Kennard · Source catalogue

Kennard asks whether the EMF in unipolar induction (motion alone, with the magnetic field unchanged at each point of the material) depends on absolute rotation, measured against a stationary aether (Lorentz/Faraday view), or only on rotation of parts relative to each other (the 'moving-line' theory, close to Neumann's). He recalls his 1912 negative result with a rotating iron bar in a stationary solenoid, Barnett's objection to it, Barnett's 1912 result that rotating the solenoid alone charges nothing, and Fehrle's confirmation, which Kennard calls marred by wrong results. His new apparatus is a brass cylindrical condenser inside a coaxial brass solenoid (1150 turns, 22.5 cm), either of which can be rotated; the inner cylinder is connected to a quadrant electrometer (about 18,000 mm/volt) and the speed and field are monitored through a Faraday disk and galvanometer. Because the electrostatic charge was computed by solving the potential problem for the two cylindrical spaces (series in Bessel-type functions), the charge on the inner cylinder is Q = -6.22 V0 (+/-0.5%), giving a predicted switch-on deflection of 14.9 mm at 25 A and 33 rev/s. To remove dependence on speed and field, he compares the electrometer/galvanometer deflection ratio with a calibrated theoretical value of 0.231. Results (Section 6): solenoid rotating alone gives a reversing average of +1.2 mm electrometer and 0 galvanometer (nil effect; an earlier group gave +0.2 mm); condenser and solenoid rotating together gives a mean ratio 0.242 (four runs 0.237, 0.237, 0.236, 0.258), 5% above theory; a half-speed group gave 0.228 (range 0.211 to 0.263), 1.4% below; an alternate method gave 0.238 (0.241 with three rejected readings included); 13 A and 25 A groups gave 0.25 and 0.27. The condenser-alone run was not finished because the solenoid short-circuited; it is inferred by superposition (both minus solenoid-alone), with partial support from a group averaging 14 mm electrometer deflection. Kennard concludes with 'fair certainty' that the condenser is charged by its own rotation as Lorentz's theory requires, independent of the solenoid's rotation. Section 7 (read from page image p.10) argues the moving-line theory is internally inconsistent because its electromotive intensity (1/c)[V x B] does not in general satisfy Laplace's equation: in free aether div E = 0, so div f = (1/c) div[V x B] 'may not vanish', contradicting div(Kf) = 4 pi rho (printed equations (1) f = (1/c)[V x B] + e + E and (2) div(Kf) = 4 pi rho; K is not defined on pp.188-189; the proof of non-vanishing is not given in the paper; the conclusion is hedged: the moving-line theory 'seems therefore to be definitely disposed of'). The same Laplace/divergence argument is already in Kennard's 1912 paper [read: research IA OCR], so it is 'disposed of'; that textbook accounts of rotating armatures vs rotating field magnets need correction; and that a rotating condenser's electrons feel a radial force proportional to distance from the axis which cannot come from acceleration, electron spin or relative motion with the apparatus, leaving only motion relative to something that does not rotate, the stationary aether. Deep read notes printed misprints: 0.117 where 0.114 is meant (14.9 mm only follows from 0.114), and '0.02 x 0.140 V0 = 0.03 V0' which works only with 1.40. Four sets were rejected for 'obvious' reasons and about as many sets were abandoned because of large disturbances; Kennard says 'the results thus remain somewhat rough'. Note: the digest has errors the deep read corrected (electrometer calibration is 20.5 mm not 26.5; the solenoid-alone reversing average is +1.2 mm not -12 mm). QE REVISION (facts added or corrected). (1) Galvanometer swing time is 15 s on the page image, not 14 s. (2) Solenoid-alone rows, exact table [read: page image p.8]: E = +0.4, +0.6, -1.1, +3.5 mm and G = +0.5, -0.3, -0.6, +0.2 mm (G is not zero row by row; the reversing average is 0); sign-weighted E values -0.4, +0.6, +1.1, +3.5 (mean +1.2, standard error about 0.9 mm, about 1.3 SE from zero). Raw electrometer triples for these rows range from 1.8 to 22.4 mm before drift removal; in a Both row they swing from -39.1 to +29.9 mm, so single-reading noise is large against the 0.5 to 16 mm quantities measured. (3) Sign of the residual (QE deep read D2, an inference by the deep reader, not stated by Kennard): the Both rows have a positive Rev. av. of +16.1 mm. If S means the same sense in both blocks of the table (the paper does not say), the moving-line theory predicts about -15 to -16 mm for the solenoid-alone rows (turning the solenoid is equivalent to turning the condenser the other way relative to the magnet system), so the +1.2 mm residual has the opposite sign, and is about 8% of that magnitude. Kennard calls the result nil and does not discuss the sign. (4) Hertz's theory: the only mention in the paper is a parenthesis on p.2, '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'; so Hertz's theory predicts no charge for the condenser rotating with the solenoid energised. Kennard does not state its predictions for the other cases or describe its equations. (5) Kennard's rebuttal of Barnett's 1912 objection (Phys. Zeits. 1 Sept 1912, p.803): the objection 'is valid, but seems decidedly weak'; it 'assumes a radical difference to exist between induced and permanent magnetism, for which there is no other evidence' and the remanence in the bar 'amounted to over 25 per cent' [read: pp.1-2]. His concession: the rotating magnet in 1912 was enclosed in a second small metallic screen which 'might conceivably act so as to cut off the effect'; the 1916 apparatus was built to test just this. (6) Kennard on Fehrle (Ann. d. Phys. 42, p.1169, 1913): confirmatory observations with a different arrangement, 'marred by several results which must certainly be wrong: one of his results even contradicts Faraday's law for closed circuits!' Kennard is a party to the dispute; no detail is given and Fehrle's paper has not been read. (7) The connecting-wire and amber-ring corrections of -0.02 V0 and +0.03 V0 'just about cancel' (asserted, not shown) [read: pp.6-7]. (8) OPEN STATUS OF -6.22 V0 (QE deep read D1, Opus, with finite-difference re-solution): Kennard's printed outer-space solution reproduces his outer-face charge (-7.58 against -7.62 V0), but it holds the inner cylinder and guard rings at about -0.53 V0 times the end fall-off g(x). The rule he states himself (any earthed rotating point sits at Nn, proportional to r^2) gives about +0.054 V0 there. Re-solved with Nn on every rotating conductor, the total charge is about -3.99 V0 (-4.2 to -4.4 for a 1 to 2 mm tube wall), giving a Lorentz-predicted ratio of about 0.148 to 0.164 and 9.6 to 10.6 mm, against Kennard's 0.231 and 14.9 mm; on that reading the measured 0.242 would be 50-60% above prediction. Assignments that hold the inner cylinder at the electrometer potential (scenarios C, D) give -6.28 to -6.37 V0, near Kennard's total but with a different split between faces. The deep reader found no stated reason in the paper for the -0.53 V0 value and offers a possible sign-and-decimal slip (the constant-plus-log term evaluates to -0.5379 at r = 0.77, against Nn = +0.05379) as an unconfirmed hypothesis; Kennard's 1912-13 Phys. Zeits. and Phys. Rev. papers, which may state the reference, are not in the folder. The charge-versus-no-charge result (qualitative) is unaffected by every assignment tried. The quantitative '5% agreement' therefore rests on -6.22 V0 not independently reproduced. Also: the 1600 G central field implies 55,400 Mx, but the finite-solenoid angle rule gives about 1470 G and 50,800 Mx; the theoretical ratio 0.231 does not depend on it (it uses the measured Faraday-disk flux ratio 0.1197), only the 14.9 mm estimate would change by about 8%.

Key claims

• A cylindrical condenser rotating inside a magnetised coaxial solenoid acquires a charge of the sign and size Lorentz's theory predicts, even though it is enclosed in a metallic screen rotating with it.
• The charge on the inner cylinder is -6.22 V0 (V0 is the potential of the outer cylinder relative to the axis), stated accurate to 0.5%, and the predicted electrometer/galvanometer deflection ratio is 0.231. (QE: this charge has not been independently reproduced; a re-solution with the paper's own Nn rule applied to every rotating conductor gives about -4.0 V0 and a ratio of about 0.15; see summary.)
• The measured ratio with condenser and solenoid rotating together is 0.242, 5% above 0.231; half-speed gives 0.228 (1.4% below). Only one group of four gives 0.242; the four runs span 0.236 to 0.258.
• Rotating the solenoid alone produces no charge on the condenser (reversing average +1.2 mm electrometer, about 1.3 standard errors from zero; galvanometer reversing average 0, individual G values +0.5, -0.3, -0.6, +0.2 mm), confirming Barnett.
• The condenser-alone case follows by superposition from the 'both' and 'solenoid alone' results, so the induced EMF depends on rotation of the condenser relative to something other than the solenoid.
• The moving-line theory is disproved: its electromotive intensity (1/c)[V x B] is not divergence-free (div(v x B) = 2 omega B for rigid rotation in a uniform axial field), so it cannot satisfy Laplace's equation in free aether; the weight is carried by the open-circuit experiments of Barnett, Fehrle and Kennard, which contradict it. Kennard words it 'seems therefore ... definitely disposed of'.
• Electromagnetic induction depends partly on absolute rotation; Kennard writes that 'apparently the only remaining alternative' for the radial force on electrons of a rotating condenser is motion relative to a stationary Lorentz aether (the same passage misprints 'square of the distance' for centripetal acceleration, which is proportional to r).

Relevance: This is the only document in the project and carries all of its claims: a primary experimental report, with a full calculation, on a classical puzzle (unipolar or homopolar induction: whether the magnetic field rotates with the magnet) and Kennard's argument that it supports a stationary aether.

Mainstream conflict: The experimental result (induction from rotation of the conductor in the field, none from rotating the magnet) agrees with the Lorentz force law, which mainstream physics accepts. The conflict is in the interpretation: modern physics reads the velocity in v x B as relative to the observer's inertial frame or rotating-frame effects, not relative to a stationary aether, and rejects the aether inference. The paper dates from the pre-1920 aether-versus-relativity debate; Kennard himself frames the aether result as an obstacle to 'ultra-relativists'.