, not demonstrated in the paper.
  • (b) Consistent with Lorentz-force prediction at the few-percent level.
  • (c) Kennard only. Other groups: 0.238 and 0.241 by a second method; 0.25 vs 0.27 in a current test he calls non-comparable. No replication of the 5% quantitative agreement is on record that I know of.
  • (d) Nothing.
  • Verdict: Established at the ~5% level (rough, one apparatus). If a reader wants a number: the five ratio groups scatter from about -1.4% to +5% about the calculation. The test cannot discriminate small modifications of the Lorentz law.

Claim 3. Rotating the solenoid alone produces no charge on the condenser (+1.2 mm vs ~15 mm), confirming Barnett.

  • (a) Consistent. +1.2 mm recomputes from the table (weighted average). A previous group gave +0.2 mm (range 0.8-2.7 mm).
  • (b) Consistent with Barnett (1912) and with the modern account that the field of an axially symmetric solenoid does not rotate with it [web: Chyba et al. 2025]. Contested by Galilean/relative-velocity theorists (Su 2005; Guala-Valverde; Wesley) [web: Investigator notes], who predict small effects only in non-ideal geometries.
  • (c) Barnett (1912, 1913, own apparatus); Kennard (1917); Fehrle (1913, which Kennard calls marred); later repeats in the spinning-magnet line (Bartlett et al. 1977, Müller 2014, Chen et al. 2017) [web: sites.md]. I did not check those results myself.
  • (d) Nothing.
  • Verdict: Established, with the caveat that Kennard's solenoid-alone runs have no speed record, so the null is an absolute-deflection bound of roughly 10% of the full effect, not a precision null.

Claim 4. Condenser-alone inferred by superposition (with a 14 mm partial check).

  • (a) The inference is valid: the induced charge is linear in the two angular velocities under both theories (see 1.5).
  • (b) Consistent.
  • (c) Not finished: the solenoid short-circuited and "it was not thought worth while to rewind it". The only check is one group with an electrometer deflection of about 14 mm and no ratio.
  • (d) Nothing.
  • Verdict: split. The inference: Established as logic (it follows from claims 1 and 3 and gives no independent test). The direct measurement: Never properly tested (abandoned for an apparatus failure; the cause is stated, so it was not dismissed). The claim is not load-bearing for the conclusion.

Claim 5. The moving-line (relative-rotation) theory is disproved: [v × B] does not satisfy Laplace's equation in free aether, and the open-circuit experiments contradict it.

  • (a) The mathematics is correct (div[v × B] = 2ωB ≠ 0 for a uniform axial field, checked) but the logic has a gap: it eliminates Barnett's added assumption (f as an ether field obeying div(Kf) = 4πρ), not the relative-velocity idea. Lorentz's own div(KE) = 4πρ is available to the moving-line theorist (1.7). Kennard half-concedes this ("the lines do not act on the ether, but only on material bodies").
  • (b) The experiments disprove the idea that induction depends only on relative rotation of the parts: the corotating condenser charges and the solenoid alone does not. Consistent with the standard account, and with Barnett 1919, who accepts the results.
  • (c) Barnett 1912/1913 (solenoid alone); Kennard 1912 (null, magnet in a fixed solenoid; Barnett calls it inconclusive because only the iron rotated), Kennard 1917 (rotating solenoid, corotation); Pegram 1917. Barnett's objections (the 1912 design) were answered by the 1917 design. Barnett's comments are those of a direct rival.
  • (d) Nothing in mainstream physics changes; the moving-line theory is already rejected, and nowadays it is not held.
  • Verdict: split. The experimental disproof of the relative-rotation-only induction: Established. The Laplace-equation argument as a stand-alone disproof: Plausible but incomplete (it defeats only the Barnett assumption set; it is not decisive without the experiments).

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

  • (a) The elimination argument has an arithmetic slip (acceleration "proportional to the square of the distance" should be linear in distance, quadratic in angular speed) and an incomplete list of alternatives that omits an inertial frame defined by dynamics (1.8). Not internally contradictory, but not a proof.
  • (b) "Depends on absolute rotation": consistent with all known tests, including the Faraday disk, and with Newtonian and relativistic mechanics (rotation is absolute relative to inertial frames). "Stationary aether": no experiment supports it over the inertial-frame reading. The aether idea was displaced by special relativity (Kennard himself calls the aether-rejecting relativists "ultra-relativitists" in §8). Chyba et al. (2025) read v in v × B as relative to the observer's frame, not an aether (their characterization) [web].
  • (c) Not tested as an aether claim: there is no experiment of Kennard's, or anyone's, designed to discriminate an ether from an inertial frame in this geometry. Kennard's 1917 paper rests on elimination.
  • (d) If true as stated (a preferred stationary ether frame felt by rotation), special relativity's denial of a privileged frame for electrodynamics would have to change, and the Michelson-Morley-type null results would need a conspiracy of compensating effects. If read only as "absolute rotation", nothing changes.
  • Verdict: split. "Induction depends on rotation relative to inertial frames, not on rotation relative to the magnet": Established. "Therefore a stationary Lorentz aether": Historically superseded but instructive. It was a reasonable inference in 1916 and was replaced by the inertial-frame reading. The argument is also Not testable as stated in the form "only the aether can do this", since no alternative was ruled out by measurement.

4. The Investigator's findings: what I kept and how I weigh them

Kept, with my reading: - Kennard 1912 (Phil. Mag. 23, 937) [web: archive.org londonedinburg6231912lond]. A steel bar rotated inside a stationary solenoid, null result of 0.0 ±0.24 divisions against about 37 predicted for moving-line. The paper already carries the Laplace argument. Kennard says the method "is not capable of distinguishing" Lorentz from Hertz, which he fixes in 1917. I find the 1912 null clean as a number (the 70 observations and the probable errors are as quoted), but Barnett's objection that only the iron core rotated is mathematically fair: the fraction of lines that would move is undefined. Bears on claims 3 and 5. - Barnett 1919 AIEE report, §23 [web: research/files/]. Barnett's concession: either "the ether does not exist and ... the tubes of induction do not move, or ... the ether exists". This is the strongest independent statement on the logic of claim 6. Barnett presents it as a dilemma, and he does not endorse the ether. It treats claim 6 as an open choice at that time. In my reading the second horn is ill-posed because an inertial frame suffices. - Barnett 1912/1913 attack on Kennard [web]. "Fallacies quite apparent", "inconclusive", "assumes, without justification, that div E = 0". These are a direct rival's statements. The div E = 0 point is the same issue as 1.7: Kennard's step uses div E = 0 for electrostatic fields in free ether, which is standard; Barnett's objection is about whether the f field is electrostatic. - Chyba, Hand & Chyba 2025 [web]. Supports claims 1-3. They credit Pegram for corotation, and Barnett 1919 credits Kennard as well. - Su 2005, Wesley, Assis & Thober, Guala-Valverde, Bartlett et al., Müller, Chen, Baumgärtel & Maher [web]. Relative-velocity and Weber-type electrodynamics treat unipolar induction without a stationary ether, and argue that the open-circuit results are not trivially relativistic. These are labelled fringe by some mainstream sources; that is those sources' characterization. For my review: such theories can reproduce the corotation result because it follows from a force on charges measured in the lab frame. They are not a refutation of Kennard's measured numbers. They are alternatives to his interpretation, which is a point in claim 6's favour as "not unique". - The anomalous Semantic Scholar abstract ("undisputable experiments that categorically disprove absolutistic Kennard-Bartlett-type interpretations") [web: research/2026-10-04-crossref-semanticscholar.md]. Source unknown; it is attached to the wrong record. I note it as that source's characterization and cannot assess it. - Absence of evidence after 1917. The Investigator lists four competing explanations. From the mathematics: (a) "settled" is supported by the fact that his own critic accepted the results by 1919. (b) The apparatus failure is stated in the paper. I add nothing mathematical to (c) and (d). The decisive record (the 1922 NRC report, the 1926 Cornell lecture notes) was not obtained, so this question stays open.

5. Summary of mathematical findings (for the arbiter)

Solid: - The prediction chain and the ratio 0.231 recompute correctly. The reduction formulas for the readings are correct. - The quantitative agreement is a few percent (about +5% to -1.4%), with a stated roughness. - div[v × B] ≠ 0 is correct.

Defects (none changes the experimental result): 1. Misprints: 0.117 for 0.114; 0.140 for 1.40. 2. The electrostatic solution and the amber (dielectric) argument are not verifiable from the paper. 3. The solenoid-alone null has no speed record (G = 0) and its bound is about 10%. 4. The current-proportionality test (0.25 vs 0.27, 8% apart) is not explained. 5. The Laplace argument defeats Barnett's assumptions, not the relative-velocity idea; the experiments carry the proof. 6. In §8, "radial acceleration proportional to the square of the distance" is an error (it is linear in r, quadratic in ω), and the elimination list omits an inertial frame defined by dynamics. So the stationary ether is an interpretation, not a derived result.

6. Verdicts

  1. Corotating condenser charges as Lorentz predicts: Established.
  2. Ratio 0.242 vs 0.231 (and 0.228 at half speed): Established at the ~5% level, one apparatus.
  3. Solenoid alone gives no charge: Established (with the ~10% bound caveat).
  4. Condenser-alone by superposition: inference Established as logic; the direct run Never properly tested (apparatus failure, stated).
  5. Moving-line theory disproved: experimental disproof Established; the Laplace argument alone Plausible but incomplete.
  6. Absolute rotation / stationary ether: "absolute rotation (relative to inertial frames)" Established; "stationary Lorentz aether required" Historically superseded but instructive.