TernionAG: Primer (Step 4)

Project: E. E. W. Kassner's patents for Ternion AG of Glarus, Switzerland (1931-1951), the Ternion company records, the F. W. O. Bauch material, and an essay in the project folder, "High Frequency Effects on Materials" (2019). Built from arbiter.md (authoritative, including its "QE revision" and "Evidence-rule revision" sections of 2026-10-03 and its "Investigator findings (2026-10-04)" section, in-place updates and QE remediation of 2026-10-04, and its "Investigator findings (2026-10-08)" section on follow-ups Q03 and Q05 about electrolysis and bond strength, with its "Related work and evidence restored" and QE remediation of 2026-10-08), the Investigator's notes (research/, sites.md), the three reviews, the deep reads and the QE remediation in qe.md. Worked example and the side calculations (fine structure; serum crossover, temperature tolerance and pulse bandwidth, added 2026-10-04; electrolysis bounds, water's Q at its band, photon ratios, field strengths and the origin of 1.28 cm, added 2026-10-08 as step 9) reproduced in example.py (run command in its header).

Tags: [read] from a project document (page given where the deep reads give one); [calc] arithmetic done here and in example.py; [web] with URL; [memory] recalled, with confidence. Where a sentence has no tag and states standard physics, it is textbook material [memory, high].

Source gap (repeated from the arbiter; it limits everything below). Every Kassner/Ternion scientific claim rests on the patents' own text. There is no lab notebook, test report, independent test or replication in the folders. That missing record is not treated as a neutral gap: a company that spent Fr. 1.12 million on research and left no papers is an anomaly, analysed in Section 4.4 ("The record goes dark"). The Investigator has since pieced together a partial biography of Kassner from the Swiss gazette and patent indexes (Berlin 1931, Arbon 1932, London 1934-36, Zürich 1943, Montana-Vermala about 1951) [web: research notes], and a third run (2026-10-04) found that he died in Munich by May 1962 (DE 1,128,930, printed with "Ernst E. W. Kassner †, München" as inventor) [web: research/2026-10-04-depatisnet.md]. Of his 1934 French patents only about 2 of 10 pages have been read. The patents are OCR'd scans, read against page images only in the deep reads. The Ternion company papers are financial and never name Kassner. The Imperial War Museum (IWM) interviews are machine transcriptions. The essay and three Morray-TH notes are interpretation; their factual statements are checked against the primary documents and cited from those, and their arguments are weighed as arguments. Web checks largely failed in Steps 2-3 (search quota exhausted). In the 2026-10-04 update the arbiter made one check in Chrome: blood at 300 MHz has a relative permittivity of about 65 and a conductivity of about 1.3 S/m (a search-result snippet, blood not serum), which supports the serum conductivity used below to the order of magnitude; the contrarian's check of water's relaxation time (8.27 ps) is also accepted. The non-thermal microwave literature is now partly documented by the Investigator (abstracts only; Section 4.5). The point, put to the review, that Goodrich held its own electronic-vulcanisation patents is still undocumented; none of the conclusions below rests on it alone. A full-text search of the Operation Paperclip book and the National Archives (NARA) microfilm records in the folders found no E. E. W. Kassner (only a "KASSNER RUDOLF" listed for jet engines), Ternion or Bauch [read: QE search]. That is weak evidence against a Paperclip link (index absence is weak, and a man living in Switzerland would not be expected in a US recruitment index); it is weighed in Section 4.4. In the 2026-10-08 update the arbiter made one web check (Cleeton and Williams, Physical Review 1934, ammonia absorption) and reran the other numbers; the papers on field-assisted electrolysis and bond weakening (Section 4.6) are known from abstracts and snippets only, as the Investigator recorded them.

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1. The idea in one paragraph

In 1931-32 a German engineer, Ernst Eduard Wilhelm Kassner, patented the idea that every substance whose molecules carry separated positive and negative charge (a "dipolar" substance such as water, fruit juice or blood serum) has its own "natural frequencies" in the short-radio and microwave range, and that bathing it in a concentrated field tuned to exactly that frequency changes it permanently in ways ordinary heating cannot: colloids change particle size, rubber vulcanises without catalysts, milk and juice keep for weeks, seeds grow faster, and molecules can be "frozen" into an aligned, energy-rich state. A Swiss holding company, Ternion AG, financed the work from 1932 until it ran out of money in 1937. Kassner also designed the hardware: valve oscillators, coaxial resonators and a resonator made of two parallel metal discs with the sample between them. An essay in the project folder goes further than Kassner, proposing that such fields could raise or lower chemical bond strengths, which might allow an energy-producing water cycle or a hidden weapon, and that defence interests may have kept the work obscure. The honest summary: the engineering and part of the physics are real and competent for the 1930s; the central claim, sharp resonances in liquids with effects beyond heating, was never tested by anyone else (later tests of similar sharp-line claims at much higher frequencies, in cells rather than serum, did not find them); in his own 1934 French patents Kassner explains his "natural frequencies" as ordinary, broad Debye relaxation, which is a different thing from a sharp resonance; some of Kassner's own numbers contradict his own later theory; and the essay's energy and bond-strength extensions conflict with basic thermodynamics in their strong form (a closed water cycle cannot gain energy), although measured relatives exist: high-frequency fields do lower the voltage cost of electrolysis at a heated catalyst, and infra-red light does weaken water's bond on a metal surface; neither has been shown to repay the field's own power, and neither works through Kassner's bands (Section 4.6). The history is stranger than the physics: a well-funded research company left patents but no papers, its people carried on under other company names, Kassner kept patenting until about 1960, and the buyer of the patents later described them only as heating. Others claimed the same kind of effect later (Orlan Arnold in the 1940s, Heller in 1959), but none of them tested Kassner's own examples. Why the research record (not the man) goes dark is an open historical question with named archives that could answer it (Section 4.4).

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2. What you need to know first

2.1 Dielectrics and polarisation. An insulator placed in an electric field E becomes polarised: its charges shift slightly, and molecules that already carry a permanent dipole moment p (charge times separation, units C·m) tend to rotate to line up with E. The result is a dipole moment per unit volume, the polarisation P. The material's relative permittivity ε (a pure number; 1 for vacuum, about 80 for water at low frequency) measures how strongly it polarises. Read: Griffiths, Introduction to Electrodynamics, chapter 4 ("Electric Fields in Matter").

2.2 Complex permittivity and Debye relaxation. In an alternating field of angular frequency ω (radians per second; ω = 2πf, with f in hertz) polar molecules cannot turn instantly; they are jostled by their neighbours and lag behind. Peter Debye (1912, book Polar Molecules 1929) modelled this with a single relaxation time τ (seconds): the time for alignment to decay once the field is removed. The permittivity becomes a complex number ε(ω) = ε′ − iε″: the real part ε′ is how much the material polarises in step with the field, and the imaginary part ε″ measures energy lost as heat each cycle. Debye's result is a broad "loss peak" at ω = 1/τ. For water τ ≈ 8.3 ps at room temperature (8.27 ps at 25 °C [web, checked by the contrarian reviewer]), giving a peak near 19 GHz, a wavelength of about 1.6 cm [calc]. Kassner calls this "friction dispersion". Read: Kremer and Schönhals, Broadband Dielectric Spectroscopy (2003), opening chapter; Debye, Polar Molecules (1929).

2.3 Resonance and the quality factor Q. A driven, damped oscillator (mass on a spring, LC circuit) responds strongly near its natural frequency f₀. The sharpness is measured by Q = f₀/Δf, where Δf is the width of the response peak. Equivalently, Q ≈ 2π × (energy stored)/(energy lost per cycle). High Q (say 50) means a narrow peak and ringing for about Q/π cycles after the drive stops; Q below about 0.5 means the system is "overdamped" and does not ring at all. Debye relaxation is overdamped. Read: Taylor, Classical Mechanics, the chapter on oscillations; or any intro ODE text on the damped driven oscillator.

2.4 Standing waves, cavities and Bessel functions. Between two parallel metal plates an electromagnetic wave bounces back and forth; only wavelengths that fit the boundaries survive (standing waves), exactly like the modes of a guitar string or a drum. For a rectangle the mode shapes are sines; for a circle they are Bessel functions J₀(x), J₁(x), ..., the "round sine waves" that solve the wave equation in polar coordinates. Their zeros (x where J = 0) and peaks are tabulated numbers, e.g. J₀ has its first zero at x = 2.405, J₁ at 3.832, and J₁′ (the slope of J₁) at 1.841. Read: Boas, Mathematical Methods in the Physical Sciences, the chapter on Bessel functions; Pozar, Microwave Engineering, the chapter on microwave resonators.

2.5 Photon energy versus thermal energy. Light (including radio) of frequency f comes in quanta of energy E = hf, with h = 6.626 × 10⁻³⁴ J·s (Planck's constant). Molecules at temperature T (kelvin) jostle with typical energy kT, with k = 1.381 × 10⁻²³ J/K (Boltzmann's constant); at 300 K, kT ≈ 0.026 eV (1 eV = 1.602 × 10⁻¹⁹ J). A chemical bond is a few eV. If hf is far below kT, a single photon is lost in thermal noise and cannot break or "re-tune" a bond by itself. Read: any intro modern physics text (e.g. Serway, Moses and Moyer, Modern Physics), the photoelectric effect and blackbody chapters.

2.6 State functions: enthalpy and Gibbs energy. For a chemical reaction, the enthalpy change ΔH is the heat released at constant pressure, and the Gibbs free energy change ΔG is the maximum useful (e.g. electrical) work. Both are state functions: their values depend only on the start and end states, not on the path. Any cycle that returns to its starting state has ΔH = ΔG = 0 overall. Read: Atkins, Physical Chemistry, the chapters on the first and second laws and on electrochemistry.

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3. The textbook view

3.1 How a polar liquid responds to a field: Debye

The Debye model (one relaxation time τ) gives

ε(ω) = ε∞ + (εs − ε∞)/(1 + iωτ)

where εs is the static (low-frequency) permittivity, ε∞ the high-frequency value, ω the angular frequency, τ the relaxation time and i = √(−1). Splitting into real and imaginary parts, the loss is

ε″(ω) = (εs − ε∞) · ωτ/(1 + ω²τ²)

which peaks at ωτ = 1 and falls to half its peak at ωτ = 2 − √3 = 0.268 and ωτ = 2 + √3 = 3.732 [calc]. Those half-maximum points are a factor 13.9 apart in frequency (about 1.1 decades, since log₁₀ 13.9 = 1.14): the band is very broad, with an effective Q of about 0.29 [calc]. (One reviewer described water's peak as spanning "about six decades"; a single Debye curve cannot do that at half height, and the arbiter marks the figure as unreconciled, probably the range over which the loss is visibly non-zero. Either way the band is hundreds of times broader than 2 percent.) Debye also gave τ = 4πηa³/(kT) (η = viscosity, a = molecular radius), which Kassner quotes [read: GB417501 complete specification, p.7-8], so τ, and hence the peak, moves with temperature through viscosity.

In conducting liquids (salt water, juices, serum) there is also ionic conduction: free ions drift and lose energy to friction. Its contribution to the loss is σ/(ωε₀), where σ is the conductivity (S/m) and ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. For serum with σ ≈ 1.5 S/m [memory, medium; supported to the order of magnitude by blood at 300 MHz, ε ≈ 65 and σ ≈ 1.3 S/m, web: https://www.google.com/search?q=blood+serum+conductivity+S%2Fm+dielectric+properties+of+body+tissues+blood+300+MHz, snippet of a ResearchGate compilation] at 333 MHz (Kassner's 90 cm serum line), σ/(ωε₀) ≈ 81 [calc, physicist] (78 at 300 MHz with the blood values [calc]): the liquid is heavily damped. Biological tissue spectra measured since the 1950s (Schwan; Gabriel and colleagues) show broad, overlapping relaxations, not narrow lines [memory, medium; web check failed]. The mainstream benchmark for "electrolyte bands", the Debye-Falkenhagen dispersion of the ionic atmosphere, is recalled as broad and in the MHz range [memory, low; not yet searched].

A coincidence worth testing (the mathematician's, accepted by the arbiter as a hypothesis, not a finding). The conduction loss and the ordinary polarisation are equal where σ = ωε₀ε_r, i.e. at the crossover frequency f_c = σ/(2πε₀ε_r). With σ = 1.5 S/m and ε_r = 80, f_c = 1.5/(2π × 8.854 × 10⁻¹² × 80) = 0.337 GHz, a wavelength of 89 cm; with the blood values, 0.36 GHz and 83 cm [calc, example.py step 8a]. Kassner's serum band is "about 90 cm". But conduction loss falls smoothly as frequency rises; it has no peak, so the crossover is a gradual change of regime, not a Q of 20-50 line. It is a candidate for what a broad "serum band" near 90 cm could be. Nobody has shown Kassner meant it, and the patent says nothing like it.

3.2 What a microwave field does to matter

Absorbed power heats the sample: power per unit volume = ½ωε₀ε″E₀², with E₀ the field amplitude. This is dielectric heating, the principle of the microwave oven and of industrial radio-frequency (RF) curing, drying and vulcanisation. RF dielectric heating was being proposed in the 1930s, e.g. a 1937 Bell Labs patent for 10-20 MHz heating [web: https://en.wikipedia.org/wiki/Dielectric_heating]. A strong field also aligns molecules a little, making a liquid weakly birefringent (doubly refracting): the Kerr effect, which in water is tiny and relaxes in picoseconds [memory, high]. If a wax is poled by a strong DC field while it solidifies, the alignment is frozen in and you get an electret, known since Eguchi (about 1919-1925) [memory, medium].

3.3 The parallel-disc resonator

Two round metal plates of radius R, gap d, with a medium of relative permittivity ε between them, hold a standing wave with the electric field normal to the plates:

E_z(r) = E₀ J₀(kr), k = 2π√ε/λ

where r is the distance from the centre, E₀ the field at the centre, k the wavenumber in the medium and λ the free-space wavelength. The edge condition fixes the allowed k: - rim shorted (E = 0 at r = R): kR = 2.405, 5.520, ... (zeros of J₀); - rim open (dE/dr = 0 at r = R): kR = 3.832, 7.016, ... (zeros of J₀′ = −J₁), and the lowest mode of an open disc overall is the one-node-diameter mode with kR = 1.841.

Therefore

λ = 2πR√ε / x, x = the relevant Bessel root.

Note what is absent: the gap d. For a thin gap the resonant wavelength depends on radius and filling, not spacing. In practice the field fringes beyond the rim, making the disc act a little larger; an engineering estimate for a circular patch is a_eff = a·√[1 + (2h/(πaε))(ln(πa/2h) + 1.7726)] (a = radius, h = gap) [memory, medium; strictly valid for h ≪ a]. Layered fillings with the field across the layers add like capacitors in series: ε_eff = d / Σ(dᵢ/εᵢ).

3.4 Energy bookkeeping for a chemical cycle

For H₂ + ½O₂ → H₂O(liquid) at 25 °C: ΔH = −285.8 kJ/mol, ΔG = −237.1 kJ/mol, and the difference TΔS = 48.7 kJ/mol is heat exchanged with the surroundings [memory, high]. Splitting water needs at least ΔG of electrical work, a cell voltage of ΔG/(2F) = 1.229 V (F = 96,485 C/mol, Faraday's constant); at 1.481 V the cell needs no outside heat [calc]. Because ΔH and ΔG are state functions, electrolysis followed by burning returns exactly to the start: no net energy, whatever happens to the bonds in between. One half of the idea is ordinary textbook physics: a cell run between 1.229 V and 1.481 V takes the missing TΔS as heat from its surroundings, like a heat pump, so its "coefficient of performance" COP = ΔH/(electrical work) can exceed 1, but never ΔH/ΔG = 285.8/237.1 = 1.205 [calc, example.py step 9a]. A cycle that makes hydrogen hot and burns it cold (a "thermally regenerative" cycle) is a heat engine, bounded by the Carnot efficiency 1 − T_c/T_h (T_c, T_h = cold and hot temperatures in kelvin), 0.20 between 373 K and 298 K [calc, step 9f].

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4. Where the researchers depart

4.1 Kassner

Box: where Kassner's numbers come from. Some of Kassner's numbers look like measurements but can be traced to a calculation. The 1932 disc figures are one case: they all follow λ = 3 × diameter (Section 5). His chemistry wavelengths are another.

What the patent says. Reactions between hydrogen, chlorine and similar substances may emit radiation at "the term differences of hydrogen, which correspond to wave-lengths of 2.74, 9.25 and 27.75 cm", and the most effective reaction bands are 2.5-3.5, 8.6-9.5 and 26.5-30.5 cm [read: GB417501 p.11, page image]. A "term" is the 1930s spectroscopists' word for an energy level written as a wavenumber ν̃ = 1/λ (in cm⁻¹). A "term difference" is the gap between two levels.

The physics you need. In the Bohr model, hydrogen's level n (n = 1, 2, 3, ...) sits at ν̃ = −Ry/n², where Ry = 109,737 cm⁻¹ is the Rydberg constant [memory, high]. Sommerfeld (1916) and Dirac (1928) showed that each level is split very slightly by relativity and the electron's spin. This is the fine structure. Each state also has an orbital quantum number l (0 to n − 1, the electron's orbital angular momentum in units of ħ = h/2π) and a total angular momentum j = l ± ½ (orbit plus spin). For given n and l, the two j states are separated by

Δν̃ = α²·Ry / (n³ · l(l + 1))

where α ≈ 1/137.036 is the fine-structure constant, a pure number [memory, high]. Then λ = 1/Δν̃. Since α²·Ry = 5.844 cm⁻¹ [calc]:

[calc, example.py step 7; the n = 2 value, 0.365 cm⁻¹, is confirmed at https://en.wikipedia.org/wiki/Fine_structure [web]; the n = 3 values rest on the calculation.]

What it means. All three of Kassner's wavelengths agree with the fine-structure intervals to within 0.1 percent, and each reaction band brackets one of them. The patent never says "fine structure", so the identification is an inference, but three matches at that precision make it very likely. These "most effective frequencies" for chemistry are therefore numbers taken from atomic theory, not reaction optima measured in the laboratory. Nothing in the documents shows that atoms in a reacting mixture emit or respond to fine-structure radiation, so the claim stays Never properly tested (arbiter, QE revision on claims 2 and 3). The general lesson: before you treat a number in a patent as data, check whether a formula produces it.

4.2 The essay in the project folder

The essay starts from real things: water is polar and Debye explained its relaxation [read: essay p.2]; the patent does name temperature (and for gases pressure) as tuning handles [read: GB417501 complete spec.]; the Ternion company existed; Bauch's 1934-35 secondment to the General Electric Company (GEC, the British firm) Research Laboratories at Wembley is confirmed by four accounts from 1953 to 1996 [read: IWM interviews, Swiss Sound 1983, 1996 memoriam; web: Wireless World Feb 1953, https://archive.org/details/sim_wireless-world_1953-02_59_2], and his work there on Ternion is documented in one published source (Section 4.4); and the essay states the first law correctly ("the energy to electrolyze water is equal to the energy received when Hydrogen and Oxygen are burned") [read: essay p.7].

It departs at four points, none of which is in any Ternion document: 1. Bonds. "Natural frequencies are used to artificially increase or decrease the strength of covalent and ionic bonds" [read: essay p.3, p.6]. Kassner's terms are "energy content" and orientation; the words "covalent", "ionic bond" and "binding energy" do not occur in the patents [read: grep, deep read]. The fuller statement (arbiter, 2026-10-08): microwave photons cannot weaken a water bond, but infra-red photons can, on a surface (Section 4.6). 2. Energy. If bond energy can be lowered during electrolysis and the gas burned elsewhere, the machine could be "economically generating electric power ... in perfect harmony with ... the laws of science" [read: essay p.7]. Textbook: ΔH and ΔG are state functions; the cycle gains nothing (Section 3.4). How the field would be applied matters for any test. A review direction of 2026-10-07 corrects an earlier wording ("RF-assisted electrolysis") that was too narrow: Ternion applies energy mainly by displacement current through the sample, in what Kassner calls a "standing field" (conductors set into natural oscillation so that standing waves fill the space holding the substance, "a pair of concentric tubes or a plate-resonator" [read: US2089966 p.3, via the Investigator]), and also by radiated RF from a wand applicator, his "radiating field". Claim 11 now reads accordingly: electrolysis assisted by a resonant standing field (displacement current) or by radiated RF. Kassner himself never wrote about electrolysis or bond energy; his chemistry statement is a rate claim (acetylene plus water to acetaldehyde, GB417501 p.4-5) with no yield, energy or control. Section 4.6 sets out what has been measured. 3. Weapons and suppression. Engineered binding energies "could be made to interfere with metabolic functions" and defence interests may have hidden the work [read: essay p.8]. The weapon premise inherits the bond-strength problem (point 1; Section 5, step 6). The suppression part is a historical claim, and it can be tested. On 20 Dec 1937 Ternion's board voted to liquidate "owing to a complete lack of further funds", with research spending of Fr. 1.12 million on a capital of Fr. 100,000 [read: Glarus register papers, AG2 p.10; calc, mathematician]. That is the board's own account of a financial end. It does not rule out outside pressure, because the lenders who stopped the money are not named. No document in the folders shows suppression, and the archives that would decide the question have not yet been searched. The premise that Kassner himself vanished is now known to be wrong: he kept filing patents until 1960 and died in Munich by May 1962. What is missing is the research record, not the man. Section 4.4 sets out the evidence. 4. Replication. Failures are blamed on uncontrolled temperature and pressure [read: essay p.3]; but no replication attempt has been found in the folders or in the searches so far (Internet Archive, Europe PMC, UK National Archives, Swiss gazette), so no failures are on record to explain. That silence is itself a puzzle: a patented process that was cited in the literature from 1935 to 1955 and bought by Goodrich and Firestone in 1945 left no recorded test. The possible explanations are that nobody tried; that someone tried and did not publish (for example the buyers, in-house); trade secrecy; or that the patentee's instruments could not be rebuilt from the patents. Test data in the Goodrich or Firestone files, or the exhibits of the Arnold v. Watson court case, would decide between them. How much does temperature matter? If the bands move like water's Debye relaxation time (about 17.7 ps at 0 °C and 8.3 ps at 25 °C [memory, medium], about 3 percent per kelvin [calc]), a band 2 percent wide stays in place only within about 0.7 K [calc, example.py step 8b]. That is a thermostat, easily met; and a true Debye hump, being broad, needs no temperature control at all, a further sign that the sharp-band claim and the relaxation claim are different things. Orlan Arnold (US 2,522,082, filed 1945) did what the essay says was missing: he stated that his "critical frequency" shifts with temperature, concentration and voltage, and that it must be tracked or the conditions held constant [web: research/2026-10-04-arnold.md]. Kassner gives no such protocol.

The essay also says Bauch was "an employee of GEC" who "collaborated jointly" with Ternion. That goes beyond the one source, which says only that he worked on a Ternion project while seconded to GEC (Section 4.4).

4.3 Two descriptions of the same patents: Kassner versus the buyer

In 1945 the B. F. Goodrich and Firestone rubber companies were reported as buying a package of patents for curing rubber by radio waves, which "originally were granted on discoveries made by" Dufour, Le Duc and Kassner [read: 1945 clippings, page images]. A 1950 paper from the Goodrich Research Center names Kassner's US 2,089,966 and US 2,109,843 in the portfolio [web: research/2026-10-03-internet-archive.md]. The buyer and the inventor described the same patents very differently. The rule here is to report a description by someone with a stake as that party's description, beside the inventor's own.

A check you can do. "About 150 million cycles per second" is 150 MHz, a wavelength λ = c/f = (3.00 × 10⁸ m/s)/(1.5 × 10⁸ Hz) = 2.0 m. In GB417501's milk example the five bands are 455, 355, 283, 163 and 27.5 cm; the four longest carry 573 of the 573.6 W, at 66 to 184 MHz [calc from read figures]. So Goodrich's figure fairly describes where most of the power went. It does not describe the "natural frequencies" the patent rests its case on: serum near 90 cm (333 MHz), fruit juice near 40 cm (750 MHz), water near 1.3-1.5 cm (20-23 GHz) [calc]. It also fits part of the apparatus range: the 2.05-2.90 m tuning table is 103-146 MHz [calc]. It is silent on the natural frequencies and on the 0.4-1 m food examples. The summary is accurate as far as it goes and says nothing about the part Kassner claimed as new.

Kassner as prior art in later patents. US 2,495,429 (Spencer, Raytheon, filed 1945, the microwave-oven patent) lists "2,094,602 Kassner" (his ellipsoidal-reflector applicator) among the references cited; US 2,833,657 (Raytheon, 1954) cites US 2,089,966; 32 later UHF-tube patents cite US 2,109,843 [web: research/2026-10-03-google-patents.md; Spencer scan read by two reviewers]. Whether the examiner or the applicant added each citation is not stated. These patents frame their inventions as heating, so the citations support Voss's historical point (an early multi-frequency applicator) and say nothing about the resonance mechanism. One anomaly, recorded and not explained: Kassner is named in the January 1945 purchase release but not in the August 1945 licensing announcements of Industry Inventions, Inc., which name only "Leduc and Dufour".

Evidence on both sides. Against Kassner's non-thermal reading: the 1945 announcements, Science News Letter and Electronic Industries all describe the process as uniform heating [web: research notes], and his own food examples report temperature rises of 2.5 to 4.5 K (Section 4.1). For it: Rubber World (Apr 1945), reporting the same purchase, adds that "the excellent results obtained by electronic vulcanization are due not only to rapid uniform heating, but also may be connected in some way with electronic power itself" (no data) [web: https://archive.org/details/sim_rubber-world_1945-04-01_112_1]. A later inventor, Orlan M. Arnold, claimed a sub-thermal effect at the dispersion frequency, and Kassner's patent was cited against him as prior art (In re Arnold, 1950; Arnold v. Watson, 1955, and on appeal 237 F.2d 584, D.C. Cir. 1956) [web: research/2026-10-03-caselaw-access-project.md; research/2026-10-04-arnold.md]. Arnold is described in Section 4.5.

Was Goodrich's account false? There is no evidence that Goodrich's staff knew of non-thermal effects and described the patents otherwise, so the arbiter does not call it a misrepresentation. It is one interested party's description, not the neutral fact of what the patents do. It has also been put to the review that Goodrich held its own electronic-vulcanisation patents; that is not yet documented in the files (the web check failed). The records that would show what Goodrich knew: Goodrich's internal test data on the Kassner process (company records, possibly at the University of Akron [memory, medium]); the 1945 purchase files of Goodrich, Firestone and their agent H. H. Giodvad Grell, including the contract of 15 Nov 1945 by which Grell sold unnamed "patent rights" for Fr. 200,000 to Vibranic Ltd, Glarus, chaired by Ternion's founder Max Stoffel (Landesarchiv Glarus) [web: research/2026-10-03-e-periodica-shab.md]; and the Arnold v. Watson trial exhibits. A purchase is not a test in either direction: it neither shows the resonance mechanism works nor that it does not.

What the Fr. 200,000 bought: partly identified by priority dates. A patent filed abroad can claim the date of an earlier first filing (its "priority date"); two patents with the same priority date belong to the same invention. Vibranic's French patent FR 926,351 (filed 6 May 1946) claims the priority date 22 Apr 1943, the same as US 2,415,025 by H. H. Giodvad Grell and Harry W. Richards ("Method and apparatus for treating matter in a high-frequency electric field", granted 28 Jan 1947, assigned to Firestone and Goodrich; its text is about uniform heating). Vibranic's Swiss patent CH 250,508 ("Verfahren und Vorrichtung zur Ultrakurzwellenbehandlung", waves under 10 m radiated into a reflecting chamber for "Erwärmen, Altern, Vulkanisieren", i.e. heating, ageing, vulcanising) shares its priority date, 4 May 1945, with Grell's own CH 254,655 [web: research/2026-10-03-google-patents.md; US 2,415,025 confirmed on the USPTO scan, research/files/US2415025.ocr.txt; physicist D2, mathematician 4a, contrarian; sites.md lead 14]. So the "patent rights" Grell sold to Stoffel's Vibranic in Nov 1945 included at least the non-US rights to Grell's own heating patents, whose US rights Firestone and Goodrich held. No document yet shows a Kassner patent in that package; the Vibranic purchase contract in the Glarus register file would decide. This documents continuity of Stoffel's patent dealings in the same field (explanation 3 in Section 4.4), not continuity of Kassner's patents. The Fr. 200,000 is 0.18 of Ternion's book research account [calc, mathematician], which shows only that the 1945 price was far below book cost.

Voss, editor of the Journal of Microwave Power, wrote in 1987 that Kassner "did some remarkable experiments", that he "'sketched' (perhaps that is the key word) our subject", and "In truth he foresaw both the microwave oven and the industrial electromagnetic energy applicators"; he then asked "Who was Ernst Kassner?" [read: Voss deep read, printed p.56].

4.4 The record goes dark

The anomaly. Ternion A.-G. was founded on 18 Apr 1932 for "participation in electro-physical enterprises and laboratories". By 31 Dec 1936 it had put Fr. 1,120,380.15 into research (93.6 percent of its assets), financed by Fr. 1,096,535.05 of loans [read: AG2 pp.6-8]. It produced a large patent family: British, US, French and Swiss filings, at least 15 [read; web: research notes]. Yet no research paper, white paper, conference talk, test report or later scientific work by Kassner or any Ternion scientist has been found, in the folders or in the archives searched so far [web: sites.md]. In 1987 Voss, editor of the Journal of Microwave Power, had to ask "Who was Ernst Kassner?" [read: Voss deep read]. For a funded research company that silence is unusual, so it is treated as something to explain.

What exactly is silent was narrowed on 2026-10-04. It is a silence of technical reports, notebooks, papers and conference talks, not of the man or the company group. Kassner is documented from about 1921 to his death in Munich by May 1962: patents throughout, a 1937 folder "Phono-Vision, Ernst E.W. Kassner" of "Fotos und vertrauliche Firmenunterlagen" (photos and confidential company papers, Kantonsbibliothek Appenzell Ausserrhoden), a 1938 visiting card to Hans Kayser (Swiss Literary Archives), General Infra Co. AG, Chur (1943-53), and his last patent, DE 1,128,930, filed 14 Apr 1960 and granted to a private applicant, Wilma Hencke of Munich (her relation to him unknown) [web: research/2026-10-04-depatisnet.md, research/2026-10-04-records-and-rechecks.md]. And the Arbon laboratory seems to have stopped early. Three Thurgau newspapers of 30 Dec 1933 to 3 Jan 1934 name "die Aufhebung der Dipol A.G." (the closing of Dipol A.G.) as one reason for a fall in Arbon's 1933 tax income [web: https://www.e-newspaperarchives.ch/?a=d&d=TGZ19331230-01.2.6.1]. The arbiter carries this as the best reading, with its limit: it is an inference from a tax remark, not a closure notice, and "Aufhebung" could mean something short of the work ending. If it holds, the laboratory ran about 18 months, and the Fr. 1.12 million research account at the end of 1936 was not spent in Arbon after 1933: Dipol's loan account on Ternion's balance sheet is only Fr. 51,155 [read: note-14 deep read, via the contrarian]. Where the rest went (patent and London work 1934-36, when Kassner was "résidant en Angleterre"; a book valuation of the patents; other spending) is undocumented. Dipol's signing chemist, Dr. Alfred Wiegner, was by his ETH dissertation and diploma an analytical and dye chemist, not a dielectrics specialist [web: research/2026-10-04-records-and-rechecks.md], weak evidence about what the laboratory could measure.

Two limits on the silence: only three rounds of archive searching have been done (Espacenet and ScienceDirect were blocked by CAPTCHA, and several archive catalogues cannot be searched online), and the patents themselves were a public disclosure that was read and cited (Chemical Abstracts 1935; Thorpe's Dictionary of Applied Chemistry, Weissberger's Technique of Organic Chemistry and Ellis's Chemistry of Synthetic Resins, which cite the claim and report no test; The Botanical Review 1944; US courts 1950 and 1955) [web: sites.md lead 7].

Six explanations, with the evidence for and against each.

Weighing, on the evidence in hand (the arbiter's conclusion). The 2026-10-04 findings move the weights modestly. Replacing a silent man with a silence only of research reports makes "the man was removed" less natural; the Dipol timing and General Infra's 1944 unwinding add to the failure explanation for the group; trade secrecy gains a little from the "confidential company papers" folder (an advertising file, so ordinary business confidentiality); wartime context gains one unread file title and nothing more. Commercial failure is the best-documented explanation for the end of Ternion A.-G. itself in 1937. Continuation under other names is also documented: the record did not stop in 1937, it moved. Neither explains why no technical report or paper from 1932-37 survives. Trade secrecy or contract work at GEC would explain that, and the memoriam sentence is the one document pointing to the second. Classification and suppression are neither shown nor ruled out: the documents in hand weigh somewhat against them (open patents, open later companies, absence from the Paperclip indexes), but they do not reach the unpublished research, which is exactly what is missing. The explanations are not exclusive; a company can fail for lack of money and keep its methods secret at the same time.

How to think about it. This is the same discipline as the physics. "No papers" is a fact; "therefore suppressed" and "therefore nothing there" are both conclusions that need more evidence. List the explanations, say what each predicts, and find the record that tells them apart. The records are named in the table; the Investigator step is searching for them. The arbiter's first archive item is now the Arnold v. Watson trial exhibits (National Archives, Record Groups 21 and 276), the only known place where an evidential test of a Kassner-type principle may have been put on file (Section 4.5); then the three Swiss Federal Archives files and the Arbon tax rolls.

4.5 Others who claimed the same kind of effect, and the tests on record

These are leads found by the Investigator, weighed by the reviewers. None of the claimants is a replication of Kassner, and none of them supplies controls, counts or statistics; the two controlled tests at the end of this section concern a related class of claim. They are kept because they show the idea did not stop with Kassner, and because they show what testing such a claim looks like.

Orlan M. Arnold (US 2,522,082, filed 1945). A trained dielectric chemist (papers in the Journal of the American Chemical Society, 1936, and the Journal of the Electrochemical Society, 1938, on electrolyte and resin dispersion) claimed selective activation of a substance at a "critical frequency", "near the center of the anomalous dispersion range", "without destructive heating" [web: research/2026-10-04-arnold.md]. That is Kassner's idea in the language of Debye dispersion. The examiner cited Kassner against him. The courts refused his broad claims as "too broad and indefinite" and did not rule on the physics; the 1955 trial court said it decided "on evidence" and that Arnold "exposed the error of certain assumptions ... by predecessors". The exhibits have not been seen. Two reviewer arguments against his mechanism (arguments, not tests): absorption is greatest at a loss peak, so "activation without heating" there needs a thin or cooled sample; and the skin depth (how far the field penetrates a conductor) is about 1 m at 27 MHz in weakly conducting water and 2.3 cm at 333 MHz for σ = 1.5 S/m [calc, physicist and mathematician], so nothing selects a micrometre surface layer. Verdicts: surface selectivity Not testable as stated; the broad Debye-centre idea Never properly tested at his frequencies.

Heller and Teixeira-Pinto (Nature 183:905, 1959; US 3,095,359, which cites US 2,089,966). Pulsed 27 MHz fields (pulses of about 5 µs, the exponent uncertain in the scan; 80-180 per second) on garlic root tips in water produced chromosome aberrations, with frequency, pulse and axis dependence; "No temperature increase in the water was noted"; no cell counts, controls or statistics [web: research/2026-10-04-heller-pearl-chain.md]. Could heating explain it? The physicist gets 0.005-0.08 K at a water conductivity of 10⁻⁴ S/m but 0.5-8 K at 10⁻² S/m; the mathematician 0.003-0.09 K and 1.3-46 K at 5 × 10⁻² S/m [calc]. They agree; the answer turns on a conductivity and field the letter does not give. So the printed information neither excludes nor establishes a thermal cause. A useful number for a learner: a 5 µs pulse has a spectral width of about 1/(5 µs) = 0.2 MHz, 0.74 percent of 27 MHz [calc, example.py step 8c], so Heller's "frequency dependence" is a claim measurable to about one percent. The pearl-chain alignment of cells he also reported is conventional: the alignment energy is 6 × 10⁴ to 10⁶ times kT for 5 µm cells [calc, physicist, assuming a Clausius-Mossotti factor of 0.5], so it needs no new physics. It is also old: pearl chains of particles in HF fields were reported by Muth (Kolloid-Zeitschrift, 1927), with theory by Krasny-Ergen (Hochfrequenztechnik und Elektroakustik, 1936-37), as cited by the 1960 Navy survey [web: research/2026-10-04-heller-pearl-chain.md; neither paper read by a reviewer]; this mainstream line (induced polarisation, Maxwell-Wagner) is contemporary with Kassner's patents. A US Navy contractor survey (Midwest Research Institute, 1960) reported Heller's work as non-thermal and offered interfacial polarisation as the mechanism; it is a hazard-standards contractor reporting a claim, not a replication. Verdict on the chromosome effect: Never properly tested (no replication found; Mittler 1976 found no genetic damage in fruit flies at 2 and 10 m wavelengths, a different organism, title only).

Earlier and parallel claimants. Liebesny and Wertheim (GB 417,863, wavelengths 1.8 mm to 120 m, chosen per organism), Benedetti, and the 1930s German dispute over a "specific effect" of short waves: Schliephake and Compère (1933) and Archangelsky ("Über die spezifische Wirkung des Ultrakurzwellenfeldes", 1930s, listed in Kowarschik's reference list; bibliographic record only, no data) for it, while Kowarschik (1936) and other texts, seen only as snippets, say none was proven [web: research/2026-10-04-related-work.md]. The Botanical Review (1944) cited GB417501, and Rubber World (Apr 1945) wrote that results "may be connected in some way with electronic power itself". Later patents also cite GB417501: Jonas, US 2,712,713 (1950), seed treatment by HF fields, which bears directly on Kassner's bean example (claim 3); Hayashibara GB 2,145,317 (1983, animal productivity); Vergara Piccaluga EP 0,848,058 (1995, cell behaviour); and "Aqua Dynamics" water-treatment patents (1990-91) [web: research/2026-10-03-google-patents.md; sites.md lead 13]. No reviewer weighed Jonas or these later citers; the arbiter records them unweighed, as further claimants, not tests, and names the Jonas text (its claims and any germination figures and controls) as the next thing to read for claim 3. These are claims with no data in hand. Over a frequency range of 6.7 × 10⁴ [calc], "choose the frequency for the organism" cannot be tested unless the organism-to-frequency map is given.

Sharp lines in cells: the tests on record. Webb and Booth (Nature, 1969) and Grundler and Keilmann (Physical Review Letters 51:1214, 1983, "Sharp resonances in yeast growth", near 41.7 GHz) reported narrow frequency windows. Gandhi and colleagues (Bioelectromagnetics, 1980) swept 26.5-90 GHz on DNA, RNA and cell suspensions, with temperature control and frozen samples, and found "Sharp spectra reported by other workers were not observed"; Gos and colleagues (Bioelectromagnetics, 1997) repeated the yeast work from 41.682 to 41.710 GHz with concurrent controls and found "no consistently significant differences" [web: research/2026-10-04-related-work.md; abstracts only, no reviewer read the full papers]. The arbiter rules this class of claim Tested, not supported. It is evidence about the class, not a test of Kassner: the frequencies are about 100 times his serum band, and the samples are cells and nucleic acids, not serum. Nothing on record tests his 0.3-4.9 m region. In chemistry the question of non-thermal microwave effects was still argued in 2013 (Kappe, Pieber and Dallinger, Angewandte Chemie): a 10 K local temperature error near 100 °C changes a reaction rate by a factor of about 2 for an activation energy of 80 kJ/mol: by the Arrhenius law k = A·exp(−E_a/RT), with R = 8.314 J/(mol·K) the gas constant, k(373 K)/k(363 K) = exp[(80,000/8.314)(1/363 − 1/373)] = 2.04 [calc, example.py step 8d; the factor 1.3 first printed by the mathematician and arbiter was an arithmetic slip, corrected to 2.04 in both files on 2026-10-04; the correction only strengthens their point]. That is how apparent non-thermal effects usually arise; it does not exclude real ones.

4.6 Electrolysis and bond strength: what has been measured (2026-10-08)

Follow-ups Q03 and Q05 asked whether a field can make splitting water cheaper. The Investigator found measured, mainstream relatives of the idea; none uses a Kassner band, and the papers are known from abstracts and snippets only [web: sites.md leads 32-40].

Where the saving could come from. A real cell needs about 0.4-0.8 V more than the 1.229 V minimum [memory, medium]: this excess, the overpotential, is lost as heat at the electrodes because the reactions there are slow. A field can attack the overpotential, which is waste, but not the 237.1 kJ/mol floor ΔG, which is thermodynamics. And any saving must be paid for in field power actually absorbed by the water: to save 24 kJ/mol (about 10 percent of ΔG) while making 1 mol of hydrogen per hour, the field must deliver at least 24,000 J / 3600 s = 6.7 W [calc, example.py step 9a]. So the only honest test counts the total work per mole, DC electrical energy plus the field's real power (drive minus reflected).

Measured relatives. - Niether and colleagues (Nature Energy 3:476, 2018). High-frequency magnetic heating of iron-carbide/nickel nanoparticles on the electrode cut the oxygen-side overpotential by 200 mV and the hydrogen side by 100 mV at 20 mA/cm², "equivalent to ~200 °C" at the catalyst while the bulk warmed only 5 °C [web: ideas.repec.org abstract, per the Investigator]. The mechanism is local heating of the catalyst. - Serra and colleagues (Nature Energy 5:910, 2020). Microwaves reduce gadolinium-doped ceria, which then splits water below 250 °C [web: nature.com abstract]. The university holds a patent (ES2726028-B2), so it is an interested party. - A 2026 review in ACS Applied Energy Materials (9:10362) speaks, in a snippet whose context is unseen, both of a "negative energy balance" made worse by coil losses and of one laboratory-scale "net energy saving of 215.6 kWh" [web: pubs.acs.org, snippet]. - Roy, Rao and Kanzius (Materials Research Innovations 12:3, 2008; Current Science 98:1500, 2010). A 13.56 MHz field of about 300 W over salt water releases a gas that burns only while the field is on; they report a Raman change in the O-H region and propose "resonant coupling"; they do not claim net energy [web: i-sis.org.uk summary; Chemistry World snippet]. No independent replication, for or against, has been found. Its wavelength, 22 m, is far from Kassner's water band. The only third-party description found is by Mae-Wan Ho (Institute of Science in Society, 2009; an outlet with an advocacy stance on science policy, which is its stake): "The phenomenon is real, but the mechanism is entirely unknown", and the 13.56 MHz photon carries about 10⁻⁸ of the energy needed per molecule [web: https://www.i-sis.org.uk/canWaterBurn.php, via the Investigator; checked: h × 13.56 MHz = 5.61 × 10⁻⁸ eV against 4.80 eV for O-H, a ratio of 1.17 × 10⁻⁸ [calc, arbiter]]. An anonymous reader comment on the same page says the Raman spectra look similar "apart from a minor difference in peak intensities". This is documented in one published source, with no second source found yet, and it cuts both ways: the effect is reported as real, the spectral evidence is questioned, and the photon energy rules out a single-photon bond effect. - The second Wien effect. A strong static field (about 10⁸ V/m [memory, medium]) orients water and speeds its dissociation into H⁺ and OH⁻ (Onsager 1934; used today in bipolar membranes, Bui and colleagues 2021) [web: sites.md lead 37]. It is DC and a rate effect, not a resonance, but it is an independent, measured relative of the orientation half of Kassner's claim 2. Evidence against its standard explanation: Stovall and colleagues (EES Catalysis, 2026) "question the model" of field-enhanced water dissociation in bipolar membranes [web: sites.md lead 37, snippet via the Investigator; not read]. The measured rate effect is not in dispute in the snippets; its mechanism is. - Hundt and colleagues (Science 344:504, 2014). Infra-red laser light tuned to the water (D₂O) stretch vibration strongly promotes its dissociation on a nickel (Ni(111)) surface, and follow-on work (J. Chem. Phys. 2018) showed O-H versus O-D selectivity in HOD [web: sites.md lead 34]. This is genuine resonant, bond-selective weakening, but its photon is 0.33-0.46 eV, 3,400-4,700 times a 1.28 cm photon [calc, step 9c]. (Earlier project notes said "about 35,000 times"; that is wrong. The arbiter traced the confusion: about 50,000 is the O-H bond, 4.8 eV, over the photon. Corrected 2026-10-08 in the arbiter and, with a dated correction note, in physicist.md C5; the Q03 note and sites.md lead 34 still carry the old figure until the orchestrator and the Investigator correct them.)

Other claimants in the same area (kept in the record, unread). These are claims by others or characterizations of them, not tests, and no reviewer read the primary texts. - Puharich, US 4,394,230 (1983): water splitting by a "complex electrical wave form" [web: Google snippets via the Investigator, sites.md lead 35; the patent text was not read]. The mathematician adds that Puharich's 1987 compilation names "22.3 GHz" as water's resonance, which is the water-vapour line (22.235 GHz) [web: snippet via the Investigator]. It is the one item in the record that ties a resonance-electrolysis claimant to the same vapour line discussed as a candidate source of Kassner's 1.28 cm (Section 4.1). Unread, so no weight either way. - Stanley Meyer's "water fuel cell": an Ohio court in 1996 found "gross and egregious fraud" after expert testimony that the cell used conventional electrolysis [web: Wikipedia snippet via the Investigator, sites.md lead 35]. That is the court's characterization in an adversarial case brought by investors, not a laboratory test, and it concerns one device; it says nothing about Kassner's principle. Meyer's own description of his device is not in the record (no reviewer read his patents).

Could the environment pay through ambient radio? Q05's "the environment pays" could in principle mean a second energy reservoir. Ambient radio is too weak: typical levels are 0.1-10 µW/cm² [web: aggregator snippet via the Investigator; the primary survey, Piñuela and colleagues 2013, not read]. At 1 µW/cm² = 0.01 W/m², the 6.7 W needed above (24 kJ/mol at 1 mol of hydrogen per hour) requires about 660-670 m² of perfect collector [calc, arbiter; the reviewers use 6.6-6.7 W], and a plate resonator tuned at 19-23 GHz does not collect broadcast bands (roughly 0.1-6 GHz [memory, medium]) anyway. The physical routes left are the TΔS heat already counted in Section 3.4 (48.7 kJ/mol) and a genuine hot/cold or sunlight-type second reservoir, bounded by Carnot (0.20 between 373 K and 298 K).

How strong would a field have to be? If a field stored energy in water linearly, u = ½ε₀(ε_r − 1)E² per unit volume, then storing 24 kJ/mol in the molar volume 18.07 cm³ needs E = 1.97 × 10⁹ V/m = 0.20 V/Å (1 V/Å = 10¹⁰ V/m) [calc, step 9d]. Simulations (Saitta and colleagues, Physical Review Letters 2012) put the field at which liquid water starts to dissociate at about 0.35 V/Å = 3.5 × 10⁹ V/m [web: https://arxiv.org/abs/1204.1120]. The two are the same order, so a 10 percent saving by stored field energy needs fields near the dissociation scale itself, where the linear formula fails, far beyond any laboratory oscillator's bulk field. (A reviewer's "correction" of 0.2 to 0.02 V/Å, with its claim that the estimate is "17 times below" Saitta's threshold, was itself wrong; the arbiter checked the unit conversion, 0.2 V/Å stands, and 3.5 × 10⁹ V/m is about 1.8 times the 1.97 × 10⁹ V/m estimate [calc]. mathematician.md D5 and E2 now carry a dated correction note.)

Kassner's own words cut against a free lunch. He wrote that "the absorption of energy [is] therefore especially great in the case of resonance" [read: US2089966 p.3, via the arbiter]. At water's band the filling has Q ≈ 1 (Section 4.1 table), so a resonator holding much water there is heavily damped; it is "lightly loaded" only if it holds little water, which means a small effect. By his own text, resonance is where the sample draws most power, and so where a heat-matched control matters most.

Weighing. These results show that an applied field can lower the voltage cost of splitting water at a catalyst, by heating it locally. They do not test a Kassner standing field or radiating field, which act on the bulk liquid through water's broad band, and none shows total work below 237.1 kJ/mol. That last silence is expected (the second law forbids it), so it weighs neither way. The silence on Roy/Rao/Kanzius is different: no one is on record as having tried; possible reasons (ordinary heating or plasma effects not excluded in the abstracts, low interest after the claimants disclaimed net energy, poor access to the 2010 paper) are untested, and the papers' controls and gas analyses would decide.

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5. Worked example: does a 6.2 cm disc pair resonate at 18.6 cm?

Why this one. Every resonance figure Kassner gives (gold sol 18.6 cm, agar 116 cm, serum 90 cm) was seen only in his plate oscillator, whose own resonance is set by the plate size. If the plates themselves cannot resonate at the stated wavelength, then either the stated geometry is wrong or the "sample resonance" belongs to something else in the apparatus. Best of all, we can test the 1932 figures with Kassner's own 1936 theory, so nothing external is being imposed on him.

All numbers below are printed by example.py [calc].

Step 1: check the formula on Kassner's own example. GB483062 works one example: R = 20 cm, d = 1 cm, ε = 1, period T = 1.09 × 10⁻⁹ s, logarithmic decrement δ = 0.3, result "R_s = 102 ohms" [read: GB483062 p.4, page image]. - Wavelength: λ = cT = (2.998 × 10¹⁰ cm/s)(1.09 × 10⁻⁹ s) = 32.68 cm. - Implied root: x = 2πR/λ = 2π(20)/32.68 = 3.845, which is the open-rim axisymmetric root 3.832 (rounding in T). Theory gives λ = 2π(20)/3.832 = 32.80 cm. - His load-resistance formula (16), R_s = 1.8 × 10¹² T d / [δ ε R² (J₀² + J₁²)], with J₀²(3.832) + J₁²(3.832) = 0.1622: R_s = 100.8 Ω, against the printed 102 Ω. - His energy formula (12) at an illustrative V₀ = 1 kV gives U = 9.01 µJ; deriving it independently in SI units, U = πε₀εR²(J₀² + J₁²)V₀²/(2d), gives 9.02 µJ. Q = π/δ = 10.5, and the load draws 2δU/T ≈ 5.0 kW.

Conclusion of step 1: Kassner's 1936 theory is correct. This matters for fairness: he knew how to compute a disc resonator.

Step 2: apply it to the 1932 gold-sol disc. Diameter 6.2 cm, so R = 3.1 cm; air gap ε = 1 for now.

The claimed 18.6 cm needs x = 2π(3.1)/18.6 = π/3 = 1.047, below every root. The same is true of all three 1932 figures: 30/10, 18.6/6.2 and 116/39 are 3.00, 3.00 and 2.97, so they follow a simple rule "λ = 3 × diameter", which is x = π/3 [calc]. It matches no Bessel root in Kassner's own tables (the smallest he lists is 1.84) [read: GB483062 p.13].

Step 3: give him the most generous allowances. - Fringing. A 1 cm gap is not small next to a 3.1 cm radius, so the field spills past the rim. With the patch-antenna estimate (Section 3.3) the effective radius grows by a factor 1.30 to 4.03 cm, and the lowest mode moves to 13.7 cm (for the 10 cm disc, 20.8 cm against the claimed 30 cm). - The sample layer. 1 mm of watery sol (ε ≈ 80) in a 1 cm gap, layers in series: ε_eff = 1/(0.9/1 + 0.1/80) = 1.110. That raises λ by √1.110 = 1.054, i.e. 5 percent: 11.1 cm without fringing. - Both together: about 14.2 cm, still 24 percent short of 18.6 cm. - What would be needed: ε_eff = (18.6/10.58)² = 3.09 across the gap. Solving 1/[(1 − f) + f/80] = 3.09 gives a water fraction f = 0.69: the sol would have to fill 6.9 mm of the 1 cm gap, not 1 mm. (The mathematician found the agar 116 cm cases can be rescued the same way with 68 percent or 92 percent filling, or with thick glass trough walls; the patents never say so.)

Step 4: the gap rule. In the theory the gap does not set the frequency; with fringing, a smaller gap shrinks the effective disc and gives a shorter wavelength (12.6 cm at 0.5 cm gap versus 13.7 cm at 1 cm) [calc]. Kassner's 1932 statements disagree with each other on this: US2089966 p.5 says the wavelength "increases when the plates are spaced at shorter distances", p.7 says "the smaller this distance, the greater the natural frequency" [read: page images]. The agar experiment (20 cm plates at 0.5 cm gap instead of 39 cm at 1 cm, same 116 cm) follows the p.5 rule, which only heavy dielectric loading could produce.

Step 5: put the claimed sharp line beside the real one. Water's Debye peak with τ = 8.3 ps: f = 1/(2πτ) = 19.2 GHz, λ = 1.56 cm, matching Kassner's "about 1.5 cm" [calc; τ web-checked as 8.27 ps by the contrarian]. Its half-maximum points are a factor 13.9 apart in frequency (Q ≈ 0.29). Kassner's resonance dispersion, 2 percent wide, is Q ≈ 50, about 170 times narrower. Nothing in the 1930s or since shows such a line in an electrolyte [memory, medium]. With Q = 20-50, a line at 333 MHz would be 7-17 MHz wide [calc, mathematician]: a modern network analyser resolves that in an afternoon.

Step 6: one photon at 18.6 cm. f = 1.61 GHz, E = hf = 6.67 × 10⁻⁶ eV = 0.64 J/mol. Thermal energy at 300 K is 3,879 times larger; an O-H bond (about 463 kJ/mol [memory, high]) is 720,000 times larger. A radio photon cannot change a bond by itself; any effect has to be collective (heating, alignment, field-driven chemistry), which is what Kassner himself proposed and what the essay's "bond strength" reading goes beyond.

What the example shows. The 1932 tuning figures do not follow from the stated geometry under Kassner's own correct 1936 theory, even with fringing and the sample layer included. Possible reasons (none in the sources; reviewer hypotheses only): the numbers came from a rule of thumb; the feed leads and valve capacitance set the frequency rather than the disc; or the sample was much thicker than stated. Any of these means the reported "sample resonances" (18.6, 116, 90 cm) cannot be taken as properties of the sample until the apparatus resonance is measured with and without the sample. That one bench measurement would settle the question (arbiter, claim 4).

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6. Evidence table

Verdicts are the arbiter's final verdicts. "Tested?" means a controlled test on record.

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7. What a learner should take away

Solid. - Kassner's water figure (about 1.5 cm) is Debye relaxation, correctly cited in 1931, and in his 1934 French patents he says in his own words that his natural frequencies are the Debye relaxation frequencies. His 1936 disc-resonator theory is correct cavity physics, and his energy, Q and impedance formulas reproduce to within 1 percent (Section 5). He was a competent microwave engineer at a time when decimetre waves were new. - Microwave heating does cure rubber, dry lacquer and, at enough temperature, preserve food. Industry used it from the 1940s; the 1945 Goodrich/Firestone buyers described their purchase as this kind of heating [read: 1945 clippings], which is their description, not Kassner's (Section 4.3). - Ternion AG and Bauch's secondment to GEC are real, documented history. The register papers also show that share ownership changed between 1932 and 1937 [read: register papers]. Bauch's work on a Ternion UHF project is documented in one published source (the 1996 memoriam); no second source has been found yet, and the other accounts are silent, not contrary. - Fields can make electrolysis cheaper in one measured way: high-frequency heating of a catalyst lowers the overpotential by 100-200 mV (Niether 2018), and microwaves can drive water splitting through ceria below 250 °C (Serra 2020). Infra-red light tuned to water's stretch vibration does weaken its bond on a nickel surface (Hundt 2014). These are real, mainstream results, known here from abstracts; they work at catalysts, surfaces or infra-red frequencies, not through Kassner's bands (Section 4.6).

Wrong, and why the mistakes are instructive. - Relaxation is not resonance. Calling both "natural frequency" makes a broad, overdamped Debye band sound like a tunable sharp line. Checking Q (Section 3.1) separates them at once. This is the most useful single lesson in the project. Kassner's own French texts take the relaxation meaning; Arnold, a trained dielectric chemist, did the same in 1945. Under that meaning the "natural frequency" is real but broad, and a 2 percent-wide band is a separate, stronger claim. A smooth regime change can also masquerade as a "frequency": serum's conduction crossover falls near 89 cm, close to Kassner's 90 cm, but it has no peak (Section 3.1). - Class evidence is not a test. Sharp-line claims in cells at 26-90 GHz were looked for and not found (Gandhi 1980, Gos 1997). That counts against the class of claim, but it is not a test of Kassner's serum band at 333 MHz. Keep the two apart. - Testing a claim with the claimant's own theory. The 1932 "λ = 3 × diameter" figures fail Kassner's own 1936 equations. When a "sample resonance" is only ever seen at the frequency the apparatus is built to produce, the apparatus has to be ruled out first. - State functions close loopholes. "If bond energies could be altered" cannot rescue a closed water cycle: ΔH and ΔG depend only on start and end states, so whatever a field does in the middle must be paid back. - A rate effect is not an energy gain. A field that speeds a slow electrode reaction attacks the overpotential (waste heat), not the 237.1 kJ/mol floor, and it must be counted as an input: 6.7 W of absorbed field power per 24 kJ/mol saved at 1 mol of hydrogen per hour. The decisive measurement is always total work per mole, field power included, against a heat-matched control. And state how the field is applied: Kassner's standing field (displacement current through the sample) and radiating field (wand) are different set-ups from a radiofrequency coil over salt water (Section 4.6). - Check the arithmetic, including the corrections. Two numbers in the project notes were wrong and are now corrected: the infra-red photon is 3,400-4,700 times a 1.28 cm photon, not 35,000; and 2 × 10⁹ V/m is 0.2 V/Å (1 V/Å = 10¹⁰ V/m), so a reviewer's "correction" to 0.02 V/Å was itself an error. Unit conversions are where careful people slip. - Absence is a question, not an answer. "No papers" proves neither suppression nor emptiness. The board's minutes document a financial end, and the people and patents demonstrably moved to other companies; but neither fact explains why five funded years left no technical record. Narrowing the question matters too: the man did not vanish (patents to 1960, death by 1962), so the anomaly is the missing research reports, and the Arbon laboratory may have run only about 18 months. Listing the explanations, the evidence for each and the record that would decide (Section 4.4) is the honest way to handle a silent record. - Whose description is it? The buyer of the patents described them as heating; the inventor said his object was "not to produce a rise of temperature". Each had a stake. Report both, check each against the numbers (Goodrich's 150 MHz fits where the power went, not the claimed natural frequencies), and do not let either stand as the neutral fact (Section 4.3). - Measured or derived? Kassner's 1932 disc figures follow λ = 3 × diameter, and his chemistry wavelengths 2.74, 9.25 and 27.75 cm are hydrogen's fine-structure intervals (box in Section 4.1). Numbers that look like data can be the output of a formula; checking this is a quick, powerful test of any old patent. - Energy-scale checks. A 1.6 GHz photon carries 0.64 J/mol, against 2,500 J/mol of thermal energy and 463,000 J/mol for an O-H bond. Any real non-thermal effect has to be collective.

Genuinely open. - Was there any narrow, non-thermal line in Kassner's samples? Nobody has rebuilt a crossed-Nicols detector and swept it with a thermostatted sample. A 0.1-3 GHz permittivity sweep of water, salt solution, milk, juice and serum, plus that optical detector, would settle it; the same sweep would show whether serum's broad conduction crossover sits near 90 cm. - Did resonant (versus heat-matched and off-resonant) exposure preserve food or change colloids? A four-arm blind test with at least 20 samples per arm has never been done. - Who sold the vulcanisation patents in 1945, and were any Kassner's resonance patents? Did Dipole A.-G. of Arbon do the actual research? What did Bauch do for Ternion? Who held the 46 shares not represented in 1937, who lent the Fr. 1.12 million, and why did funding stop in 1937? Did the work continue under Dipol, Universal Inventions, General Infra or Vibranic, and did any of them keep research records? Is there a second record (or the memoriam author's source) of Bauch's Ternion project, and was GEC a contractor to Ternion? Leads: Bauch's 1934-35 radiation-therapy patent sold to Marconi (search British patents of 1934-36). (Archive questions, now handed to the Investigator step.) - New open questions (2026-10-08): Where does the 1.28 cm "characteristic of water" come from (a thermostatted 0.2-25 GHz permittivity sweep of water, 0.1 M salt solution and serum would show whether it matches water at some temperature)? Do Niether 2018 and Serra 2020 count the field power in an overall efficiency, and does any field method keep a net saving (the 2026 ACS review's 215.6 kWh figure, context unseen)? What controls and gas analysis did Roy, Rao and Kanzius use, and has anyone independent tried it? The decisive experiment for claim 11: isothermal calorimetry of a cell, total work per mole of hydrogen = DC electrical energy plus real field power into the resonator or wand, against a heat-matched off-band control; below 237.1 kJ/mol would be the anomaly. - Open questions from 2026-10-04: Do the unread eight of ten pages of FR 788,428 (and the rest of FR 786,294) mention the sharp 2 percent band, or only relaxation? Did Dipol A.-G. stop work in 1933, and where was the Fr. 1.12 million spent (patents, London 1934-36, a book valuation)? What is in the Swiss Federal Archives files on General Infra and "Ernst Kassner", and are they the same man? Was Heller's garlic root-tip result ever repeated with conductivity and temperature logged (and did Grundler and Keilmann answer Gos 1997)? Why is Kassner named in the January 1945 release but not in the Industry Inventions licensing notices? Who was Wilma Hencke, and where are Kassner's later papers? - Why does the scientific record go dark? Commercial failure, trade secrecy, continuation under other names, contract work at GEC, classification and suppression are all still in play for the missing 1932-37 research record. First, inspect the Arnold v. Watson trial exhibits (NARA RG 21, RG 276), the only known place an evidential test of a Kassner-type principle may be on file; then order the three Swiss Federal Archives files and the Arbon tax rolls 1932-34. After that, in priority order, the records that would decide: (a) Ternion's 1936 protocol, share register and lenders (Landesarchiv Glarus); (b) the Dipol A.-G. file (Staatsarchiv Thurgau) and Wiegner's papers; (c) the Vibranic contract of 15 Nov 1945 and USPTO assignments of US 2,089,966 and 2,109,843; (d) Goodrich and Firestone test data and purchase files, and the Arnold v. Watson exhibits; (e) GEC Research Laboratories reports 1934-35, Bauch's HO 405 file, the memoriam's source; (f) the General Infra and Universal Inventions files; (g) UK, Swiss and Allied files on Kassner and any patent secrecy direction (Section 4.4).

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8. Check yourself

1. Water's Debye relaxation time is about 8.3 ps. At what frequency and free-space wavelength is its loss largest, and is this band sharp?
2. A disc resonator has R = 5 cm, air gap, open rim. What is the wavelength of its lowest mode? Does halving the gap change it, in the thin-gap theory?
3. Kassner's electrolytes are said to have bands "scarcely wider than 2/100 λ". What Q is that, and roughly how many cycles would such a system ring after the drive stops?
4. Why can't a field that "momentarily lowers the bond energy" of water during electrolysis make a closed electrolysis-and-burning cycle produce net energy?
5. In the gold-sol experiment, what single control measurement would tell you whether the 18.6 cm "resonance" belongs to the sol or to the apparatus?
6. Using Δν̃ = α²·Ry/(n³ l(l + 1)) with α = 1/137.036 and Ry = 109,737 cm⁻¹, compute the fine-structure interval of hydrogen's n = 2, l = 1 level as a wavenumber and as a wavelength. Which of Kassner's numbers does it reproduce?

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9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics: chapter 4 (fields in matter) and chapter 9 (electromagnetic waves). - P. Debye, Polar Molecules (Chemical Catalog Co., New York, 1929): the theory Kassner cites. - F. Kremer and A. Schönhals (eds.), Broadband Dielectric Spectroscopy (Springer, 2003): modern relaxation measurements. - D. M. Pozar, Microwave Engineering: resonators and transmission lines (Kassner's eqs. 13-20 are standard forms found there). - C. A. Balanis, Antenna Theory: the circular microstrip patch, including the fringing correction used in Section 5. - M. L. Boas, Mathematical Methods in the Physical Sciences: Bessel functions. - S. Gabriel, R. W. Lau and C. Gabriel, "The dielectric properties of biological tissues" (Physics in Medicine and Biology, 1996) [memory, medium on exact citation]: measured tissue spectra. - P. W. Atkins, Physical Chemistry: enthalpy, Gibbs energy, electrochemical cells. - Dielectric heating history: https://en.wikipedia.org/wiki/Dielectric_heating [web]. - O. P. Gandhi and others, "Millimeter wave absorption spectra of biological samples", Bioelectromagnetics 1:285-298 (1980), https://onlinelibrary.wiley.com/doi/abs/10.1002/bem.2250010305; P. Gos and others, Bioelectromagnetics 18:142-155 (1997): the controlled searches for sharp lines in cells [web]. - C. O. Kappe, B. Pieber and D. Dallinger, "Microwave Effects in Organic Synthesis: Myth or Reality?", Angewandte Chemie International Edition 52:1088-1094 (2013): the modern state of the non-thermal argument [web, entry only]. - Field-assisted electrolysis and bond weakening (Section 4.6) [web: abstracts and snippets, sites.md leads 32-40]: Niether and others, Nature Energy 3:476 (2018), magnetic-induction heating of catalysts; Serra and others, Nature Energy 5:910 (2020), microwave-driven water splitting with ceria; "A Systematic Guide to Experimental Designs in Magnetic Electrocatalysis", ACS Applied Energy Materials 9:10362 (2026), on energy balances; Hundt and others, Science 344:504 (2014), infra-red bond-selective dissociation of water on Ni(111); Saitta, Saija and Giaquinta, Physical Review Letters 108:207801 (2012), field-induced dissociation of water, https://arxiv.org/abs/1204.1120; L. Onsager (1934) and Bui and others, J. Phys. Chem. C (2021), the second Wien effect. - Cleeton and Williams, Physical Review 45:234 (1934), microwave absorption in ammonia (maximum near 1.25 cm), https://link.aps.org/doi/10.1103/PhysRev.45.234 [web].

Others who claimed the same kind of effect (Section 4.5). - O. M. Arnold, US 2,522,082 (filed 1945); In re Arnold (1950); Arnold v. Watson, 237 F.2d 584 (D.C. Cir. 1956) [web: research/2026-10-04-arnold.md]. - H. Heller and A. A. Teixeira-Pinto, "A new physical method of creating chromosomal aberrations", Nature 183:905-906 (1959); US 3,095,359; Midwest Research Institute, "Survey of Radio Frequency Radiation Hazards" (US Navy contract NObs-77142, 1960) [web: copies in research/files/run3/]. - J. W. Webb and A. D. Booth, Nature 222:1199 (1969); W. Grundler and F. Keilmann, "Sharp Resonances in Yeast Growth Prove Nonthermal Sensitivity to Microwaves", Physical Review Letters 51:1214 (1983); S. Mittler, Environmental Research 11:326 (1976) [web, entries only]. - Puharich, US 4,394,230 (1983), water splitting by a "complex electrical wave form" (not read); S. Meyer's "water fuel cell", Ohio court finding of 1996 (the court's characterization) (Section 4.6) [web: snippets via the Investigator, sites.md lead 35]. - Roy, Rao and Kanzius, Materials Research Innovations 12:3-6 (2008), and Rao and others, Current Science 98:1500 (2010): 13.56 MHz salt-water "burning", the claimants' own reports (Section 4.6) [web: summary at https://www.i-sis.org.uk/canWaterBurn.php].

The researcher's own works (in the project folders). - GB 417,501 and US 2,089,966, "Process for Altering the Energy Content of Dipolar Substances" (priority 9 Dec 1931): the central claims and all the experiments. - GB 417,564: plate resonators. GB 483,062 (1936, application void): the full disc-resonator theory used in Section 5 (its pp.8-12 add no measurements). - GB 448,417, GB 448,419, GB 448,494, US 2,109,843: valves, coaxial resonators, wavemeter, polarimeter. - GB 383,508, US 1,951,731 (assigned to Ternion A.-G.), FR 732,805: Tesla applicator and oscillator-radiator. US 2,104,697 (Universal Inventions Ltd) and US 2,558,568 (Vibranic Ltd, 1951): lamps. - Found by the Investigator (not in the folders; DEPATISnet and Google Patents, only partly read) [web: research/2026-10-04-depatisnet.md, research/2026-10-03-google-patents.md]: FR 786,294 and FR 788,428 (1934), the French texts that state the Debye-relaxation meaning and repeat the GB417501 examples; ES 135,727, the Spanish member of the same family (not read by anyone; the Spanish patent office's historical archive would give its text); GB 435,643 (plate-resonator light detector, divided from GB417501); GB 448,418 and US 2,094,602 (ellipsoidal-reflector applicator, a liquid in a glass sphere at the second focus; cited by Spencer's Raytheon patent); US 2,096,459 (repeats "about 40 percent" with no method); DE 1,128,930 (1960-62, rotating UHF fields; his last patent). - Unread or unidentified leads, kept in the record without weight (arbiter "Investigator findings", priority 4; sites.md) [web: sites.md leads 7, 9, 17, 18, 29; research/2026-10-03-swiss-archives.md; research/2026-10-04-records-and-rechecks.md]: - Thorpe's Dictionary of Applied Chemistry, Weissberger's Technique of Organic Chemistry and Ellis's Chemistry of Synthetic Resins cite GB417501 (besides Chemical Abstracts 1935, vol. 29, 1178); they cite the claim and report no test. - An "Ernst Kassner, Berlin" held 1923-28 patents for adding machines and cash registers (the US ones vested by the Alien Property Custodian in 1943); identity with E. E. W. Kassner unknown. - A 1929 "Ernst Kassner", with patents assigned to the Elektro-Physikalische Gesellschaft m.b.H., Berlin (electro-optical); identity likely, not proven. - Bodleian Library, Society for the Protection of Science and Learning (SPSL, refugee aid) file MS. S.P.S.L. 508/1-4, "W Kaeser - E Kassner"; which E. Kassner is unknown. It could hold an account of his London years. - B. F. Goodrich Company Records (University of Akron), "Series VII: Research and Development", the series to ask for Goodrich's test data on the Kassner process (finding aid blocked online). - Swiss Federal Police dossiers on "Kassner, Ernst (20.11.1900)": E4264#2000/63#1515 (1939, enquiries about foreigners) and E4264#1988/2#24190 (1946-47, identity papers and passports), beside the General Infra "Schwarze Liste" file E2001E#1968/78#9311; the owner must order them. - Stadtarchiv Arbon municipal tax rolls 1932-34: when the Dipol laboratory closed. - US Proclaimed List and British Statutory List (wartime blacklists): General Infra was not found in any online text searched; the 1943-46 supplements are still to check in full. - NARA catalogue matches for "Ernst Kassner" (seized German records) and "Giodvad" (State Department and Army lists, 1940-50); contexts unread. - Closed as false: the 1941 Swiss gazette hit "Kassner Ultrakurzwellen"; US 2,190,668 (it is Llewellyn's, Bell Labs); "Vibranic ... sterilizing canned foods" in a 1951 index (a misreading of adjacent entries); GB 435,043 is a misreading of GB 435,643. - G. Voss, note in Journal of Microwave Power and Electromagnetic Energy 22 (1987): "Who was Ernst Kassner?" - Essay in the project folder, "High Frequency Effects on Materials" (draft 17, 2019), with its deep read in deep/. - F. W. O. Bauch memoriam, Journal of the Audio Engineering Society 44 no. 6 (1996): the one published source for the Ternion project at GEC (in the project folder). - Goodrich Research Center (Miller and Wittig), "Radio-Frequency Heat in the Rubber Industry", Rubber World, Oct 1950: the buyer's description of the Kassner patents [web: https://archive.org/details/sim_rubber-world_1950-10-01_123_1]. - Wireless World*, Feb 1953, author note on Bauch [web: https://archive.org/details/sim_wireless-world_1953-02_59_2]. - Review files: arbiter.md (verdicts; "The record goes dark" and its table of deciding records; "Investigator findings (2026-10-04)" with its seven rulings; "Investigator findings (2026-10-08)" on electrolysis, bond strength, the claim 11 wording, two numerical corrections and the related work restored by QE: Puharich, Meyer, Ho, Stovall, ambient radio), research/ and sites.md (the Investigator's archive findings: Swiss gazette, Internet Archive, court cases), mathematician.md (disc-resonator and loading calculations), physicist.md (Debye and conduction), contrarian.md (strongest case and the four-arm test design).

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Answers

1. f = 1/(2πτ) = 1/(2π × 8.3 × 10⁻¹² s) = 19.2 GHz; λ = c/f = 1.56 cm. It is not sharp: the half-maximum points are a factor 13.9 apart in frequency (Q ≈ 0.3). It is a relaxation, not a resonance.
2. λ = 2πR/x with x = 1.841: λ = 2π(5)/1.841 = 17.1 cm. In the thin-gap theory the gap does not appear, so halving it changes nothing (fringing gives a small change, and in the direction of a slightly shorter wavelength). Kassner's 1932 claim that the 10 cm disc gives 30 cm is 75 percent longer than this.
3. Q = λ/Δλ = 1/0.02 = 50. Ringing lasts about Q/π ≈ 16 cycles (energy falls by e in Q/(2π) ≈ 8 cycles). At 333 MHz (90 cm) that is about 48 ns of ringing in a liquid whose molecules reorient in picoseconds and whose conduction loss term σ/(ωε₀) ≈ 81 is about as large as its permittivity (ε′ ≈ 70-80), so it loses roughly as much energy per radian of a cycle as it stores (a damping-limited Q of order 1, not 50) [calc; σ memory, medium, supported to the order of magnitude by the web-checked blood value of 1.3 S/m]: hence the strong mainstream expectation against it.
4. ΔH and ΔG are state functions. The cycle starts and ends with liquid water, so its net ΔH and ΔG are zero. If the field lowers the work of electrolysis, either the field supplied that energy (count it as input) or the products are in a changed state and returning them to normal water on burning gives back correspondingly less. Turning ambient heat at one temperature into net work in a cycle is forbidden by the second law (Kelvin-Planck). What a field can do, and has been measured to do at heated catalysts, is cut the overpotential (the waste above 1.229 V); even then the field's own power must be counted, and no total below 237.1 kJ/mol is possible (Section 4.6).
5. Measure the resonance of the plate oscillator (e.g. with a wavemeter or a network analyser today) with the plates empty, with a 1 mm water layer, and with the 1 mm gold sol, at fixed temperature. If 18.6 cm appears without the sol, or shifts only by the small ε_eff effect, the "resonance" is the apparatus.
6. α² = 1/137.036² = 5.325 × 10⁻⁵, so α²·Ry = 5.844 cm⁻¹. With n = 2, l = 1: n³·l(l + 1) = 8 × 2 = 16, so Δν̃ = 5.844/16 = 0.3652 cm⁻¹ and λ = 1/0.3652 = 2.74 cm (f = c/λ ≈ 10.9 GHz). This is Kassner's first "term difference of hydrogen", 2.74 cm, inside his 2.5-3.5 cm reaction band. The number came from atomic theory, not from a chemistry measurement.