Morton-Wall: Primer

Project: two short articles in the Journal of the Franklin Institute (JFI), vol. LXI (January to June 1871), the only file in the project folder (a 623-page scan of the whole volume): - Edwin J. Houston, "On a New Connection for the Induction Coil", JFI June 1871, journal pp.417-419 (PDF pp.594-596) [read]. - William H. Wahl, "A Large Induction Coil", same volume, journal pp.212-216 (PDF pp.319-323), on the giant coil E. S. Ritchie built for Henry Morton [read].

The folder name "Morton-Wall" is taken to mean Morton and Wahl (Step 1's assumption). Houston and Wahl were close colleagues: Wahl taught Houston's classes at Central High School, Philadelphia, in 1872-73 while Houston studied in Germany (Edmonds 1902, as read by the Investigator) [read: research/files].

Source gap. None for the two articles: the text layer is good, and both articles were read in full. One trap: the scan's OCR turned printed fractions into digits. Wahl's "44 1/3 miles" became "443 miles", his Leyden jar of "1 1/3 square feet" became "14 square feet", and his "2 3/4 inch" spark became "2 inches". Some earlier project files (claims.md, facts.json, digests, the deep read, and parts of the mathematician's and contrarian's reviews) still carry the wrong figures; the arbiter corrected them from the page images, and I checked the jar line on the page image myself [read: page image p.322]. After the quality check (QE), a deep reader transcribed every number in Wahl's article from 400 dpi page images and confirmed the corrections: 44 1/3 miles, 44 1/2 lb, 325 sq ft of condenser, 2 3/4 in jar spark. The jar area, 1 1/3 sq ft, is the one moderate-confidence reading (the small denominator could just possibly be 1 1/8) [read: deep read of pp.319-323, per arbiter "QE revision"]. The same pass found two more OCR slips that touch no claim: the base is 13 in wide (not 18), and the core wires are about 1/18 in thick (not 1/8). This primer uses only the corrected figures. Not read by anyone in the review: Elihu Thomson's notebooks and his 1922 recollections (American Philosophical Society, APS), Brenni 2015, Susskind 1964 (paywalled), Wills 2007 (blocked), Morton's papers at the Stevens Institute. So everything below about who made the 1871 observations, and about whether "waves" were involved, rests on the published record only.

Read this first. Neither article has a single equation or a single instrument reading. "Quantity" was judged by eye. Every electrical number in this primer (capacitance, voltage, energy, frequency) is a textbook formula applied to the areas and distances the articles give, or an assumption, and each is labelled. The model shows the shape of what Houston saw; it cannot predict his numbers.

Source tags: [read] = from the document (journal page "j." or PDF page "p."); [read: page image] = read from a rendered page; [web] = Internet source with URL; [memory] = general knowledge, with confidence; [computed] = arithmetic in example.py.

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1. The idea in one paragraph

An induction coil makes long, thin, high-voltage sparks. Houston wanted sparks that were fatter and brighter (more "quantity", as the 1870s said) without losing too much length. He tried hooking one end of the coil's output to the building's gas pipe (the earth) and the other end to a big lecture table, then to a stove, then to old tin stills set on glass jars. The spark became thicker, shorter and silvery white, just as it does when a Leyden jar (an early capacitor) is put in the circuit. While it ran, sparks could be drawn from any metal within eight or nine feet, from a person's finger (lighting a gas burner), from a steam engine thirty feet away and from a wire in the room below. He guessed that one very large insulated conductor, "several hundred square feet", would give the biggest gain. In the same volume Wahl described Morton's huge coil, which gave 21-inch sparks and showed the same trade-off with a Leyden jar. In today's words, the big metal objects were adding capacitance: places to store charge. The articles claim nothing beyond ordinary electricity, and no energy was ever measured. Their lasting interest is historical: the stray sparks look like radio pickup fifteen years before Hertz, and they became evidence in an 1875-76 priority fight with Thomas Edison.

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2. What you need to know first

Capacitance and stored energy. A capacitor is any pair of conductors that can hold opposite charges. Its capacitance C (farads, F) is charge per volt: Q = CV, with Q the charge in coulombs (C) and V the voltage in volts. Charging it stores energy E = ½CV² joules (J). A single isolated piece of metal also has a capacitance, to the far-away "ground" around it. For a sphere of radius r in air, C = 4πε₀r, where ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space. Practical sizes are tiny: a 1-foot-wide object is about 10 picofarads (pF, 10⁻¹² F). Read: Griffiths, Introduction to Electrodynamics, chapter 2 (electrostatics, conductors, capacitors); Purcell and Morin, Electricity and Magnetism, chapter on conductors and capacitance.

Series and parallel capacitors. Capacitors side by side (parallel) add: C = C₁ + C₂. Capacitors in a chain (series) combine as 1/C = 1/C₁ + 1/C₂, so C = C₁C₂/(C₁ + C₂), which is always smaller than the smaller one. Any introductory circuits text covers this.

The induction coil (Ruhmkorff coil). A transformer with a few hundred turns of thick "primary" wire on an iron core, and many miles of fine "secondary" wire wound around it. A battery drives current I through the primary, which stores magnetic energy E₀ = ½L_pI² (L_p is the primary's inductance in henries, H). A "break" (interrupter) suddenly opens the primary circuit; the collapsing magnetic flux induces a very high voltage in the secondary, from Faraday's law e = −N dΦ/dt (N turns, flux Φ in webers). The output is a short, high-voltage burst at each break, not a steady voltage. A condenser (capacitor) across the break makes the primary current stop faster and so raises the kick. Coils were rated by the longest spark they could throw in air ("a six-inch coil"). Read: Griffiths ch. 7 (Faraday's law, inductance, magnetic energy); for the historical instruments, Wikipedia "Induction coil" [web] https://en.wikipedia.org/wiki/Induction_coil.

Sparks in air. Air is an insulator until the electric field is strong enough to tear electrons off molecules; then a conducting channel forms and a spark jumps. For a gap of a few centimetres between smooth electrodes this takes about 30 kV per cm [memory, high]; long gaps between points need less per centimetre. So a longer spark means a higher voltage, roughly. A published table for induction coils (from Schall, 1914) gives 4 in = 110 kV, 8 in = 150 kV, 12 in = 190 kV, 16 in = 230 kV [web] https://en.wikipedia.org/wiki/Induction_coil. Treat it as rough: the same page says a 42-inch spark was "roughly one million volts", twice the table's slope (arbiter, Correction 9). Read: F. W. Peek, Dielectric Phenomena in High Voltage Engineering (1915, free online) [memory, high on its existence].

LC oscillation. A charged capacitor C discharging through a wire loop of inductance L does not just drain: the current overshoots and charges it the other way, again and again, dying away. This is a damped oscillation at frequency f = 1/(2π√(LC)). A spark gap is a switch that starts it. With a few microhenries (μH, 10⁻⁶ H) of lead wire and tens of picofarads, f is millions of cycles per second (megahertz, MHz). Read: any circuits text on RLC circuits; Griffiths ch. 7 problems.

Near field and radiation. A charge that oscillates at frequency f makes an electric field around it. Close to the source (within about λ/2π, where λ = c/f is the wavelength and c = 3.0×10⁸ m/s) the field is mostly the ordinary "quasi-static" field of the moving charges; it falls off fast and stores energy that comes back to the source. 1870s physicists called coupling through it "induction". Far out (many wavelengths) the field is a travelling wave that carries energy away: radiation. Both are one field described at different distances. Read: Griffiths ch. 11 (radiation; dipole radiation).

1870s vocabulary. "Quantity": the amount of electricity in a spark, judged from its thickness, brightness and noise. "Tension" or "intensity": roughly voltage. "Coupled for quantity": cells or coil sections joined in parallel; "for intensity": in series [memory, medium]. "Electro-poion": a chromic-acid battery cell. "Leyden jar": a glass jar coated inside and out with tinfoil, a capacitor. "Cascade": capacitors joined in series.

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3. The textbook view

3.1 What a conductor on the coil's terminal does

The coil's secondary has some capacitance of its own between its two terminals. Hang a large piece of metal on one terminal and earth the other, and you add that metal's capacitance to earth in parallel with the gap. At each break the coil delivers a packet of energy E₀ (set by the primary: E₀ ≈ ½L_pI²). That energy charges the total capacitance C at the terminals. The voltage rises until either

• the gap breaks down at its breakdown voltage V_b (the spark length you set), or
• the energy runs out first: ½CV² = E₀ gives the most voltage the coil can reach,

V_max = √(2E₀/C), and the charge then is Q = CV_max = √(2E₀C).

The crossover is the "knee" capacitance

C_knee = 2E₀ / V_b².

Below the knee the spark is full length, but carries only Q = CV_b and only part of the energy. Above it, the voltage, and so the spark length, falls as 1/√C, the charge rises as √C, and the energy per spark stays at E₀. Length times charge is roughly constant. That is a short, thick, bright, loud spark. This is exactly the Leyden-jar effect that Morton had published in 1867: "the introduction of a Leyden jar into the secondary circuit of the Coil, shortens the spark and increases greatly its brightness", which he called "well known to all" [read: Morton 1867, JFI vol. 83 p.256, research/files]. Morton also found that jars in series ("cascade") lengthen the spark again: one jar gave 1 in, six in cascade 4 in [read: Morton 1867, per physicist and Investigator]. That is the series rule: n equal capacitors in series give C/n.

Why white? The whole stored charge goes through the gap in one quick, hot burst. A hotter spark is whiter and, as Morton noted citing Plücker's spectra, richer in ultraviolet [read: Morton 1867].

3.2 Capacitance of real objects

An isolated conductor of surface area A has roughly the capacitance of a sphere with the same area: r = √(A/4π), C = 4πε₀r [computed]. Because C grows only as √A, a conductor 300 times larger has only √300 ≈ 17 times the capacitance. A real plate near floors, walls and pipes has more, perhaps 2 to 5 times (mathematician, [memory, medium]). A Leyden jar is a different kind of object: two foils a few millimetres apart on glass, C = ε₀ε_rA/d (ε_r is glass's relative permittivity, about 6 [memory, medium]; d the glass thickness). A small gap d makes it hundreds of times bigger than an isolated sheet of the same area.

3.3 Why things nearby spark

The discharge rings at megahertz (section 2). The large conductor, the table, the stoves and the pipes are part of the oscillating circuit, or sit in its rapidly changing electric field. Their potential swings by kilovolts relative to a person or another piece of metal, and a small spark jumps across the last millimetre. Where metal is wired to the same pipes, the high-frequency current is simply conducted. The 1870s word for this was "induction". At larger distances the same field becomes radiation; Hertz used an induction coil and a capacitance-loaded spark gap (two 1 m wires with 30 cm zinc spheres, about 30 kV, about 50 MHz) to prove radio waves in 1887-88 [web] https://en.wikipedia.org/wiki/Heinrich_Hertz (as checked by the physicist).

Slow instruments see none of this. A gold-leaf electroscope or a slow galvanometer averages an oscillation that goes both ways millions of times a second, and reads zero.

3.4 Key equations in one place

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4. Where the inventor departs

First, what Houston got right, because it is most of the paper. His starting points rest on real physics:

• The Leyden-jar comparison. He saw that the earthed table made the spark "silvery white, as when a Leyden jar is placed in the path of the discharge" [read: j.418]. That is the correct identification: the table was acting as one coating of a capacitor, the earth as the other.
• The frictional-machine analogy. He wrote that his connection is "somewhat similar to that used in the common cylinder or plate machine, in which one of the conductors, generally the negative, is connected with the earth, and the quantity of the electricity thereby increased" [read: j.418]. Earthing one side of a friction machine really does increase its output, because the machine can then draw charge from the earth instead of from its own insulated conductor. The analogy is loose (a friction machine is a charge pump; a coil's secondary is closer to a voltage source with a capacitance) but the instinct, give the source a big partner to work against, is sound.
• The need for a large conductor. He reasoned that the effect showed "the need for a large conductor, probably to allow the rapid discharge of the secondary wire" [read: j.418], and built one from tin stills on glass jars. Larger capacitance does give a larger, faster discharge.
• His own correction. By 1876 he stated the mechanism in exactly the modern way: "These results I attributed entirely to a condensation of the spark by connection with extended surfaces, similar to the condensation produced by the introduction of a Leyden battery into the circuit" [read: Houston, JFI vol. 101, January 1876, research/files].

Where the 1871 text departs from the textbook view:

Other readings of the same experiment (kept in the record, each as its author's characterization):

• Historians: radiation before Hertz. Susskind (Isis, 1964) lists the 1871 observation and the tin still among pre-Hertz observations of electromagnetic radiation [web] https://www.jstor.org/stable/227753 (snippets only). Atherton (1984) says the grounded coil and the insulated tin still "(intentionally or not) acted as an antenna", with sparks "up to at least 30 m" [read by the Investigator and physicist: Atherton PDF, research/files]. Woodbury (1944) calls it "wireless signaling actually going on at the Central High School in 1871" [read by the Investigator: Woodbury, research/files]. Physically, a ringing spark gap on a big conductor does radiate; what no 1871 experiment shows is a propagating wave (that needed Hertz's standing-wave measurements). Atherton's "30 m" does not match Houston's "fully thirty feet" (9 m); it is probably a unit slip and should not be attached to 1871 (arbiter, Correction 6).
• Free-energy writers: "radiant energy". A widely copied passage (Patrick J. Kelly's guide, the Energetic Forum thread) says "In 1872, Elihu Thomson took a large Ruhmkorff Spark Coil, attached one pole of the coil to a cold-water pipe and the other pole to a metal table top", and that "any insulated metal object anywhere in the building would produce long continuous white sparks"; posters read it as a "scalar or radiant wave transmitter" with the pipes in resonance and a frequency "probably not more than 5 kHz" [web] https://www.energeticforum.com/forum/energetic-forum-discussion/renewable-energy/5299-1872-elihu-thomson-anyone-got-this-document-in-scientific-american-1872. Part of that wider reach comes from Houston himself. The June 1871 note gives "eight or nine feet" (stove, tin ware), "fully thirty feet" (the engine only) and a wire in a room below [read: j.417-419]. But in January 1876, writing about the 1871 experiments, Houston said "sparks could be drawn from any metallic objects in the neighborhood of the coil, and, indeed, in adjoining rooms", and for the December 1875 repetition "from all metallic objects in the same room with the coil, or in adjoining rooms" [read: Houston, JFI January 1876, research/files, as checked by QE and arbiter]. So "any metal object nearby, even in adjoining rooms" is the inventor's own later wording, not something the forums added. What still differs in the retelling is the year (1872, not 1871), the person (Thomson, not Houston), "anywhere in the building" (Houston says adjoining rooms, not the whole building) and "long continuous white sparks" (Houston never says continuous). The earlier arbiter wording, "a retelling that grew", was withdrawn for this reason (arbiter, "QE revision" §1). The 5 kHz figure mixes the coil's own slow ringing with the megahertz ringing of the gap discharge; neither was ever measured. Neither Houston nor Wahl claims more energy out than in, and no energy was measured, so the "radiant energy" reading is neither supported nor refuted by data.

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5. Worked example: why a bigger conductor gives a shorter, fatter spark

All numbers are reproduced by example.py (run: .venv/bin/python review/Morton-Wall/example.py). The script runs cleanly.

The one big assumption. The energy E₀ the coil delivers per break is not in any source: Houston gives no battery, current or inductance. I take E₀ = 0.125 J (for example L_p = 10 mH carrying 5 A; the physicist's choice). Step 4 shows how much rides on it.

Step 1. Capacitance of the conductors Houston names

Use C = 4πε₀r with r = √(A/4π). One square foot is A = 0.0929 m²:

r = √(0.0929 / 12.566) = 0.086 m, C = 4π × 8.854×10⁻¹² × 0.086 = 9.6×10⁻¹² F = 9.6 pF.

For 20 sq ft (an illustrative tin-ware half): 42.8 pF. For 300 sq ft ("several hundred", Houston's proposal): r = 1.49 m, 166 pF [computed]. All three reviewers and the arbiter agree on these values.

Step 2. The voltage of Houston's 6 in spark, and the knee

The table's four points lie exactly on V(kV) = 70 + 10 × (length in inches) between 4 and 16 in. For 6 in: V_b ≈ 130 kV (interpolated; the physicist used 125 kV). Then

C_knee = 2E₀/V_b² = 2 × 0.125 / (1.30×10⁵)² = 1.48×10⁻¹¹ F = 14.8 pF [computed].

So, on this assumption, any capacitance larger than about 15 pF on the terminals stops the coil from reaching 6 in.

Step 3. Walk up the capacitance

V_max = √(2E₀/C), capped at V_b; Q = CV; spark energy = ½CV² [computed]:

(μC = microcoulomb, 10⁻⁶ C.) Read the table from top to bottom and you see Houston's whole note: as the conductor grows, the voltage (and length) falls, the charge (thickness, "quantity") rises, and above the knee the energy per spark stops growing. Voltages under 110 kV mean sparks under 4 in, below the range of the table, so I do not convert them to inches. The bottom row is his proposed "maximum": about five times the charge of a bare 6 in spark, but at well under a third of the voltage. It trades away nearly all the length he wanted to keep.

Step 4. How much depends on E₀

The knee moves in proportion to E₀ [computed]:

So the pleasing result that "the knee sits near Houston's 1 sq ft" holds only if E₀ is about 0.1 J. That is plausible for a 6 in coil but not known. This is why the arbiter calls the model an order-of-magnitude consistency, not a prediction.

Step 5. The two-conductor experiment: series capacitors

In Houston's last arrangement neither pole was earthed: each pole went to one half of the tin-ware conductor [read: j.418]. The gap now sees the two capacitances to ground in series. Taking an illustrative 40 sq ft total (Houston gives no area except "less than one square foot" for the small piece) [computed]:

The series value is pinned by the smaller conductor. Shrinking one piece while enlarging the other raises the voltage the gap can reach, so the spark lengthens back toward the coil's 6 in, exactly the direction Houston saw ("a fine quantity spark of about five inches").

"Without sensible diminution in quantity": in the energy-limited regime Q × V = 2E₀ is constant, so Q(5 in)/Q(6 in) = V(6 in)/V(5 in). With the table line that is 130/120 = 1.08; if voltage were simply proportional to length it would be 6/5 = 1.20 (the mathematician's figure). Either way the charge changes by 8 to 20 percent, which no eye can judge [computed].

Step 6. A units check on Wahl's coil (why "443 miles" is wrong)

Wahl states the secondary is "234,100 feet" of wire "·007 of an inch in diameter" weighing "44 1/2 pounds" [read: page image p.321, per arbiter and the 400 dpi deep read]. - 234,100 ft ÷ 5,280 ft/mile = 44.34 miles, matching the page image's "44 1/3". - Bare copper of 0.007 in diameter: cross-section π(0.0001778 m)²/4 = 2.48×10⁻⁸ m²; length 71,354 m; volume 1.77×10⁻³ m³; at 8,960 kg/m³ that is 15.9 kg = 35.0 lb. Silk covering plausibly makes up the stated 44 1/2 lb. - At "443 miles" the same wire would weigh 350 lb, more than the whole 250 lb coil. - Sanity check of the method: 200 ft of 0.1655 in primary wire comes to 16.7 lb against Wahl's stated 17 lb. - Secondary resistance: R = ρL/A = 1.7×10⁻⁸ × 71,354 / 2.48×10⁻⁸ ≈ 49 kΩ [computed].

Wahl's real point is therefore that Ritchie's coil, with one third of the wire of App's London coil (150 miles, 29 in, about sixty cells, "soon failed"), gave 21 in from three cells and stayed in good order. The earlier project reading ("more wire, more reliable") was the wrong way round.

Step 7. Wahl's Leyden jar: how much energy?

Wahl: "In connection with a leyden jar of 1 1/3 square feet surface, it produces sparks of 2 3/4 inches in length" [read: page image p.322]. With A = 0.124 m², ε_r = 6 (assumed), glass 3 mm: C = ε₀ε_rA/d = 2.2 nF (5 mm glass: 1.3 nF), about 230 times a 1 sq ft isolated conductor [computed]. The 2 3/4 in is confirmed by the deep read; the 1 1/3 sq ft is a moderate-confidence reading, and if the page actually says 1 1/8 sq ft the jar is 1.9 nF (3 mm glass), which changes nothing below [computed]. A 2 3/4 in spark is below the table; taking 60 to 90 kV, the jar holds ½CV² = 2 to 9 J per spark. Whether three bichromate cells can put that much into the secondary per break cannot be checked: Wahl gives no primary current. This is an open item, not an inconsistency (arbiter).

Step 8. Induction or radiation at 8, 9 and 30 ft?

With an assumed lead-loop inductance of 1 to 10 μH and 30 to 100 pF, f = 1/(2π√(LC)) = 5 to 29 MHz, λ = 10 to 60 m, near zone λ/2π = 1.6 to 9.5 m [computed]. Houston's 8 to 9 ft is 2.4 to 2.7 m: inside the near zone below about 15 MHz. His 30 ft is 9.1 m, near the boundary, and in any case the engine was "in metallic connection with the water-pipes" [read: Houston 1876]. Since no frequency was ever measured, this arithmetic cannot decide between induction and radiation, which is exactly the arbiter's conclusion.

What the example teaches. Every qualitative statement in Houston's note follows from one textbook relation, ½CV² = E₀, and the series-capacitor rule. None of his numbers can be checked, because the one number that would anchor the model (E₀) was never recorded.

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6. Evidence table

Verdicts are the arbiter's (Step 3).

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7. What a learner should take away

What is solid. Adding capacitance to an induction coil's output shortens, thickens, brightens and whitens the spark; capacitors in series undo it. Houston saw this with tables, stoves and tin stills instead of jars, and identified it correctly with the Leyden-jar effect. Large metal objects and pipework near a running spark coil can give sparks at several metres. Wahl's specification, once the OCR fractions are restored, is self-consistent to within a few pounds of copper.

What is wrong, and why the mistake is instructive. - "Rapid induction by rapid discharge" puts cause and effect in the wrong place. The energy comes from the primary at the break; capacitance only decides how it leaves. Houston fixed this himself by 1876. Good scientists revise their wording; the useful habit is to ask where the energy comes from. - The "maximum" at several hundred square feet forgets that charge and length trade against each other. Whenever someone says "maximum", ask "maximum of what, holding what fixed?". Houston's own split-conductor data already showed the trade-off. - The project's own error is instructive too: "443 miles" survived several steps until someone divided 234,100 by 5,280. A one-line units check catches what careful reading misses.

What is genuinely open. - Who made the 1871 observations. Woodbury (1944; Thomson's credit at stake) says Elihu Thomson did ("One day Elihu disconnected the 'coffin' from the spark coil and substituted a water pipe and metallic table top as the condenser plates") and that Houston "took sole credit" [read by the Investigator and contrarian: Woodbury, research/files]. Houston's note names no assistant. Woodbury's details differ from Houston's (jar spark "vivid blue" versus "silvery white"; water pipe versus gas pipe), and his story includes a "knife blade" that appears only in Houston's 1876 paper. Thomson's notebooks at the APS (Mss.Ms.Coll.74) would decide. Three further leads, seen only as search snippets and not read: Susskind (1964), "...Thomson's 1871 experiments while his own paper was in proof" (the subject of the sentence is cut off, so it may concern another author); Compton, "Elihu Thomson the Scientist" (1939), a Thomson-side account that "tiny sparks could be obtained from metal objects wherever they were, in the cases or outside, from the door-knobs or from apparatus"; and Coulson (1957, JFI vol. 264), which cites Houston 1871 as part of Thomson's story [web, snippets only; arbiter "QE revision" §4]. The physics does not depend on it. - What frequency and field strength the sparks had, and how much (if any) was radiated rather than conducted. Never measured. The arbiter's deciding experiment: a loop antenna or spark-gap detector at 1, 3, 10 and 30 ft, with and without the pipe connection, plus a frequency count. - The "quantity versus capacitance" curve. Never measured. Prediction: an optimum C (a knee), not a monotone gain; a curve with no knee would be an anomaly. - How much energy per break Morton's coil delivered, and so whether the jar figures fit. Context from the same volume: Sharples reports that a nitric-bichromate cell has "the same electro-motive force as an ordinary Bunsen", with internal resistance 50 percent higher, steady for twelve hours [read: p.433, via the QE deep read]. He gives no volts or ohms, so this fixes no number for Morton's three cells. - Three silences (arbiter, "Absence of evidence"): Wahl promised "at a future time we will give some further account of experiments with this huge instrument" [read: j.216] and none appeared in JFI to June 1872 (unwritten, published elsewhere, or not done; Morton's papers at Stevens would decide). Houston published nothing more on the connection until Edison's November 1875 "etheric force" claim prompted his December 1875 note (he was in Germany in 1872-73; the note was reprinted in Scientific American, 10 June 1871, and abstracted in German, so it was not hidden). Edison's own line of work stopped after 1876; Wikipedia attributes this to Western Union's financial pressure [web] https://en.wikipedia.org/wiki/Etheric_force (not verified elsewhere). Houston and Thomson's balanced-battery tests of April 1876 were a clean demonstration that the sparks depend on stray capacitance, though they addressed "no new force", not "is it radiated"; and the authors had a priority stake. The JFI editors' note of 1876 says "whatever there may be remarkable in the phenomena of so-called Etheric Force, was described by Prof. Houston, previous to the discovery of Mr. Edison" [read: per Investigator] (the Institute's own member's priority). None of the three silences is evidence of suppression; each has at least one ordinary explanation; none can be closed from the files at hand.

Context: how the same editors handled extra-energy claims in this volume. Readers who come to these articles through the "radiant energy" literature should know that the same JFI editors met several claims of extra energy in the same six months (arbiter "QE revision" §3; QE deep read). Houston and Wahl themselves made no such claim, so none of this bears on their verdicts. - Highton's "doubled wire" electromagnet (PDF pp.266-267): the editors called it an attack on the conservation of force and perpetual motion. Their reply was an argument, not an experiment: a coil with doubled wire length and section has the same resistance and twice the lifting force, but takes twice as long to charge, so twice the zinc is used per cycle. Highton answered that the current is so fast the time difference is negligible. His own papers (Chemical News) are not in the folder, so his side is known only through the editors' adverse account. - A Newark "galvanic engine" (PDF p.448): not seen or tested; the editors predicted it "will reveal the true origin of its force". An expectation, not evidence either way. - Tinfoil between electromagnet windings (PDF pp.448-449): tested, with Mayer's comparison apparatus, and reported as "no improvement whatever", signed "H. M." (probably Henry Morton, an inference). One qualitative null result, with no numbers or apparatus details, by editors who had stated their view beforehand. - Zinc against coal (PDF pp.256-257): the editors' arithmetic reproduces. One pound of zinc oxidised gives 1,808,390 ft-lb (about 0.91 horsepower-hour); one pound of carbon burned gives 10,981,000 ft-lb, but real steam engines of the day captured only about 4 percent of it, so a perfect zinc battery and motor would be about five times as effective as a real coal plant. Their conclusion: "When, then, zinc is less than five times as costly as coal, and a perfect battery and electric engine have been invented, these will compete favorably with the steam engines of the present day" [read: p.257, via the QE deep read]. This is the energy-budget question ("where does the energy come from?") applied in 1871.

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8. Check yourself

1. A friend says "double the area of Houston's conductor and you double its capacitance". Using C = 4πε₀√(A/4π), what is the capacitance of an isolated 4 sq ft conductor, and by what factor did it grow from 1 sq ft?
2. Suppose Houston's coil actually delivered E₀ = 0.25 J per break instead of 0.125 J. Where does the knee move, and would a 1 sq ft conductor then shorten the 6 in spark?
3. Two conductors of 10 pF and 90 pF hang on the two poles, neither earthed. What capacitance does the gap see, and why does making the 90 pF one bigger hardly matter?
4. Houston and Thomson found that the distant sparks did not move a gold-leaf electroscope or a galvanometer. Why does that not prove there was no radiation?
5. Wahl's text layer says the secondary weighs "443 pounds". Without the page image, how could you show this is impossible from his other numbers?

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9. Further reading

Mainstream physics - D. J. Griffiths, Introduction to Electrodynamics: ch. 2 (conductors, capacitors), ch. 7 (Faraday's law, inductance), ch. 11 (radiation). - E. M. Purcell and D. J. Morin, Electricity and Magnetism (capacitance; the RLC circuit). - F. W. Peek, Dielectric Phenomena in High Voltage Engineering (1915): spark breakdown of air versus gap length. - H. Hertz, Electric Waves (English translation, 1893): the experiments that turned coil sparks into proven radio waves. - Wikipedia, "Induction coil" [web] https://en.wikipedia.org/wiki/Induction_coil (history, the spark-length table); "Etheric force" [web] https://en.wikipedia.org/wiki/Etheric_force.

The inventors' own works and the contemporary record - E. J. Houston, "On a New Connection for the Induction Coil", JFI vol. 91 (third series vol. LXI, June 1871), pp.417-419; reprinted in Scientific American 24 (10 June 1871) [web] https://archive.org/details/sim_scientific-american_1871-06-11_24_24. - W. H. Wahl, "A Large Induction Coil", JFI vol. 91 (third series vol. LXI, 1871), pp.212-216. - H. Morton, "An Important Adjunct to the Induction Coil", JFI vol. 83 (April 1867), pp.256-260 [web] https://archive.org/details/sim_journal-of-the-franklin-institute_1867-04_53_4. - E. J. Houston, "Phenomena of Induction", JFI vol. 101 (January 1876) [web] https://archive.org/details/sim_journal-of-the-franklin-institute_1876-01_71_1. - E. J. Houston and E. Thomson, "The Alleged Etheric Force. Test experiments as to its identity with induced electricity", JFI vol. 101 (April 1876) [web] https://archive.org/details/sim_journal-of-the-franklin-institute_1876-04_71_4.

History and later readings - C. Susskind, "Observations of electromagnetic-wave radiation before Hertz", Isis 55 (1964) [web] https://www.jstor.org/stable/227753. - W. A. Atherton, From Compass to Computer (1984), pp.183-184. - D. O. Woodbury, Beloved Scientist: Elihu Thomson (1944) [web] https://archive.org/details/in.ernet.dli.2015.177396 (Thomson-side biography). - P. Brenni, "Very large induction coils", Bulletin of the Scientific Instrument Society 125 (2015) [web] https://www.academia.edu/13825373/Very_large_induction_coils (not read). - K. T. Compton, "Elihu Thomson the Scientist" (1939), JSTOR 1664186; and T. Coulson, "Some prominent members of the Franklin Institute: Elihu Thomson, 1853-1937", J. Franklin Inst. 264 (Aug. 1957): Thomson-side accounts (snippets only; not read). - Thomson Papers, American Philosophical Society, Mss.Ms.Coll.74 [web] https://as.amphilsoc.org/repositories/2/archival_objects/919813 (the record that would settle authorship).

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Answers

1. A = 4 × 0.0929 = 0.372 m²; r = √(0.372/4π) = 0.172 m; C = 4πε₀ × 0.172 = 19.2 pF. Four times the area gives only twice the capacitance, because C grows as the square root of area.
2. C_knee = 2E₀/V_b² doubles, to about 30 pF. A 1 sq ft conductor (9.6 pF) plus the coil's own few pF is then well below the knee, so the gap still breaks at 6 in: the spark keeps its length and carries charge CV_b. Only conductors of roughly 10 sq ft or more would visibly shorten it. The lesson: the size at which Houston's effect appears depends on the unknown E₀.
3. C = (10 × 90)/(10 + 90) = 9 pF. In series the smaller capacitor dominates: as C₂ → ∞, C → C₁ = 10 pF. Enlarging the big conductor adds almost nothing; shrinking the small one controls the result. That is why Houston's spark came back when one piece was under 1 sq ft.
4. The discharge oscillates at megahertz. A gold-leaf electroscope or a slow galvanometer responds to the average charge or current, and the average of an oscillation is zero. The tests show "no steady charge or current", which rules out a steady new force (Edison's claim) but says nothing about a fast oscillating field, radiated or not (the contrarian's point, accepted by the arbiter).
5. From his own figures: 234,100 ft ÷ 5,280 = 44.3 miles, and 0.007 in copper wire weighs about 1.5×10⁻⁴ lb per foot, so 234,100 ft is about 35 lb bare. A 443 lb secondary would be heavier than the whole "about 250 pounds" coil. So the printed figure must be 44 1/2 lb (silk-covered), and the OCR dropped a fraction.