Kelly-Patrick primer: what a "free-energy" claim has to account for

Project document: Patrick J. Kelly, The Practical Guide to Free-Energy Devices, version 32.9, 16 February 2018, 2,481 pages (PJKbook.pdf) [read]. Companion files: arbiter.md (final verdicts, authoritative), example.py (the worked example of section 5, Parts A-D, and the Puharich balance of section 5b, Part E; runs cleanly with .venv/bin/python review/Kelly-Patrick/example.py).

Source note (repeated from claims.md and the arbiter). The book's text layer is readable (79 of 2,481 pages needed OCR, optical character recognition), so this is not a source gap in the strict sense. But: - The book is a compilation. Kelly says it is mainly a report of what other people say, that he has not built or proved most devices, and that "you are welcome to consider this a work of fiction" (p.11) [read]. It is the primary source for what Kelly and the inventors he reproduces claim. It is almost never evidence that a device works. - About 60 percent of the pages were deep-read in the first pass. The quality check (qe.md, verdict MINOR) found that the rest had been sampled rather than read, and eight further deep reads followed: Chapters 1-3 (pp.42-211), Chapter 14 (pp.1151-1277), the health pages (pp.1060-1071, 1203, 1210-1212, 1375-1417), the water-splitting appendix (pp.1901-1960, 2003-2037), the high-mpg patents and booster reports (pp.2041-2087, 2280-2313) and the Papp and Britt patents (pp.2196-2238). The arbiter's "QE revision" section rules on that material, and this primer now includes it. Still digest-level: Kelly's true-power passage (pp.1089-1091; I read the extracted text of those pages for the quotation in section 7), the Aguero, Horvath, Eccles and Blue items of the water appendix, Asaoka, Kunel, Coler, Plauson and Rayburn [read: arbiter.md, QE revision Q8]. - Most circuit diagrams, graphs and patent figures are images that no reviewer rendered. For this primer I rendered one page, p.457 (the Benitez calculation used in section 5) [read: page image p.457]. - "Patrick J. Kelly" was a pen name; the FESIG memorial (2020) gives his real name as Edward Dickson Williams, and he died on 11 July 2020 [web: https://www.youtube.com/watch?v=MnrNmV-vYO4; a forum snippet, see sites.md]. V32.9 is not the last edition (V34.5, June 2019; V34.8, 26 February 2020); changed figures in the later editions have not been checked [web: https://archive.org/details/pkj_free_energy].

Page numbers are the PDF page numbers of V32.9. Tags: [read] the book or project files; [read: page image p.N] I rendered that page; [web] with URL; [memory] recalled, with confidence; [calc] arithmetic, reproduced in example.py where marked.

Health claims in the book: not assessed here. The book also makes medical claims, and this primer does not assess them (the review has no medical reviewer, and no controlled study is cited for any of them in the pages read). They include: Beck's blood electrification, presented as an experimental HIV protocol (Beck's own title: "hypothetical protocols for experimental sessions"), which Kelly builds as the electronics project of Chapter 12 (two hours a day for about two months; "50 to 100 uA through blood is essential", pp.1060-1071); a home-built Lakhovsky oscillator with settings "based on very limited patient experience" for brain, liver and pancreas tumours (p.1413); suramin for autism (p.1375); an audio recording "claimed to reverse Alzheimer's disease", of which Kelly writes "I have no way of knowing" (p.1416); colloidal silver said to cure AIDS, Ebola, cancer and malaria and to have "no side effects of any kind" (pp.1210-1212, 1417); and Keshe "GaNS" water said to reverse genetic modification in seed (pp.1418-1423) [read: arbiter.md, QE revision Q6, from the deep reads]. The book's own safety warnings are real and worth repeating: mains and high voltage are "liable to kill you"; capacitors can "hold lethal levels of charge for a very long time"; nobody with a pacemaker should be within ten metres of the oscillator; and Kelly's disclaimer on p.1408 says the text "must not be construed as being an encouragement to make or use any such equipment" [read: arbiter.md Q6]. The pages contain no advice to see a doctor or to continue conventional treatment. They also do not mention argyria, the documented skin discoloration from long-term silver ingestion [memory, high; the arbiter's note of an omission, not a medical verdict]. The essays on finance, media and climate (pp.993-1005) are also outside this review.

---

1. The idea in one paragraph

Kelly's book collects hundreds of devices, from Tesla and Moray in the 1920s to forum builders in the 2010s, that are said to deliver more useful power than their operator puts in: spark-gap and pulse circuits that keep batteries charged, permanent-magnet "transformers" that give hundreds of watts for a milliwatt of drive, flywheels and pendulums that gain energy from gravity, water split into fuel gas for a fraction of the textbook energy, and aerials that draw kilowatts from the air. His unifying argument is simple and starts from something true: the law of conservation of energy forbids getting more out than goes in in total, but a device can be open to an outside source, as a sail is to the wind and a heat pump is to the warmth of the outdoor air, and then the output can exceed what the operator pays for. Kelly believes the outside source for these devices is an all-pervading "zero-point energy field", that sharp pulses, resonance and magnets are ways of tapping it, and that the reason none of this is on sale is opposition by people who profit from fuel. The physics question every device in the book has to answer is the same: which outside source, how many watts per square metre does it supply, and was the input really measured?

---

2. What you need to know first

Energy, power and the first law. Energy (joule, J) is conserved: in any process, the energy that leaves a region equals the energy that entered minus the increase of the energy stored inside it. Power (watt, W = J/s) is the rate of energy flow. One watt-hour (Wh) is 3,600 J; one horsepower (hp) is 745.7 W [memory: high]. The first law of thermodynamics is this bookkeeping with heat Q and work W included. It applies to open systems as well as closed ones, provided every flow across the boundary is counted. Read: Halliday, Resnick & Walker, Fundamentals of Physics (the chapters on energy and on the first law); Schroeder, An Introduction to Thermal Physics, ch. 1.

Efficiency versus COP. Efficiency η = (useful output) / (total energy input, all sources counted); it can never exceed 1. The coefficient of performance (COP) = (useful output) / (the input the operator pays for). A heat pump moving heat from cold outdoor air into a warm house has COP 3-4 because the outdoor air supplies the rest; its efficiency, counting the outdoor heat, is below 1 [memory: high]. A COP above 1 is legitimate only when the extra source is named and its inflow could be metered. Read: Schroeder ch. 4 (engines and refrigerators).

Series RLC circuits and resonance. A resistor R (ohm, Ω), inductor L (henry, H) and capacitor C (farad, F) in a loop obey L d²q/dt² + R dq/dt + q/C = 0 when left to themselves (q is the capacitor charge, current i = dq/dt). This is the damped harmonic oscillator of mechanics with L as mass, R as friction and 1/C as spring stiffness. Its natural angular frequency is ω₀ = 1/√(LC); its characteristic impedance is Z₀ = √(L/C); its quality factor is Q = Z₀/R, roughly the number of times it rings before the energy is gone. Driven by a sinusoidal voltage at ω₀ it "resonates": the reactances ωL and 1/(ωC) cancel and the current is V/R, while the voltage across L or C alone is Q times the drive. Read: Nilsson & Riedel, Electric Circuits (the chapters on natural and step response of RLC circuits and on frequency response); Griffiths, Introduction to Electrodynamics, ch. 7.

Energy stored in fields. A capacitor charged to voltage V holds E = ½CV²; an inductor carrying current I holds E = ½LI². These are finite stores; a circuit that rings or sparks can only move this energy around and turn it into heat or radiation, never multiply it [memory: high]. Read: Griffiths ch. 2.4 and 7.2.

Real, apparent and peak power. For AC or pulsed signals, the true average power is the time average of v(t)·i(t). The product of an rms (root-mean-square) voltmeter reading and an rms ammeter reading is apparent power (volt-amperes, VA); it equals true power only when the current is in phase with the voltage (power factor 1). For spiky waveforms, peak voltage times peak current can exceed the true power by orders of magnitude. Bulb brightness and battery terminal voltage after a rest are not power measurements. Read: Horowitz & Hill, The Art of Electronics (the early chapters on AC circuits and power).

Permanent magnets, gravity and conservative forces. A permanent magnet can hold a weight forever without using energy, because holding is force without motion. The energy that can be got from a magnet is bounded by its stored field energy, of order the maximum energy product (BH)max times its volume. Here B is the magnetic flux density (tesla, T), the field that exerts force on moving charges, and H is the magnetic field strength (ampere per metre, A/m), the part of the field set up by currents and by the magnet's own magnetisation; on a magnet's demagnetisation curve (B plotted against H) the largest value of the product B × H is (BH)max, in joules per cubic metre (J/m³), about 30 kJ/m³ for ferrite and about 300 kJ/m³ for neodymium magnets [memory: high]. The force between rigid magnets of fixed magnetisation is conservative too: it is the gradient of a potential energy, so a rotor driven by magnets alone does zero net work round each closed turn [memory: high; arbiter.md QE revision Q1]. Gravity is a conservative force: the work it does around any closed path is zero, so a machine that returns to its starting configuration can get no net energy from gravity [memory: high]. Read: Taylor, Classical Mechanics, ch. 4; Fitzgerald, Kingsley & Umans, Electric Machinery, ch. 1.

Electrolysis thermodynamics. Splitting water, H₂O → H₂ + ½O₂, needs a Gibbs free energy ΔG = 237 kJ/mol (a minimum electrical input of 1.229 V per cell) and a total enthalpy ΔH = 286 kJ/mol; at 1.48 V per cell (the "thermoneutral" voltage) the electricity supplies all of it, and between 1.229 V and 1.48 V the cell draws the difference as heat from its surroundings and cools. Faraday's law fixes the charge: two electrons per H₂ molecule, F = 96,485 C per mole of electrons [memory: high]. Read: Schroeder ch. 5 (free energy; it uses electrolysis of water as an example); Bard & Faulkner, Electrochemical Methods, ch. 1-2.

---

3. The textbook view

3.1 Open systems and where extra energy can come from

The first law for any region is

dE_stored/dt = P_in,operator + P_in,environment − P_out,useful − P_loss,

where every symbol is a power (W): the operator's input, all other inflows (sunlight, wind, heat from the air, a fuel), the useful output, and losses (heat, radiation). COP = P_out,useful / P_in,operator. COP > 1 needs P_in,environment > 0 or a falling stored energy E_stored. So the textbook asks every device the same two questions: what is P_in,environment, and is E_stored running down? Known environmental sources have known sizes [calc: arbiter.md, with web sources there]:

3.2 Ringing circuits, spark gaps and back-EMF

When a capacitor charged to V₀ is switched (by a spark gap) into an L-R loop, the current is a transient, not a steady sine. For R < 2Z₀ (underdamped):

i(t) = (V₀ / (ω_d L)) e^(−αt) sin(ω_d t), α = R/(2L), ω_d = √(ω₀² − α²).

Here α (per second) is the decay rate and ω_d (radians per second) the ringing frequency. All of the stored ½CV₀² ends as heat in R, energy delivered to whatever else is in the loop (a battery being charged), or radiation; the sum cannot exceed ½CV₀². An inductor switched off produces a high voltage, v = L di/dt (back-EMF, electromotive force), because its stored ½LI² has to go somewhere fast; the energy returned is the energy that was put in [memory: high].

3.3 Magnets and gravity

Energy available from a magnet of volume V_m is at most about (BH)max·V_m. For a ferrite bar of 3.75×10⁻⁴ m³ and (BH)max = 30 kJ/m³ that is about 11 J, really about half that [calc: arbiter.md; web: https://www.magnetexpert.com/magnetic-properties-of-ferrite-magnets]. A magnet steers flux cheaply (the principle of a saturable reactor and of Flynn's patent), which is real and useful, but steering does not create energy: in a generator, the electrical output is paid by the mechanical or electrical drive that changes the flux. For gravity, ∮F·dl = 0 around any closed path; a buoyancy cycle in water of density ρ gains at most ρgHV when a volume V rises a height H and costs at least ρgHV to push the air back down [memory: high].

3.4 Electrolysis by the numbers

One litre of the 2:1 hydrogen-oxygen mixture ("HHO") at 0 °C and 1 atm holds 1/22.414 mol of gas, two thirds of it H₂, so it needs

q = 2 × 96,485 × (2/3) / 22.414 = 5,740 C per litre [calc: arbiter.md].

At 1.229 V per cell that is 7.06 kJ = 1.96 Wh per litre (the Gibbs floor); at 1.48 V it is 8.50 kJ = 2.36 Wh per litre. Kelly's "Faraday" figure of 2.34 Wh per litre is this thermoneutral figure (the small difference is the choice of standard conditions) [read: Chapter 10; calc]. A cell can legitimately run between 1.229 V and 1.48 V by absorbing heat, so up to about 120 percent of Kelly's baseline is textbook-possible; below 1.229 V per cell is not.

---

4. Where the inventor departs

Kelly's departures, side by side with the textbook. In each row, the left column is fair to Kelly: it states the real physics his point starts from.

---

5. Worked example: does the Benitez patent's own arithmetic give 400 W in and 2,400 W out?

Why this one. Carlos F. Benitez's British patent GB 121,561 (24 December 1918) is the one device in the book whose inventor gives a complete numerical design: voltages, currents, efficiencies, capacitance, inductance and frequency [read: pp.452-458]. Kelly calls it "a brilliant 2 kilowatt, self-powered, free-energy design" and says "400 watts of input power produces 2400 watts of output power (COP=6)" [read: pp.452, 458]. Every number below is Benitez's own (as reproduced by Kelly), so the check is internal: no mainstream assumption is imported except the standard circuit laws that Benitez himself uses. Benitez is the patentee and so an interested party; the patent is a paper calculation, and no build or test is on record. example.py reproduces every step.

Step 1. The patent's design chain (it is mostly right)

The plant has two 60 V, 40 Ah batteries. Battery 1-2 discharges at 40 A (60 × 40 = 2,400 W). A DC motor in the line drops 10 V, so it takes 40 × 10 = 400 W; the remaining 40 A at 50 V = 2,000 W does "useful work" [read: pp.456, 458]. The 400 W drives a motor (95 percent efficient, 380 W), an alternator (95 percent, 361 W) and a step-up transformer (89 percent): 321 W reaches the spark circuit.

The alternator runs at 500 Hz, two voltage peaks per cycle, so the capacitor fires 1,000 times per second. Benitez wants 40 A in an oscillating circuit of resistance R = 15 Ω, so he needs 40 × 15 = 600 V, and charges the capacitor to V₀ = 1,200 V "because the average voltage during discharge is V/2" [read: page image p.457]. Then:

• secondary current 321 W / 1,200 V = 0.267 A;
• charge per spark 0.267 A / 1,000 s⁻¹ = 267 μC (microcoulombs);
• capacitance C = Q/V = 267 μC / 1,200 V = 0.222 μF.

For the inductance, Benitez writes that an oscillatory discharge needs √(1000 L[mH] / K[μF]) > R (K is his symbol for capacitance), then "using 20 ohms" computes L = 400 × 0.222 / 4000 = 0.0222 mH = 22.2 μH, "or equal to 22,200 centimetres of wire" [read: page image p.457]. Two things are worth seeing here:

• "Centimetres" is the old CGS electromagnetic unit of inductance: 1 cm = 1 abhenry = 10⁻⁹ H, so 22,200 cm = 22.2 μH exactly. The patent is in the units of its day, correctly [memory: high; calc].
• His arithmetic, L = R²C/4, makes √(L/C) = R/2, i.e. R = 2√(L/C) = 20 Ω: that is the textbook critical-damping boundary. So the calculation uses the correct condition (R < 2Z₀) even though the sentence as printed states a rule twice as strict. Z₀ = √(22.2 μH / 0.222 μF) = 10.0 Ω [calc].

Frequency: Benitez's Hz = 5,033,000 / √(L[cm] × K[μF]) is Thomson's (Kelvin's) formula f₀ = 1/(2π√(LC)) in those units, since 1/(2π√(10⁻⁹ × 10⁻⁶)) = 5,032,921 [calc]. It gives 71,690 Hz; the patent prints 71,900 Hz (a 0.3 percent slip), "72 oscillations in each of the 1000 sparks per second" [read: page image p.457; calc].

Current: Benitez uses the steady-state AC formula I = V / √(R² + (ωL − 1/(ωC))²). At ω = 2π × 71,900, ωL = 10.03 Ω and 1/(ωC) = 9.97 Ω, so the reactances cancel and I = 600/15 = 40 A, as he says [calc]. (The printed line on p.457 has the capacitance as 0.00000222 F, ten times too large, which would give 34 A; the 40 A answer needs 0.000000222 F, so it is a decimal slip in the printed line, whether Kelly's or the patent's is unknown [read: page image p.457; calc].)

Up to here the patent is a competent 1918 design calculation.

Step 2. The number the patent never computes: energy per spark

The capacitor holds, at the moment it fires,

E = ½ C V₀² = 0.5 × 0.222×10⁻⁶ F × (1,200 V)² = 0.160 J.

At 1,000 sparks per second the circuit can therefore dissipate or deliver, on average, at most

P_max = 0.160 J × 1,000 s⁻¹ = 160 W [calc; the deep reader, physicist and arbiter all give this figure].

That is less than the 321 W arriving, so the supply side is consistent (the difference is the classic loss of half the energy when a capacitor is charged from a source; note that 0.267 A × 1,200 V counts Q·V₀ = 0.32 J, twice what the capacitor stores) [calc].

Step 3. What the discharge actually does

The steady-state formula answers the question "what current flows if a 600 V sine wave drives this circuit forever?" But nothing drives it forever: a charged capacitor is switched into the loop once per millisecond and left alone. That is the transient of section 3.2. With the patent's values:

• decay rate α = R/(2L) = 15 / (2 × 22.2×10⁻⁶) = 3.38×10⁵ s⁻¹;
• ω₀ = 1/√(LC) = 4.50×10⁵ rad/s; ω_d = √(ω₀² − α²) = 2.98×10⁵ rad/s, i.e. 47.4 kHz (the 71.9 kHz is the undamped value);
• Q = Z₀/R = 10/15 = 0.67; damping ratio R/(2Z₀) = 0.75: underdamped, but barely;
• amplitude left after one ringing period: e^(−α·2π/ω_d) = 8×10⁻⁴ [calc].

SymPy solves L q'' + R q' + q/C = 0 with q(0) = CV₀, i(0) = 0 and gives

i(t) = −181.4 e^(−3.38×10⁵ t) sin(2.98×10⁵ t) A

(the sign is just the direction of discharge). Integrating numerically over the millisecond between sparks [calc, example.py Part C]:

So there is a brief 50 A pulse, and Benitez's 40 A is about right for its height. The mistake is to treat a 7-microsecond burst as a current that flows all hour. The ringing does not repeat 72 times: it is gone within one cycle.

Step 4. What the claim needs against what the circuit can give

The charger, taken as a machine, returns at most 160 W for 400 W taken (out/in ≤ 0.40), and Kelly's COP 6 needs 15 times more than this ceiling [calc]. Note that the ceiling holds whatever the 40 A: it comes from ½CV² and the spark rate alone, and adding the battery to the loop only shares the same 0.16 J between the resistance and the battery.

What the example teaches

1. Every step that is ordinary circuit theory is correct, including the CGS units, Thomson's frequency formula and the critical-damping condition. The error is one step of modelling: using the steady-state AC current formula for a single damped discharge, and then treating a peak current as a continuous one.
2. The energy check is the fastest test. Before any detail of waveforms, ½CV²·f bounds the power. The same bound (energy per event times events per second) settles Mohamed's Tesla-coil example in the book (charging 10 nF to 30 kV 100,000 times a second costs 450 kW for a claimed 30 kW output) [calc: arbiter.md].
3. Kelly himself flags the battery figures ("this is not so and is only being stated here for discussion purposes", p.456) [read], but not the energy problem, and he still headlines COP 6.
4. What this does not show. It refutes this worked example, not every Benitez-type circuit. The arbiter's deciding test is cheap: build or simulate (SPICE) the 1918 circuit with its own R, L and C at 1,000 sparks per second and integrate the battery energy over hours; the prediction is at most 160 W [read: arbiter.md].
5. A patent grant is not a test. Lyden US 11,588,421 B1 (granted 21 February 2023, "Receiver device of energy from the earth and its atmosphere") cites these same Benitez patents as showing it is "possible to generate electrical energy and to maintain the same in at least two batteries with relatively little or possibly no energy loss", and also cites Moray's US 2,460,707. That is the applicant's description of prior art, written by a patentee with a stake in it, not a measurement; the Benitez arithmetic above is unchanged by it [web: Google Patents, via sites.md; read: arbiter.md QE revision Q7].

Arbiter's verdict on this example: Refuted by calculation and Internally inconsistent [read: arbiter.md, Claim 2].

5b. A second, shorter example: Puharich's water-splitting "surplus"

Why this one. Andrija Puharich's article "Cutting the Gordian Knot of the Great Energy Bind" and his patent US 4,394,230 (reproduced on pp.1902-1931) are the most carefully measured water-splitting report in the book: the gas was analysed by gas chromatography and mass spectrometry in two laboratories (Gollob Analytical Services, Berkeley Heights, New Jersey, is named; the second is not), with a stated error of ±10 percent. Yet the article prints a 15 percent energy surplus. The example shows how a careful measurement can still turn into a surplus through bookkeeping. example.py Part E reproduces it [read: deep read pp.1902-1931, equations from page images pp.1909-1912, 1930-1931; arbiter.md QE revision Q5].

Puharich's numbers. 0.9 percent saline at 600 Hz; 25-38 mA rms at 4.0-2.6 V rms, about 100 mW for 30 minutes, a "debit" of 180 J. The volts and amps were read on separate meters: "since we were interested in following the voltage and current separately, it was decided not to use the watt meter" (p.1909), so 180 J is apparent power times time, not a measured energy (section 2). Measured gas: 10.80 cc H₂ + 5.40 cc O₂ (16.20 cc in all).

Step 1, the honest balance. 10.80 cc ÷ 22,414 cc/mol = 0.482 mmol of H₂, so 0.482 mmol of water was split. - Work that splitting needs at the minimum (ΔG = 237.1 kJ/mol): 0.482 × 10⁻³ × 237,100 = 114 J, so the Gibbs efficiency is 114/180 = 63.5 percent (58 percent if the volumes were at 25 °C, not 0 °C; the article uses both). The article itself gives 50-71 percent for ordinary DC electrolysers (p.1908), so this is an ordinary result. - Heat back if the gas is burnt (ΔH = 285.8 kJ/mol): 137.7 J, against 180 J in: a net loss of 42 J before any engine or fuel-cell loss [calc, example.py E2].

Step 2, where the printed surplus comes from. The article divides ΔG by 22,400 cc ("one mole of gas") to get 10.578 J/cc, and the patent divides ΔH by 22,400 cc to get 12.769 J/cc. But one mole of water gives 22,400 cc of H₂ plus 11,200 cc of O₂, so those are energies per cc of hydrogen. The patent then multiplies 12.769 J/cc by all 16.20 cc of mixed gas, counting the oxygen as fuel: 16.20 × 12.769 = 206.85 J, "114.92%", "+26.85 J (surplus)", "approximately 15%". The printed credit is 1.50 times the correct 137.7 J [read: page image p.1930, via the deep read; calc, example.py E3]. The article's own Faraday section one page later uses the correct 33,621 cc of mixed gas per mole of water, so the two sections disagree with each other. (A smaller slip: the page prints "10.80 cc / 11.33 cc = 91.30%", but 10.80/11.33 is 95.3 percent [read: p.1911; calc].)

Step 3, the textbook root. Even without the slip, ΔH/ΔG = 285.8/237.1 = 1.205, the "20 percent" the article starts from (p.1902). Section 2 explains it: between 1.229 V and 1.48 V a cell draws the difference as heat from its surroundings. A fuel cell gives back at most ΔG as work; the extra comes back as heat. So a "surplus" appears only if heat drawn from the room is counted as work. The patent's own quotation of Penner and Icerman says the same thing: "with heat absorption from the surroundings ... energy-conversion efficiencies during electrolysis greater than unity" (p.1928) [read: deep read; memory: high].

Step 4, a loose end the article does not notice. Faraday's law caps the hydrogen that the stated current can make: 25 mA for 30 minutes is 45 C, enough for at most 5.23 cc of H₂; 38 mA allows 7.94 cc. The reported 10.80 cc is 2.07 and 1.36 times those limits [calc, example.py E5]. So the stated current, duration and gas volume cannot all be right: the gas may have been made at a higher current (the article's own table starts at 100 mA, which allows 20.9 cc), the rms ammeter may have under-read a pulsed, half-wave-rectified current, the volumes may not be 30-minute totals, or the yield was genuinely above Faraday's law, which the article does not claim. The text cannot decide between these [read: arbiter.md Q5].

Arbiter's verdict: the printed 91.3 percent, 114.9 percent and 15 percent surplus are Internally inconsistent and, on the measured gas, Refuted by calculation as a net surplus; the gas yield itself (63 percent of Gibbs) is an Established, ordinary result; the conflict with Faraday's limit is open. Kelly's statement that Puharich drove a motor home "hundreds of thousands of miles" on water (p.1902) has no source, and neither the article nor the patent mentions a vehicle: Never properly tested [read: arbiter.md Q5].

---

6. Evidence table

Verdicts are the arbiter's (final). "Tested?" means a controlled measurement of input and output by someone other than the claimant, on this record.

---

7. What a learner should take away

What is solid. - Kelly's open-system point is correct physics: COP is not efficiency, and heat pumps, sails and solar panels legitimately give more than the operator pays for. His own text concedes that conservation holds once outside inflows are counted (p.15) [read]. - The circuit phenomena he builds on are real: resonance multiplies voltage and current by Q; a spark gap is a fast switch; an inductor's back-EMF spike is high voltage; a magnet holds force without consuming energy and can be steered by small currents (Flynn, Asaoka). Benitez's 1918 design calculation is competent up to the point where it goes wrong. - Kelly is often candid: the "work of fiction" preface, his warning that bulbs light brightly at low power (p.314), his note that the only reliable test of a battery charger is a timed discharge through a known load (p.544), and his own lux test that came out against the Joule Thief (p.476) [read]. The added deep reads show more of the same: Perendev's 100 kW "has not been confirmed" (p.78); Tewari "does not mention anything about 20 kilowatts of self-powered output" (p.102); motors run by permanent magnets alone are "very difficult" to make work (p.72); the basic Adams motor "will never reach 100% efficiency" (p.90); and he is "not at all convinced" that the mains-rod circuits draw net power (p.211) [read: arbiter.md QE revision Q1, Q2, Q7].

What is wrong, and why the mistake is instructive. - Unnamed sources. "The environment" or "the zero-point field" is not an energy account until it has a number in W/m². Where a source is named (atmospheric electricity, radio, gravity, a magnet's field, the chemical energy of water gas), the budget is short by factors from 15 to 10¹². - Peaks and products are not power. The Benitez example, Sweet's microamp readings, Newman's V × I products and the pulsed electrolysers all use quantities (peak current, rms voltage times rms current, peak V times peak I) that are not the time average of v·i. The general lesson is to integrate energy over time on both sides. Kelly states this lesson himself, clearly, in his electronics tutorial (Chapter 12): with an input of 12 V at 2 A and AC meters reading 15 V and 2.5 A on the output, "just before you go rushing off to announce on YouTube that you have made a prototype with COP = 1.56 or 156% efficient, you need to consider the real facts. This is an AC circuit and unless your prototype is producing a perfect sine wave, then the AC voltmeter reading will be meaningless ... The odds are that both readings are wrong"; and "The power is not the average current multiplied by the average voltage if there is a coil involved in the circuit"; true power is found "by sampling the voltage and current many times per second and averaging those combined results", with a wattmeter (pp.1089-1091) [read: extracted text pp.1089-1091]. Set that beside his own bench claim on p.1259: a cheap LM2587 boost converter on three NiMH cells, "an input of 800 mA at 3.33 volts (2.664W) driving the 10-LED array displays with 389 mA at 10.3 volts (4.01W) which is COP=1.5". A switching converter draws its input current in pulses, which is exactly the case his own warning covers, and a converter normally 80-95 percent efficient would give about 233 mA, not 389 mA. It is the only COP above 1 in the book that Kelly says he measured himself, and he did not apply his own rule to it [read: arbiter.md QE revision Q3; calc]. The book contains both the correct warning and an example of not following it; the reader can learn from both. - Heat is not work. Between the Gibbs energy ΔG and the enthalpy ΔH of water there is a real 20 percent (ΔH/ΔG = 1.205), and Puharich's printed 15 percent surplus grows out of it (section 5b). A cell can take that 20 percent from the room as heat, but a fuel cell or engine returns it as heat, not work. Any electrolysis "surplus" up to about 20 percent should first be checked for heat counted as work. - A closed magnetic cycle gives nothing. Gravity and the force between rigid magnets are both conservative. A motor driven by magnets alone (Johnson, Wang, Perendev) gets zero net work per turn, and a design that gates or moves the magnets with a second drive has to be judged on that drive's energy. Kelly's own advice points readers there. - Energy per event times events per second is a one-line test that would have caught most of the numerical claims in the book before anyone built anything. - Numbers that change on retelling. Sweet's input is 0.31 mW, 1 mW or 10 mW and his output 500 W, 1 kW or 5 kW in different sources; Skinner's "1,200 per cent" becomes COP 1,200 in Kelly's reading; Heins's COP is "thirty times", 39.6 and 3.77 on three consecutive pages; Barbosa and Leal's patent family is COP 100, 273, 104 and 102.4; Papp's demonstration ran 35 minutes on p.642 and 40 on p.37 [read: arbiter.md]. Going back to the earliest primary source changes the story every time it has been tried here.

What is genuinely open. - No neutral, instrumented test (true-power meters on both sides, the drive circuit's own supply counted, run for hours) is on record for Sweet's VTA, Smith, Kapanadze, Ainslie's COP 17, the Campbell flywheel loop, Skinner's machine or Moray's device. "Never properly tested" is a real gap, not a polite refutation. The cheapest such tests are named by the book itself. - Historical records that would settle specific episodes have not been obtained: the USPTO file for Moray's serial 550,611 (the family says the contents are gone), the 1987 Sweet video meters and Roberts's 1986 lab notes, NBS's handling of Newman's MHz spikes, the Papp suit files, the 1996 Meyer judgment, and the provenance of the "Subject matter of special interest in TC 2800" list Kelly reproduces on p.17 [read: arbiter.md]. - Records that would test the larger new claims have not been obtained either: the Chinese government's 2008 "Reliability and Safety" test of Wang's generator, Perendev's later record, the 1902 Daily Mail report on Figuera, Gollob Analytical Services' records of the Puharich gas measurements, and Sweet's stated 1969 MIT thesis [read: qe.md, Investigator leads]. - Puharich's reported gas (10.80 cc of H₂) exceeds what his stated current (25-38 mA for 30 minutes) can make by Faraday's law, by 1.4 to 2.1 times. Which of the stated numbers is wrong is not decidable from the text (section 5b). - The Murdoch thesis on hydrogen injection in a diesel generator, with a measured but load-dependent effect, is a reminder that small combustion effects are real and different from an energy surplus.

---

8. Check yourself

1. Kelly's book says Bob Cramton's electrolyser makes 6 litres of HHO gas per minute on 36 W, "2,340 percent of Faraday". Using 5,740 C per litre, what average cell voltage does that imply, and how does it compare with the 1.229 V floor?
2. A United Press story of 1939 says Skinner estimated his machine would "increase the horsepower of a motor about 1,200 per cent", for a one-eighth horsepower motor. What output does that imply in watts? What would it be on Kelly's reading of "1,200 times"?
3. Sweet's VTA is said to give 500 W from a barium-ferrite magnet set of about 3.75×10⁻⁴ m³ with (BH)max = 30 kJ/m³. How long could the magnets' own field energy run that output? What does that tell you about where any real output must come from?
4. Ainslie's patent example 1 reports 12.28 V across, and 0.196 A through, a load that includes a 68 Ω resistor. What resistance does V/I give, and why should that make you suspicious of the measurement rather than excited by the COP?
5. A heat pump moves heat from outdoor air at 0 °C into a house at 35 °C. What is the largest COP physics allows? Why is a COP of 3 here not "over-unity", and what would a free-energy device need to state to make the same kind of claim?

---

9. Further reading

Mainstream. - D. J. Griffiths, Introduction to Electrodynamics (ch. 2 energy in electrostatics; ch. 7 induction, inductance and magnetic energy; ch. 8 conservation laws and the Poynting vector). - J. W. Nilsson and S. A. Riedel, Electric Circuits (natural and step response of RLC circuits; frequency response and resonance). - P. Horowitz and W. Hill, The Art of Electronics (AC circuits, power and measurement practice). - D. V. Schroeder, An Introduction to Thermal Physics (ch. 4 heat engines and refrigerators; ch. 5 free energy, with electrolysis of water). - A. E. Fitzgerald, C. Kingsley and S. D. Umans, Electric Machinery (ch. 1 magnetic circuits and permanent magnets). - R. P. Feynman, The Feynman Lectures on Physics, Vol. I ch. 4 (conservation of energy, including his weight-lifting machine argument against perpetual motion) [memory: high]. - National Bureau of Standards, NBSIR 86-3405 (1986), the test of the Newman motor: https://nvlpubs.nist.gov/nistpubs/Legacy/IR/nbsir86-3405.pdf [web].

Kelly and the inventors' own key works. - P. J. Kelly, The Practical Guide to Free-Energy Devices, V32.9 (2018, the project copy); final edition V34.8 (2020) at https://archive.org/details/pkj_free_energy [web]. Start with the introduction (pp.11-17), Chapter 5 (Benitez, pp.438-458), the Sweet section (pp.244-249) and Chapter 10 (electrolysis). - C. F. Benitez, GB 17,811 (filed 1914, published 1915), GB 5,591 (1915), GB 14,311 (1916), GB 121,561 (1918) [web: Google Patents, via sites.md]. - F. Sweet, letter of 26 April 1987 ("Sparky" to "Maurice"): https://www.rexresearch.com/sweet/sparky1987.pdf [web; read: page image p.1, research/files/rex-sweet-sparky1987.pdf]. A fund-raising document; it says so. - Skinner 1939: United Press story as transcribed at https://rexresearch.com/skinner/skinner.htm; British Pathé "Gravity Power!" (1939) at https://www.britishpathe.com/asset/68269/ [web]. - Moray witness excerpts from The Sea of Energy: http://www.rexresearch.com/moray2/morayrer.htm [web]. - Newman v. Quigg, 681 F. Supp. 16 (D.D.C. 1988): https://law.justia.com/cases/federal/district-courts/FSupp/681/16/1800217/ [web]. - A. Puharich, "Cutting the Gordian Knot of the Great Energy Bind" and US 4,394,230 (1983), both reproduced in the book, pp.1902-1931 [read]; the source of section 5b. - Kelly's own true-power tutorial, Chapter 12, pp.1089-1091 [read], and his LM2587 measurement, p.1259 [read: arbiter.md].

---

Corrections to earlier documents

(For the orchestrator, under CORRECTIONS ARE WELCOME. I edited no other file.)

1. contrarian.md, Claim 2 verdict line calls the Benitez circuit "overdamped". Its own figures (damping ratio 0.75, Q 0.67) make it underdamped, barely; the mathematician and arbiter say "barely underdamped". The conclusion (it cannot ring 72 times) is unaffected. Evidence: R = 15 Ω < 2√(L/C) = 20 Ω [calc: example.py Part C].
2. New, not in any earlier file: the printed current formula on p.457 gives the capacitance as 0.00000222 F (2.22 μF), ten times the 0.222 μF computed a few lines above; with that value the formula gives 34 A, not 40 A. The 40 A result needs 0.000000222 F, so it is a decimal slip in the printed line [read: page image p.457; calc]. Whether the slip is Kelly's or in the 1918 patent is unknown (the patent original was not read).
3. New, refines the reviews: the patent's inductance arithmetic (L = 400 × K / 4000 at R = 20 Ω) is the correct critical-damping condition R = 2√(L/C), although the sentence before it states √(L/C) > R, which is twice as strict. Benitez's circuit theory is therefore correct at this step; the error lies in applying the steady-state AC formula to a single discharge [read: page image p.457; calc].
4. Minor, refines the arbiter's table: the patent's 71,900 Hz is 0.3 percent above the undamped frequency its own formula gives (71,690 Hz); the arbiter's statement that 71.9 kHz "is the undamped value" is right to that precision [calc].
5. This primer, earlier version (QE remediation, 2026-10-09). The source note said Chapters 1-2, 3a, 14, 20 and appendix pp.1901-2238 were "covered by digest only". That is now out of date: the QE remediation deep reads cover them (source note corrected). The evidence-table row "Kawai 3.18, Heins, Kunel, Tseung frame: Never properly tested" rested on digests; the arbiter now gives Heins's COP 39.6 Not testable as stated (row replaced). The Papp row gave no verdict on the mechanism the patent actually states (helium fusion); a row now gives it. The primer was also silent on magnet-only motors, Kelly's own "COP 1.5" measurement, his true-power warning, the water-appendix patents, Lyden US 11,588,421, Sweet's 1986 outputs, Mark Goldes's stake and the book's medical claims; all are now included.
6. New, refines the deep read and arbiter Q5: Puharich's page prints "10.80 cc / 11.33 cc = 91.30%" (p.1911), but 10.80/11.33 = 95.3 percent. This is a second arithmetic slip, separate from the factor-1.5 gas-volume slip. The deep read's explanation of the gap between 91.30 and 63.48 percent ("the rest is the 0.666 rounding") is therefore not right: the factor-1.5 slip gives 95.3 percent, and the printed 91.30 is a further error in the division. No verdict changes [read: extracted text p.1911; calc, example.py E3].
7. QE's misprint footnote applied: the p.476 lux row "200 lux 0.936 watts 101 lux per watt" should read 214 lux/W; noted in the evidence table [read: extracted text p.476; calc].

---

Answers

1. 6 L/min = 0.1 L/s, so the cells pass 0.1 × 5,740 = 574 C/s, i.e. 574 A summed over cells. 36 W / 574 A = 0.063 V per cell on average, about one twentieth of the 1.229 V floor. As a check, 6 L/min for an hour is 360 L × 2.34 Wh/L = 842 Wh, and 842 / 36 = 23.4, Kelly's "2,340 percent" [calc: arbiter.md]. Either the input or the flow is misreported, or another energy source (such as a chemical reaction between the electrolyte and the plates, which Boyce mentions, p.807) was not counted.
2. 1/8 hp = 93.2 W; 1,200 per cent is a factor of 12, so about 1.12 kW, plausible for a small lathe, drill press and hacksaw in light use. On "1,200 times" it would be 112 kW, which is absurd for that workshop. Even 1.12 kW from a 93 W motor needs an energy store or an unmetered input; the 1939 examiners did not publish measurements [calc; web: rexresearch Skinner page].
3. Field energy is at most about 30,000 × 3.75×10⁻⁴ = 11 J. At 500 W that lasts 11/500 = 0.022 s. Any output lasting seconds or hours must come from somewhere else, most likely the oscillator's own supply or a current path the input meter did not see; the magnet can only steer flux [calc: arbiter.md].
4. 12.28 / 0.196 = 62.7 Ω, less than the 68 Ω resistor alone. A series load cannot have less resistance than one of its parts, so the voltage and current readings are not measuring what the calculation assumes (phase errors, shunt inductance, the resistor's temperature coefficient, or rms readings on a spiky waveform). A COP built on those readings inherits the error [calc: arbiter.md, from the mathematician].
5. Carnot COP for heating = T_h / (T_h − T_c) = 308 / 35 = 8.8. COP 3 is not over-unity because the heat delivered = electrical work + heat taken from the outdoor air, and the air's contribution is named and could be measured (by the temperature drop and air flow across the outdoor coil); total efficiency is below 1. A free-energy device would need to state its outside source, the power it supplies per square metre or per kelvin, and a measurement showing that inflow, just as the heat pump can [memory: high; calc].