Primer: Schuster and Hemsalech, "The Constitution of the Electric Spark" (1899)

Study document (Step 4). Verdicts are the arbiter's (arbiter.md); this primer adds none. Source tags: [read] the project document (the 6-page Royal Society abstract, pp. 331-336, read 2 Feb 1899); [web] with URL (mostly found by the Investigator, sites.md and research/); [calc] arithmetic reproduced in example.py; [memory] recalled, with confidence.

Source gap (repeated from the arbiter). The project holds only the 6-page abstract. The full paper (Phil. Trans. A 193 (1900) 189-213, DOI 10.1098/rsta.1900.0006), with its tables for aluminium, magnesium, bismuth, cadmium and mercury and its photographs, was read by no one in this review. Everything about metals other than zinc rests on one sentence each in the abstract. Hull 1906, Royds 1908, Hemsalech 1901 and Schaeffer 1908 are known through the Investigator's reading (and, for Hull, the Contrarian's direct reading), not from the project folder.

What kind of project this is. Unlike most projects in this collection, this is a mainstream experimental paper by Arthur Schuster F.R.S. (Manchester) and Gustave Hemsalech, refereed favourably (Crookes: "The paper marks an important step in understanding the electric spark") and published in the Philosophical Transactions [web] https://makingscience.royalsociety.org/items/rr_14_230. Its interest for this review is a real open question it left behind: what the speeds it measured are speeds of.

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1. The idea in one paragraph

When a big capacitor (a bank of Leyden jars) discharges through a 1 cm air gap between two metal rods, the flash contains light from the air and light from the metal of the rods. Schuster and Hemsalech passed that light through a prism and photographed the spectrum on film glued to a disc spinning at about 100 m/s. A light source that flashes for an instant in one place draws a straight line on the moving film. The air lines came out straight. The metal lines came out slanted and curved, as if the glowing metal started at the rods and travelled out into the gap at a few hundred to about 1500 metres per second, taking about six millionths of a second to reach the middle. They concluded: the spark first runs through air; the heat boils metal off the rods; that metal vapour rushes into the gap at roughly the speed of sound in hot vapour; and the later back-and-forth oscillations of the discharge run through the metal vapour, not the air. A coil added to the circuit, which slows the discharge, made the air lines nearly disappear, which fitted that picture. The open question, raised in 1906 and 1908 and never settled by a direct test, is whether the slanted line shows metal atoms moving, or a glow spreading through vapour that is already in place.

2. What you need to know first

Spectral lines. Each kind of atom (or ion, an atom missing one or more electrons) emits light at its own set of sharp wavelengths, its "lines". A prism spreads light by wavelength, so a slit-shaped source gives one slit-shaped image per line. Wavelengths here are in angstroms (1 angstrom = 10^-10 m; visible light is about 4000-7000 angstroms). Neutral zinc is written Zn I, singly ionised zinc Zn II. Read: Serway, Moses and Moyer, Modern Physics, chapter on atomic spectra; or Krane, Modern Physics.

The capacitor-inductor (LC) circuit. A capacitor of capacitance C (farads) discharging through an inductance L (henries) does not simply drain; current sloshes back and forth with period T = 2 pi sqrt(LC), decaying because of resistance. A spark is such a circuit: the jars are C, the wires and gap give a small L. More L means a longer period and a smaller peak current. Read: Griffiths, Introduction to Electrodynamics, the chapter on electrodynamics (inductance); any circuits text on RLC circuits.

Speed of sound in a gas. Sound in an ideal gas travels at c = sqrt(gamma R T / M), with T the absolute temperature (kelvin), M the molar mass (kg/mol), R = 8.314 J/(mol K) the gas constant, and gamma the ratio of specific heats (5/3 for a gas of single atoms, about 1.4 for air). Hotter and lighter means faster. A gas released into a near-vacuum expands at a speed of order c; its leading edge can run faster, up to 2c/(gamma - 1) [memory: high; standard gas dynamics]. Read: Halliday, Resnick and Walker, Fundamentals of Physics, chapters on sound waves and the kinetic theory of gases; Landau and Lifshitz, Fluid Mechanics, for the expansion result (advanced).

Diffusion. Molecules spreading by random collisions, with no bulk flow, cover a distance of order sqrt(2 D t) in time t, where D is the diffusion coefficient (m^2/s). Distance grows only as the square root of time, so diffusion is slow over short times. Read: Schroeder, An Introduction to Thermal Physics, section on diffusion.

The Doppler shift. Light from a source moving toward you at speed v (much smaller than the speed of light c) has its wavelength shortened by Delta lambda = lambda v / c. At v = 500 m/s that is about 1.7 parts in a million: tiny, but measurable with a high-resolution instrument. Read: Griffiths or any modern physics text, section on the Doppler effect.

Streak photography. If an image is swept sideways at a known speed while the event happens, position across the sweep becomes a time axis. Schuster and Hemsalech's spinning film is an early streak camera; the method was borrowed from Professor Dixon's studies of explosion waves [read: p.1].

3. The textbook view

3.1 A spark, in modern terms. [memory: medium-high, standard plasma physics] Breakdown of air starts with an electron avalanche that makes a thin, very hot, conducting channel of ionised air. Within the first fraction of a microsecond the channel heats to tens of thousands of kelvin (electron temperatures of order 10^4 K or more) and drives a shock into the surrounding air. Where the current meets the electrodes, it concentrates in small hot spots that boil metal off; that vapour expands from the electrode surface as a jet. In modern vacuum-arc and laser-ablation work, electrode plasma jets moving at 10^3 to 10^4 m/s are standard [memory: medium], and so are ionisation fronts that travel through gas that is not itself moving. Both kinds of motion exist; which dominates the light at a given place and time depends on conditions. (The arbiter left the spark-temperature figure as [memory: medium], not web-checked by any role. The "Historically superseded" half of verdict 4 rests on it together with the premise problem in section 5, step 4; the "Not testable as stated" half rests on the premise problem alone; arbiter QE revision, item 6.)

3.2 The circuit. With C = 0.033 microfarad (six jars) [read: p.2] and the stated period of about 2 microseconds [read: p.6], T = 2 pi sqrt(LC) gives L = T^2 / (4 pi^2 C) = 3.07 microhenry [calc], a plausible value for a short, compact circuit. Adding a coil of 30 microhenry would lengthen the period to 6.3 microseconds [calc] and reduce the peak current by sqrt(30/3.07), about 3x. Slower, gentler oscillations give metal vapour time to fill the gap; this is the textbook reading of the self-induction experiment, and it agrees with the authors' own.

3.3 Streak kinematics. Symbols: x = distance along the gap from the pole; t = time; V = speed of whatever makes the light appear at x (so x = V t); v_f = film speed; d = sideways displacement on the film (d = v_f t). With the spark imaged at unit magnification [read: p.2], the line drawn on the film has slope

x / d = V / v_f, so V = (x / d) v_f.

This is pure geometry and is correct. What it measures is the speed at which light-emission appears at successive points. It does not say what carries it.

3.4 Sound speed with the authors' units. The authors wrote density as rho, the vapour density "referred to hydrogen" (hydrogen gas H2 = 1 in their scale, so rho = molar mass / 2.016 g/mol; for cadmium, 112/2 = 56). Then M = 2.016 x 10^-3 rho kg/mol and

c = sqrt(gamma R / 2.016 x 10^-3) x sqrt(T / rho) = 64.2 sqrt(gamma) sqrt(T / rho) m/s.

The bracketed number is 76.0 for gamma = 1.4, 80.0 for gamma = 1.55, 82.9 for gamma = 5/3 [calc]. The authors' "V = 80 sqrt(T/rho)" [read: p.5] is this formula with gamma about 1.55, consistent with their remark that they "neglect the differences in the ratio of specific heat".

4. Where the authors depart (and where they don't)

These authors did not depart from the physics of their time; they made one interpretive step that the measurement does not by itself justify. Side by side:

The challenge, in the challengers' words. - G. F. Hull (1906; initials and Dartmouth affiliation [memory: medium], Proc. R. Soc. A 78, 80), with cadmium/mercury amalgam electrodes, found "no variation of the wave-lengths of the strong Cd, Hg, lines greater than 0.002 tenth-metres" between viewing along and across the discharge, so "the luminous particles do not acquire a velocity in the direction of the discharge greater than 150 metres per second," and the curving "appears to be due not so much to motion of luminous particles as to the propagation along those particles of a condition of luminosity" [web] https://archive.org/stream/proceedingsroya02britgoog/proceedingsroya02britgoog_djvu.txt (read directly by the Contrarian). Hull calls it preliminary; his conditions (smaller capacity, light collected over the whole spark) differ from the six-jar spark, and a symmetric outflow from both poles could cancel a net shift (the Contrarian's point; Hull does not report line widths). - T. Royds (1908, Phil. Trans. A 208, 333), working in Schuster's own Manchester laboratory: the 1899 authors "did not discuss any possibilities of the propagation of luminosity through vapour which may be, as a whole, stationary."

The authors' own evidence that cuts against their simplest reading. - Calcium H and K. In his summary of the 1899/1900 results (point 5 of his list), Royds reports that calcium H and K lines (from an impurity in silver electrodes) "became luminous first in the centre of the gap, and were propagated towards the electrodes" [web, Royds 1908 p.333, read by the Investigator from the page image; https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1908.0023]. The Investigator notes this is "not in the abstract; in the full paper", so it is most probably Schuster and Hemsalech's own observation, recorded in their full 1900 paper and reported by Royds (arbiter QE revision, item 2). Caveat: the full 1900 paper was read by no one here, so this rests on Royds's summary; documented in one published secondary source by a colleague in the same laboratory, no second source found yet. Calcium that must come from the electrodes yet lights from the middle outward is awkward for a pure "vapour streams out of the poles" picture and fits a luminosity front better. The inventors recorded it themselves; the abstract does not mention it or draw that conclusion. - Purity. The referee Crookes asked the authors about the purity of their metals [web, https://makingscience.royalsociety.org/items/rr_14_230, archivists' summary, via the Investigator]. That bears directly on the calcium result, which is an impurity line, and on line-to-line differences (claim 5). - Centre stays luminous longest. "The metallic vapours remain luminous in the centre of the spark for a longer period than near the poles" [read: p.6]. This fits either reading (matter that has arrived and stays hot, or a front that leaves the centre emitting longest); it does not separate them, but it shows the picture was not a simple stream from the poles (arbiter QE revision, item 3).

The case for the authors' reading, kept beside it: the speeds are just what gas dynamics predicts for hot metal vapour (section 5); the metal must get into the gap somehow, and only pressure-driven flow is fast enough; the authors themselves flagged that the oscillation period "was rather too small" and the metal "was possibly affected in its motion by the subsequent oscillation" [read: p.6], so they saw the complication; and modern electrode-plasma work treats vapour jets as real [memory: medium].

5. Worked example: from a slanted line to a "temperature", and the test that would decide

All steps are reproduced in example.py: .venv/bin/python review/SchusterAndHemsalech/example.py

Step 1. Film speed. The disc is 33 cm across, covered in the middle by a 22.2 cm disc, so the photographed band runs from radius 11.1 cm to 16.5 cm [read: p.1]. At 120 turns per second [read: p.1-2], v_f = 2 pi r f: - inner edge 2 pi (0.111)(120) = 83.7 m/s; middle (13.8 cm) 104.0 m/s; outer edge 124.4 m/s [calc]. The authors say "about 100 m/s". Note the speed varies by about 40 percent across the band; the abstract does not say whether this was corrected for [calc; arbiter open question].

Step 2. Slope to speed. Take zinc, "not far off 500 metres/second" [read: p.2], over the authors' V1 interval of 2 mm from the pole. - Time to cover 2 mm: t = 0.002 / 500 = 4.0 microseconds. - Sideways film shift in that time: d = 104 x 4.0 x 10^-6 = 0.42 mm. - Slope x/d = 2 / 0.42 = 4.8, and V = 4.8 x 104 = 500 m/s. [calc] So the whole measurement rests on reading a sideways shift of about 0.4 mm on a fuzzy spectral line. Misreading it by 0.05 mm (50 micrometres) moves V to 446 or 568 m/s [calc]. This is why the authors warn that "a very slight error in measurement will also affect the results considerably when the total displacement measured is small" [read: p.2].

Step 3. Where 80 comes from. From section 3.4, k = 64.2 sqrt(gamma); k = 80 requires gamma = 1.552; monatomic vapour (gamma = 5/3) gives 82.9 [calc].

Step 4. Temperature of cadmium vapour. Invert V = k sqrt(T/rho): T = rho (V/k)^2, with rho = 56 [read: p.5]. - V = 560 m/s, k = 80: T = 56 x 7.0^2 = 2744 K (printed "2700") [calc]. - V = 560 m/s, k = 82.9: T = 2555 K [calc]. But the abstract also says cadmium vapour reaches the centre of the 1 cm gap (5 mm) in about 6 microseconds [read: p.6]: 5 mm / 6 microseconds = 833 m/s, not 560. The full timeline on p.6 [read: p.6]: - the air lit by the first discharge stays luminous about 5 x 10^-7 s (0.5 microsecond). At about 100 m/s film speed the film resolves about 1 microsecond (physicist's figure, not rechecked), so this duration is an inference, not a resolved measurement; - "the metallic vapours then begin to diffuse and reach the centre ... in a time which in the case of cadmium was about 6 x 10^-6 second". The words "then begin" allow the 6 microseconds to be counted from the start of the vapour motion (5 mm / 5.5 microseconds = 909 m/s) or from the discharge (833 m/s); neither equals 560 m/s [calc]; - the oscillation period with six jars and minimal self-induction is about 2 x 10^-6 s; - the vapours "remain luminous in the centre of the spark for a longer period than near the poles", and some light can be traced for about 1.5 x 10^-5 s (15 microseconds).

With V = 830 m/s: - k = 80: T = 6028 K; k = 82.9: T = 5613 K [calc]. Because T goes as V^2, the factor 1.48 in speed becomes a factor (830/560)^2 = 2.20 in temperature [calc]. The abstract does not say whether the two figures are different kinds of average; the arbiter records the mismatch as unreconciled. Lesson: the "temperature" is an output of the assumption "slope = gas speed = sound speed", and it is uncertain by about a factor of 2 from the paper's own numbers before that assumption is even questioned.

Step 5. Why diffusion cannot do it. Pure diffusion spreads a distance sqrt(2 D t). Assume D = 1 to 5 cm^2/s (10^-4 to 5 x 10^-4 m^2/s) for metal vapour in hot air [memory: medium]. In t = 6 microseconds: - D = 1 cm^2/s: sqrt(2 x 10^-4 x 6 x 10^-6) = 3.5 x 10^-5 m = 0.035 mm; - D = 5 cm^2/s: 0.077 mm [calc]. Against the 5 mm needed, diffusion falls short by a factor of about 65 to 145. To cover 5 mm in 6 microseconds by diffusion alone, D would have to be x^2/(2t) = (0.5 cm)^2 / (2 x 6 x 10^-6 s), about 2 x 10^4 cm^2/s, four orders of magnitude above ordinary gas values [calc]. (This agrees with the arbiter's QE revision, item 1, which withdrew an earlier factor-of-10 slip; the physicist's original estimate of about 0.1 mm was close. The conclusion, that pressure-driven flow and not diffusion is the right picture if atoms move, holds.) For comparison, the sound speed in Cd vapour at 2700 K is 576 m/s, and a free-expansion front could run to 3 x 576 = 1727 m/s [calc], which covers the whole range the authors report (400-1500 m/s).

Step 6. The decisive test: Doppler shift. If atoms move toward the observer at v, a line at lambda shifts by lambda v / c (c = 2.998 x 10^8 m/s): - 500 m/s at 4800 angstroms: 0.0080 angstrom; - 560 m/s at 5086 angstroms (a cadmium line): 0.0095 angstrom; - 1420 m/s (the bismuth figure) at 5086: 0.024 angstrom [calc]. A glow front moving through stationary atoms gives no shift. Hull's stated resolution, 0.002 angstrom at 4800, corresponds to 125 m/s; he quoted 150 m/s [calc]. So a coherent 500 m/s drift would have given a shift four times his limit, and he saw none. The catch: you must look along the gap, where vapour streaming from both poles moves both toward and away from you, which can broaden a line instead of shifting it. A clean test needs time gating (looking only during the first few microseconds) and a single-pole geometry or a check of line width.

Step 7. The clock inside the spark. With L = 3.07 microhenry and C = 0.033 microfarad the period is 2.0 microseconds, so the 6 microseconds cadmium takes to reach the gap centre spans about three oscillations [calc]. That is why a moving glow tied to successive current half-cycles could mimic a moving vapour, and why the authors' own remark that the period was "rather too small" matters.

6. Evidence table

Three untested explanations for the zinc line difference, all on the table: (i) a measuring artefact from the unresolved doublet (the authors' own); (ii) the 4925 line is from Zn II (ion) and 4811 from Zn I (neutral), so different emitters (the Contrarian; NIST lists Zn II lines at 4923.889 and 4924.013 A and no Zn I line there [web] https://physics.nist.gov/cgi-bin/ASD/lines1.pl, checked by the arbiter); (iii) the period grows as sqrt(C) with more jars, so a glow tied to half-cycles mimics a velocity change (physicist and Contrarian).

A wording slip worth knowing: page 3 of the abstract says "the uniformly higher velocity deduced from the double line 4925", while its own Table I shows 4925 lower in every cell; the next sentence agrees with the table [read: p.3, page image].

7. What a learner should take away

Solid. The streak-photography idea and its geometry (slope = speed ratio) are correct and became a standard tool. The time order (air light first, metal light later and spreading into the gap) was seen and repeated. The self-induction trick, a coil that lengthens the discharge and suppresses air lines, is real and was put to practical use in spectroscopic analysis. The sound-speed formula and the authors' arithmetic check out to two figures.

Wrong or overstated, and why it is instructive. The step from "the emission front moves at V" to "the atoms move at V" is an assumption, not a measurement. It is the most common trap in reading any streak or time-of-flight record: a pattern can move without the stuff moving (think of a stadium wave, or a row of lights switched on in sequence). Building a temperature on top of that assumption, with V squared amplifying every uncertainty, gives a number (2700 K) that is really a consequence of the premises. The authors were careful in their wording ("seems a possible value"; "approximately"), and their own caveats (period too short; lines drawn out; small displacements) point straight at the weaknesses later critics named.

Genuinely open. - Matter or glow? No time-gated Doppler measurement on a six-jar spark is on record (Hull's test was preliminary and under other conditions). Steps 6-7 above show it is within modern instrument reach. - Why did calcium impurity light from the gap centre outward? This is most probably the authors' own observation in the full 1900 paper, known here only through Royds 1908's summary (one source, plate not seen); Crookes's purity question bears on it. - Is the zinc line difference an ion-versus-neutral effect? - Which electrode supplies the vapour: both, positive, or negative? Three sources say three things. - Do the velocities survive correction for the 84-124 m/s film-speed gradient?

On the record. Nothing here was suppressed. The paper was refereed, published and continued by Hemsalech, Royds and Strutt. The record goes quiet only on the specific matter-versus-front question after 1908; the arbiter sets out the explanations (interest moved to analytical spectroscopy and then atomic structure; the right tools came later and the question migrated into plasma physics under new names; or later answers exist that this review did not find, since Royds 1910, Strutt 1913 and Hull's later work were not opened).

8. Check yourself

1. The film moves at 104 m/s. A metal line on the film covers 3 mm along the gap while shifting 0.26 mm sideways. What apparent speed does that give, and what would it be if the photograph had been taken at the outer edge of the band (124 m/s)?
2. Using c = 64.2 sqrt(gamma) sqrt(T/rho), find the temperature of zinc vapour (atomic weight 65.4, so rho = 32.7) if it moves at 500 m/s as a monatomic gas.
3. Why does a glow front moving through stationary atoms produce a slanted line on the moving film but no Doppler shift?
4. Hull looked for a shift between viewing along the discharge and across it. Why could vapour flowing out of both electrodes at 500 m/s fail to show a net shift, and what would you look for instead?
5. Adding a 30 microhenry coil to the 0.033 microfarad circuit: what is the new period, and why would that make the air lines fade, according to the authors?

9. Further reading

The authors' own and directly related: - A. Schuster and G. Hemsalech, "The Constitution of the Electric Spark", Proc. R. Soc. Lond. 64 (1899) 331-336 (the project document; abstract). - A. Schuster and G. Hemsalech, "On the constitution of the electric spark", Phil. Trans. R. Soc. A 193 (1900) 189-213, DOI 10.1098/rsta.1900.0006 [web] https://royalsocietypublishing.org/rsta/article/doi/10.1098/rsta.1900.0006/108275/VI-On-the-constitution-of-the-electric-spark (read this first: the full tables and photographs). - G. A. Hemsalech, Recherches expérimentales sur les spectres d'étincelles (Paris, Hermann, 1901) [web] https://archive.org/details/recherchesexpri01hemsgoog. - Royal Society referee reports RR/14/229-231 (Crookes, Abney) [web] https://makingscience.royalsociety.org/items/rr_14_230 ; https://makingscience.royalsociety.org/items/rr_14_231.

The challenge and follow-ups: - G. F. Hull [memory: medium on initials], Proc. R. Soc. A 78 (1906) 80 (Doppler test) [web] https://archive.org/stream/proceedingsroya02britgoog/proceedingsroya02britgoog_djvu.txt. - T. Royds, Phil. Trans. A 208 (1908) 333-347 [web] https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1908.0023 ; Phil. Mag. (6) 19 (1910) 285-290 (not read). - R. J. Strutt, Proc. R. Soc. A 88 (1913) 110, DOI 10.1098/rspa.1913.0013 (afterglow of spark vapours; not read). - J. A. Schaeffer, Astrophys. J. 28 (1908) 121 (not read in full).

Mainstream background: - D. J. Griffiths, Introduction to Electrodynamics (inductance, LC circuits). - D. V. Schroeder, An Introduction to Thermal Physics (diffusion, ideal gas). - Yu. P. Raizer, Gas Discharge Physics (Springer, 1991): sparks, breakdown and discharge channels (advanced). - I. I. Beilis, review of the history of vacuum-arc cathode spots, IEEE (2018), which cites the macroscopic expansion of electrode vapour [web, listed by the Investigator; not read].

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Answers

1. V = (x/d) v_f = (3 / 0.26) x 104 = 1200 m/s. At 124 m/s: (3/0.26) x 124 = 1431 m/s. Not knowing where on the band the line was taken is a 20 percent uncertainty by itself.
2. k = 64.2 x sqrt(5/3) = 82.9. T = rho (V/k)^2 = 32.7 x (500/82.9)^2 = 32.7 x 36.4 = 1190 K. (With the authors' k = 80: 1277 K.) Note this is lower than the cadmium figure, although the zinc and cadmium speeds were "almost identical" [read: p.4]: same speed, lighter atom, lower inferred temperature.
3. The film records when light appears at each point; if successive points start glowing in sequence, the record slants whatever the atoms do. Doppler shift depends on the velocity of the emitting atom; stationary atoms emit at their rest wavelength.
4. Looking along the gap, vapour from the near pole moves away from you and from the far pole toward you; the shifts are opposite and the line centre can stay put, while the line gets wider. Look for broadening, or view one pole's jet alone (e.g. at an angle near one electrode), and gate the observation to the first few microseconds.
5. T = 2 pi sqrt(30 x 10^-6 x 0.033 x 10^-6) = 6.3 microseconds. The discharge lasts longer with a gentler current, so metal vapour has time to fill the gap and carry the current; energy goes into heating metal atoms rather than air (the authors' explanation [read: p.5]; the mechanism itself is rated Plausible, untested).