Physicist review: Schuster and Hemsalech, "The Constitution of the Electric Spark" (1899 abstract)

Reviewer: PhD physicist (Step 2). Tags: [read] from the project document (extracted text and the Step 1 deep read, with my own checks of the text layer), [web] with URL (Investigator's findings in sites.md and research/, which I read but did not re-fetch; I did not repeat web searches), [calc] my own arithmetic, [memory] with confidence.

No source gap: the 6-page Proceedings abstract is fully readable. But it is only an abstract. The full paper (Phil. Trans. A 193 (1900) 189-213, all tables, photographs) is not in the project folder and I have not read it. Anything about metals other than zinc rests on one sentence each in the abstract.

Reader orientation (what the experiment is)

When a Leyden jar (an early capacitor: glass jar lined with tin foil) discharges across a 1 cm air gap between metal electrodes, the spark shows two kinds of spectral lines: lines from air (nitrogen, oxygen) and lines from the electrode metal. The authors photographed the spark's spectrum on film bolted to a disc spinning at about 100 m/s. If a spectral line comes from light emitted at one place and for a very short time, it is a straight line on the film. If the light source moves across the gap, the film moves under it, and the line is drawn out into a slanted or curved trace. The slope is then (film speed)/(source speed). They saw air lines straight, metal lines slanted, and read the slant as the speed of metal vapour crossing the gap: hundreds of metres per second, reaching the gap centre (5 mm) in about 6 microseconds for cadmium [read: p.1, p.6].

Mainstream view, fairly stated

1. Streak (time-resolved) spectroscopy of sparks is a respected technique and the delayed arrival of electrode-metal emission in the gap is real physics. Modern spark and vacuum-arc work (Beilis 2018 history in IEEE, per the Investigator [web] listing, not read by me) treats expansion of electrode vapour as an established topic.
2. A discharge in air at atmospheric pressure first breaks down through the air (the "streamer/leader" channel), then the channel is heated and, as the current rises, electrode material is ablated and enters the channel. Which species radiates at a given instant depends on the electron temperature and density, not only on which atoms are present. [memory: high]
3. What the line slope measures is the question. Either (A) the atoms themselves move at that speed (bulk vapour flow), or (B) a front of excitation or luminosity moves through vapour that is largely stationary. The second reading was raised by Schuster's own laboratory in 1908 and by Hull in 1906 (see Investigator's findings below). The authors themselves chose reading A and noted no alternative [web: Royds 1908 p.333 via Investigator, https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1908.0023].

Investigator's findings I weighed (kept whatever the verdict)

• Full paper exists: Phil. Trans. 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 . Not read. Royds reports it contains calcium H and K lines (an impurity in silver electrodes) that "became luminous first in the centre of the gap, and were propagated towards the electrodes" [web: Royds 1908 p.333]. This is awkward for a simple "vapour streams out from the electrodes" picture, and the abstract does not mention it.
• Hull 1906, Proc. R. Soc. A 78, 80: Doppler test with Cd/Hg amalgam electrodes, no wavelength shift above 0.002 Angstrom; he concludes luminous particles move along the discharge at no more than 150 m/s, and that the Feddersen/Schuster-Hemsalech curvature "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 . Hull's note is preliminary.
• Royds 1908 (Schuster's own lab, Manchester) repeated the moving-film method and states the 1899 workers "did not discuss any possibilities of the propagation of luminosity through vapour which may be, as a whole, stationary"; he summarises their result as "the lighter metals had a greater velocity than the heavier metals" [web, same URL].
• Hemsalech 1901 thesis (Paris), dedicated to Schuster: calls the self-induction effect "la découverte faite par M. Schuster et moi"; sorts 14 metals into two groups (Fe, Mn, Co, Ni lines strengthened by self-induction; Cd, Zn, Mg, Al, Sb, Sn, Bi, Pb, Cu, Ag weakened); argues the spark-vapour temperature "ne peut dépasser de beaucoup la température de l'arc électrique" [web] https://archive.org/details/recherchesexpri01hemsgoog . He is an interested party (co-author), reported as such.
• Schaeffer 1908 (ApJ 28, 121) credits the pair with first finding that sufficient self-induction makes air lines disappear [web, via Investigator]. Crookes (13 Feb 1899): "The paper marks an important step in understanding the electric spark"; Abney recommended it for Phil. Trans. [web] https://makingscience.royalsociety.org/items/rr_14_230 . Hemsalech 1906: metal "projected solely from the positive electrode" (as summarised in Nature 1908) versus Schaeffer's negative-pole disintegration versus the 1899 abstract's bands from both poles: three different statements, not reconciled in anything I have read [web, via Investigator; none of the three primary papers read by me].
• Historical record: not an anomaly of disappearance. The work was refereed, published, continued by Hemsalech and Royds, cited in the 1911 Britannica and in 2018-2022 plasma literature [web, via Investigator]. This is mainstream physics, so there is no suppression question here.

Checks I did myself on the abstract

• Film speed: mean annulus radius (16.5 + 11.1)/2 = 13.8 cm; 2 pi (0.138)(120 rev/s) = 104 m/s [calc], matches "about 100 m/s" [read: p.1-2].
• Time resolution: unit-magnification slit image, so spatial resolution is of order the slit width (about 0.1 mm, my assumption; not stated). At 100 m/s film speed 0.1 mm is 1 microsecond. The claimed 6 microsecond arrival is resolvable; the 0.5 microsecond air-luminosity figure is not [calc]. For a 500 m/s particle the line is tilted about arctan(100/500) = 11 degrees from the film-motion direction, so the geometry is sensitive enough.
• Sound-speed formula: c = sqrt(gamma R T / M) with M = 0.1124 kg/mol, T = 2700 K gives 447 m/s (gamma = 1), 529 (1.4), 577 (5/3) [calc]. The authors' V = 80 sqrt(T/rho) with rho = 56 gives 555 m/s, i.e. equals gamma of about 1.55. Cadmium vapour is monatomic, so gamma = 5/3 and the formula is right to about 4%. T = (560/80)^2 x 56 = 2744 K, printed as 2700: correct [read: p.5, calc].
• Cadmium crossing time: 5 mm in 6 microseconds is 830 m/s (910 if the 0.5 microsecond air phase is subtracted), versus the quoted average 560 m/s [read: p.5-6, calc]. Unreconciled in the abstract. A 560 m/s mean would need about 9 microseconds.
• Pure diffusion cannot do this: with a diffusion coefficient D of order 1 to 5 cm^2/s for a metal atom in hot air [memory: medium], the diffusion length in 6 microseconds is sqrt(2Dt) of order 0.1 mm [calc], fifty times too short for 5 mm. The authors' own remark that it is "gas under pressure flowing into a vacuum" rather than "pure thermal diffusion" [read: p.5] is therefore the physically right description, and the word "diffusion" in their introduction is loose.
• Stored energy: if the 0.033 microfarad is charged to about 30 kV (breakdown of a 1 cm air gap is of order 30 kV/cm [memory: high]), E = (1/2)CV^2 = 15 J [calc]. Ample to ablate micrograms to milligrams of metal; no energy-budget problem.
• Implied circuit inductance from the quoted 2 microsecond period: L = T^2/(4 pi^2 C) = 3 microhenry [calc]; plausible for a short jar circuit.
• Doppler scale: v/c for 560 m/s is 1.9e-6, which is 0.009 Angstrom at 5086 Angstrom (strong Cd line) and 0.024 Angstrom for the 1420 m/s bismuth figure at 5086 [calc]. A genuine bulk flow of that size would exceed Hull's 0.002 Angstrom bound unless streams in opposite directions cancelled in the centroid, in which case they broaden lines instead. Hull's geometry (viewing along versus across the discharge) and low-capacity conditions differ from the six-jar spark, as the Investigator notes. Collision (pressure) broadening in an atmospheric spark is much larger than 0.002 Angstrom anyway [memory: high], so the test is a centroid-shift test, not a width test.

Claim 1. Metal vapour crosses the gap at measurable speed (about 6 microseconds to centre for Cd; 400-1500 m/s)

a. Mathematics: consistent as far as given. The speeds follow from film displacement over film speed. The Cd numbers are loosely reconciled: 830 m/s implied by the 6 microsecond figure versus 560 m/s quoted [calc, above]. Zinc: 2 mm at about 500 m/s is 4 microseconds, again loosely consistent with 6 microseconds over 5 mm only if speed rises beyond 2 mm; the authors say near-pole values vary a lot [read: p.2]. No error bars or counts of photographs [read]. b. Established results: The time sequence (air lines first, metal vapour emission later and extending into the gap) agrees with all later spark work [memory: high]. Quantitatively, the vapour speed order of hundreds of m/s agrees with the sound speed in hot metal vapour (calc, above) and with modern ablation-jet expansion (vacuum-arc cathode jets are faster, about 10^4 m/s, a different regime) [memory: medium]. Against the bulk-motion reading: Hull's Doppler bound of 150 m/s [web], and Royds's stationary-vapour alternative [web]. c. Tested: moving-film method repeated by Royds 1908/1910 in the same laboratory, with the Schuster connection (not independent in the strict sense) [web, via Investigator]. Independent Doppler test: Hull 1906, preliminary, different conditions, contrary. No test I know of which settles reading A against B with a neutral experiment of the 1899 conditions. I did not read Royds's tables or Strutt 1913. d. If true as bulk motion: nothing in mainstream physics changes. Hot vapour driven by its own pressure moves near the sound speed. The only open point is the ambiguity of what is moving. Verdict (split): the qualitative delayed appearance of metal emission across the gap is Established. The quantitative reading of the slope as bulk vapour velocity is Never properly tested (one preliminary Doppler note contrary, one same-laboratory repeat, and the abstract's own caveats). It was not dismissed without testing, but the testing was thin and unresolved.

Claim 2. Film on a spinning disc records metal lines as slanted, air lines straight; slope measures particle motion

a. Mathematics: the kinematics is trivial and correct. Internal wrinkle: the p.3 prose says "uniformly higher velocity deduced from the double line 4925", but Table I gives 4925 lower than 4811 in every row (e.g. 814 vs 1014; 1061 vs 1526) and the next sentence says "smaller apparent velocity derived from 4925" [read: p.3, my own check of the text layer and Step 1's table]. I agree with Step 1 that the word "higher" is a slip (possibly meaning higher displacement). b. Established results: streak spectroscopy with rotating mirrors or drums is standard; air lines straight, metal lines slanted is reproduced by Royds and described in the Hemsalech thesis (same circle) [web]. The slope-to-velocity step is the contested one (Hull, Royds), see claim 1. c. Tested: the technique, yes (above). The interpretation of slope, not decisively. One test of the line-dependence: velocity differs between lines of one metal (bismuth lines 1420 m/s, some zinc-like, one smaller; [read: p.4]). If vapour of one species moved bodily, every line of that species would share one velocity. Different velocities for different lines point to excitation fronts, to different charge states (neutral atoms vs ions, which respond to electric fields), or to different emission durations, as well as to different molecular masses. The authors say they "hesitate" to ascribe it to mass [read: p.3]. This is my physical reading [memory: medium] and not tested by the authors. d. If true: no change. Verdict: Established as a method of timing the appearance of emission; the identification of slope with particle velocity is Not testable as stated from the abstract alone (the two readings give the same film image) and Never properly tested otherwise.

Claim 3. Discharge begins in air; metal vapour then carries the later oscillations; adding self-induction makes air lines nearly vanish (against Feddersen's 1862 view)

a. Mathematics: no equations; qualitative argument. The self-induction experiment is physically coherent: added inductance L lengthens the oscillation period (T = 2 pi sqrt(LC)) and lowers peak current and current rise rate, so the spark gap carries a gentler, longer discharge; this favours the metal vapour already in the channel. Coherent. The explanation "energy heats metal molecules instead of air molecules" is qualitative but sensible [read: p.5]. b. Established results: the effect that inductance suppresses air (N, O) lines and enhances metal lines is a standard fact of analytical spark spectroscopy (the "high-inductance spark" sources, de Gramont, Feussner type) [memory: high]. Schaeffer 1908 credits the discovery [web via Investigator]. Hemsalech 1901 found the effect is not universal: Fe, Mn, Co, Ni lines strengthen, others weaken [web, interested party]. Complication from the full paper (Royds): Ca H and K lines start at the gap centre and propagate outward, which fits "oscillations through vapour" less well than the Cd/Zn pictures [web]. c. Tested: by the authors, Hemsalech (1899-1906 Comptes rendus, 1901 thesis), Schaeffer, Berndt (who disputed the ultraviolet results; Hemsalech replies that Berndt's inductance range was too small [web, thesis; partisan]). Broadly replicated in spark-source practice [memory: high]. Feddersen's idea that vapour is thrown out "independently of the current" is called "partly true", especially for magnesium [read: p.5]. d. If true: nothing; this has become standard. Verdict: Established (the self-induction effect and the air-first sequence). Detail on which electrode supplies the vapour is unsettled (three different statements, above).

Claim 4. Vapour speed approximates the speed of sound in the vapour: V = 80 sqrt(T/rho), so Cd at 560 m/s gives T about 2700 K, and the spark molecule is not much lighter than the normal vapour molecule

a. Mathematics: arithmetic and constant check out (above). The constant 80 corresponds to gamma = 1.55 (monatomic 5/3 gives 83). No derivation shown. Identifying a flow into a rarefied region with the sound speed is a mid-level approximation: an expanding gas front can exceed the local sound speed (free expansion into vacuum reaches speeds of order a few times the initial sound speed [memory: high]); the authors note it is approximate. The temperature is then inferred, not measured. b. Established results: Cd temperature of 2700 K is a gas-kinetic temperature, whereas spark lines are excited by electrons at far higher effective temperatures (order 10^4 K and more in a spark channel [memory: medium]). Hemsalech later argued vapour temperature stays near arc values [web]. The "mass not much smaller" conclusion is weak: cadmium vapour is monatomic [memory: medium] (the density rho = 56 relative to H2 equals atomic weight 112 over 2), so a molecule "not much lighter" than an atom just says the carrier is not a fragment of the atom; there was no way to split it below the atom in 1899 short of ionisation, which does not change the mass. c. Tested: no independent temperature measurement, no repetition of this inference in the abstract. Hull's bound (150 m/s) conflicts with the 560 m/s premise if read as bulk speed. d. If true: nothing. Verdict (split): the calculation is internally consistent and the order of magnitude is physically reasonable, so the sound-speed relation is Plausible, untested as applied to the spark; the molecular-mass conclusion is Historically superseded but instructive (a sensible inference with the knowledge of 1899, not decisive then or now).

Claim 5. Velocity has no simple relation to atomic weight; different lines of one metal differ; velocity falls with capacity at short gaps (flagged by the authors as unsettled)

a. Mathematics: Table I trends check out as the authors describe: at 0.51 cm velocity falls with jars (814, 556, 416 for 4925); at 1.03 cm flat; at 1.54 cm erratic [read: page image p.3 via Step 1 deep read; I re-read the text layer rows]. The authors' expectation that higher capacity means higher temperature and velocity is not borne out, and they say so [read: p.4]. A plausible, untested explanation is in their own caveat: the oscillation period is lengthened by more jars (T goes as sqrt(C)), so the later current half-cycles have more time to act on already-moving vapour and the film-slope reading mixes in later-arriving emission [read: p.6, calc]. That is my inference, not the authors' claim. b. Established results: a rough "lighter is faster" trend (Al over three times Zn) agrees with a thermal speed scaling as 1/sqrt(M); Bi at 1420 m/s on some lines is the exception and is "remarkable" to the authors [read: p.4]. Under pure thermal scaling at fixed T, Bi (209) should be slower than Zn (65) by sqrt(65/209) = 0.56; the Zn/Cd near-equality and Al/Zn ratio are also not pure 1/sqrt(M) [calc: Al/Zn would be sqrt(65/27) = 1.55, observed > 3]. Differences are what an excitation-propagation picture would allow. c. Tested: Royds's six-point summary of the full paper reads simply "the lighter metals had a greater velocity than the heavier" [web]; the abstract reads "no simple law" [read: p.4]. The two are compatible (a trend with exceptions), but the emphasis differs and the full paper's tables would decide. The authors themselves gave no confidence limits; Al "not laying any claim to accuracy", Hg unsatisfactory, Mg unmeasurable [read: p.4]. d. If true: nothing; it would constrain models of spark vapour and excitation. Verdict: Never properly tested (as a quantitative statement): honest preliminary observations flagged unsettled by the authors, not systematically tested or replicated beyond Royds's later same-laboratory work.

Corrections to Step 1

1. claims.md item 2 states the slope "measures the motion of the emitting particles". The abstract does say this, but Royds (1908) and Hull (1906) record that it was disputed; Step 1 did not have this. It should read "was taken by the authors to measure".
2. Step 1 deep read section 12 repeats the "which zinc line is higher" slip correctly; I confirm in the text layer (lines 143-158) that "higher velocity ... 4925" is contradicted by the table. No correction, just confirmation.
3. claims.md item 5 ("no simple relation to atomic weight") is in tension with Royds's summary ("lighter metals had a greater velocity") per the Investigator; both are valid readings of different documents (abstract vs full paper) and should both be shown.
4. claims.md item 4 says the 2700 K "implies the molecule in the spark is not much lighter than the normal vapour molecule". Correct as the authors' wording, but note the weakness I explain in claim 4 (monatomic vapour, no test).
5. Step 1 deep read already flagged the 830 vs 560 m/s mismatch; I confirm the arithmetic (5 mm / 6 microseconds = 833 m/s).
6. Step 1 said the project was "a mainstream experimental physics paper, not a fringe claim". Confirmed; the review also confirms there is no suppression story in the Investigator's record (refereed by Crookes and Abney).
7. No errors found in Step 1's Table I transcription as compared to the text layer.

Items not verified

• The full Phil. Trans. paper, Royds 1908 tables, Royds 1910, Strutt 1913, Hemsalech Comptes rendus papers and Schaeffer 1908 were not read by me; their content above is as reported by the Investigator [web, secondary]. Hull's text I did not re-fetch.
• The exact Doppler claim in Hull's geometry was not verified; my broadening argument is physical reasoning, not a finding.
• Spatial resolution (0.1 mm slit) and the 2 microsecond oscillation period's origin (measured or estimated) are not given in the abstract.

Summary table