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Internet Archive, 2026-10-08

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Downloaded OCR text: https://archive.org/download/theorycalculatio00stei/theorycalculatio00stei_djvu.txt (saved as research/pages/ia-electric-circuits-1917.txt)

Other Steinmetz items seen (not opened): Four Lectures on Relativity and Space 1923 (fourlecturesonre00stei), Engineering Mathematics 1911, General Lectures 1908/1918, Theory and Calculation of Electric Apparatus 1917, Theoretical Elements 1915, Electric Discharges 1914 (ElectricDischargesWavesAndImpulses), letter to A. H. Moore 29 March 1897 (charlespsteinme00stei), Steinmetz centennial memorial lecture 1965 (charlesproteusst00engs).

Found: Steinmetz, Theory and Calculation of Electric Circuits (McGraw-Hill, 1917), Chapter X "Instability of Circuits: The Arc" [web: https://archive.org/details/theorycalculatio00stei]

Contents (printed pp. 165-200): 81-85 types of instability, permanent instability, cumulative and sustained oscillations; 86-95 the arc as unstable conductor, dropping volt-ampere characteristic and its equation, stability conditions with series resistance, shunted capacity; 96 "Production of Oscillations by Capacity, Inductance and Resistance Shunting Direct-current Arc - Arc as Generator of Alternating-current Power - Cumulative Oscillations - Singing Arc - Rasping Arc"; 97 limiting resistance of arc oscillations; 98-99 transient arc characteristics, condition of oscillation, limitation of amplitude, with calculation; 100 arcing ground on a transmission system; 101 cumulative oscillations in high-potential transformers.

Quotes [web, OCR of printed pp.165-200]: - Sec. 85: continual or cumulative oscillation "is possible only by an energy supply to the oscillating system brought about by the oscillation"; "The mechanism of this energy supply to an oscillating system from a source of energy differing in frequency from that of the oscillation is still practically unknown, and very little investigating work has been done to clear up the phenomenon." (Same wording as Discharges p.142-147.) - Sec. 97 (printed p.190): "the arc, when shunted by an oscillating circuit, has an effective negative resistance" (R = de/di from the stationary characteristic), "and thereby generates alternating power, from the consumed direct-current power". Worked instance (Figs. 87, 94; mean current 3 A): R = 18.5 ohm for very small oscillations, 20.3 ohm for 1 A swings, 27.5 ohm for 2 A swings. A load resistance below 18.5 ohm starts oscillation spontaneously; with 22.5 ohm oscillation starts only after a disturbance outside 1.5-4.5 A. On the stationary characteristic the oscillation always grows to extinction: a "rasping arc", not a "singing arc". - Sec. 98 (p.191-192): the stationary characteristic does not hold for rapid change; the arc stream and terminal temperatures "still partly correspond to previous values of current", so voltage lags current, the transient characteristic flattens, and this limits the amplitude (the condition for a stable singing arc). Oscillograms of singing arcs (Figs. 90-91) and rasping arcs (Figs. 92-93), in massed and distributed circuits. - Sec. 101 (p.199-200): with very low resistance in the discharge path "a sustained or cumulative oscillation results"; transmission lines usually have too much resistance, cables too little inductance, but in the high-potential windings of large transformers "destruction by high voltages resulting from the cumulative oscillation of some arc in the system ... have frequently been observed"; arcing ground (recurrent impulses), arcing-ground oscillation (hundreds to a few thousand cycles) and stationary oscillation in transformer windings (10,000 to 100,000 cycles) "are the same phenomena of the dropping arc characteristic ... and differ from each other merely by the relative amount of resistance in the discharge path".

Bearing on the claims

Claim 2: claims.md and facts.json say Steinmetz "gives no equation for this". True of Discharges Lectures VIII-X, but three years later (1917) he gives a quantitative treatment: the negative effective resistance of the arc from its falling characteristic, the stability condition (load resistance against -de/di), a worked numerical instance, and the lag (thermal inertia) of the transient characteristic as what limits amplitude. Both mechanisms the deep reader set side by side (falling characteristic vs. lag loop) appear in Steinmetz's own 1917 text, in that order. See "Corrections to earlier documents" in sites.md.
Claim 4: the 10,000-100,000-cycle "danger" range is repeated in 1917 with "frequently been observed", still with no cited measurement.
Not yet read: secs. 86-95 equations, sec. 99 calculation, Chapter XI (hunting). A deep read (pages 165-200 of the 1917 book) is recommended.