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Steinmetz Decoded

Equation Atlas

This atlas exposes the mathematical breadth already present in the processed corpus. It is a review map, not a final equation canon: OCR formula lines can contain wrong symbols, missing fractions, page headers, figure references, prose contamination, or broken typography.

Use rule: read these as formula candidates. A formula becomes canonical only after scan verification, notation cleanup, variable definition, derivation review, and physical-meaning review.

3845

equation and formula candidates in the corpus.

2528

reviewable relation candidates after OCR scoring.

1330

strong formula candidates to prioritize.

15

processed sources with mathematical records.

Formula Families

Section titled “Formula Families”
Symbolic AC And Complex Quantities364 candidates. Routes equations where Steinmetz turns alternating quantities into symbolic algebra.Impedance, Reactance, And Admittance211 candidates. Routes the formulas that became the everyday language of AC circuit calculation.Inductance, Capacity, And Stored Energy329 candidates. Routes equations involving field storage, charge, discharge, and frequency-dependent opposition.Transients, Oscillation, And Damping907 candidates. Routes time-domain formulas that separate permanent terms from natural or temporary terms.Waves, Lines, Radiation, And Frequency354 candidates. Routes equations connecting electric waves, propagation, light, transmission lines, and frequency.Magnetism, Hysteresis, And Core Loss38 candidates. Routes formulas for magnetic materials, flux, loss, effective resistance, and hysteresis behavior.Power, Energy, Work, And Efficiency73 candidates. Routes equations where electrical quantities become work, heat, output, loss, or system performance.Engineering Mathematics Foundations336 candidates. Routes the mathematical language Steinmetz used to train engineers in calculation itself.Apparatus, Machines, And Power Systems410 candidates. Routes formulas tied to machines, apparatus, synchronism, and operating power systems.General Equation Candidates823 candidates awaiting classification.

Highest-Priority OCR Formula Candidates

Section titled “Highest-Priority OCR Formula Candidates”

The cards below are intentionally not rendered as KaTeX. They preserve the OCR line as a verification target so researchers can compare the scan, correct the notation, define variables, and promote only the reviewed result into the canonical math pages.

#1Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3090
Priority OCR formula candidateLet A = a(cos a+j sin a) be divided by J5 = 6(cos ,5+y sin /5),
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#2Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3131
Priority OCR formula candidateIf, A=ai +ja2 = a (cos a+j sin a), then
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#3Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3525
Priority OCR formula candidateAt the moment 0 = 0, let the e.m.f. e = E cos (0 - 00) be
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#4Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3660
Priority OCR formula candidatei = io cos (0 - 7) = io cos 7 cos <j> + i0 sin 7 sin
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#5Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4573
Priority OCR formula candidatee = 2;oCe-”’ sin (0 =F co - 7) j
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#6Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 5086
Priority OCR formula candidatei = e~ ”’ J ai cos </) cos co + 6i sin cf) cos co + Ci cos 0 sin co
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#7Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2398
Priority OCR formula candidateand ai + ja2 = a (cos 6 + j sin d) ;
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#8Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2400
Priority OCR formula candidateor ai -\-ja2 = A(cos 0+j sin 6).
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#9Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2414
Priority OCR formula candidateand A ==5 (cos 37 deg. H-j sin 37 deg).
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#10Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2844
Priority OCR formula candidateC = AB = ah (cos a+j sin a) (cos /?+ / sin /5)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#11Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3115
Priority OCR formula candidateA = ai +ja2 = a(cos a+j sin a),
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#12Theoretical Elements of Electrical EngineeringTheory Section 3: Generation of E.m.f.- line 1101
Priority OCR formula candidatee = 2 7r/n$ sin r the instantaneous generated e.m.f.
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#13Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3242
Priority OCR formula candidateB = 6’ + jh” = 6(cos 13 + j sin /3)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#14Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4185
Priority OCR formula candidateis r - j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ;
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#15Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5453
Priority OCR formula candidateis r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#16Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 1689
Priority OCR formula candidate= - J = (tan a - j) (7)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#17Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3545
Priority OCR formula candidateSince e = E cos (0 - 00) = impressed e.m.f.,
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#18Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3661
Priority OCR formula candidatei = -z | cos (I? - 00- 0J- i~x° cos (00 + OJ j (9)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#19Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3943
Priority OCR formula candidateif = 140 cos 0.2 1 - 80 sin 0.2 1,
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#20Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2282
Priority OCR formula candidate20. If ai+y6i=6+2.5 J is represented by the point Pi;
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#21Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2284
Priority OCR formula candidateand the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#22Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1257
Priority OCR formula candidateIf an alternating current i = I0 sin 6 passes through a resist-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#23Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 976
Priority OCR formula candidate1.) Ohm’s law : i = e j r, where r, the resistance, is a
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#24Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1237
Priority OCR formula candidate1.) Ohm’s law : i = e j r, where r, the resistance, is a
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#25Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2645
Priority OCR formula candidateor, if E = e -\-je’ is the impressed E.M.F., and 7 = i ’ -\- ji’
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#26Theory and Calculation of Alternating Current PhenomenaChapter 6: Topographic Method- line 3017
Priority OCR formula candidateE.M.F. of the generator OE°, where Z0 = r0 - jx0 = inter-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#27Theory and Calculation of Alternating Current PhenomenaChapter 7: Polar Coordinates And Polar Diagrams- line 3818
Priority OCR formula candidate/, upon the e.m.f., or by IE cos d, where 9 = angle of time-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#28Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4264
Priority OCR formula candidatebut E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#29Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4580
Priority OCR formula candidateThen, if E0 = impressed E.M.F.,-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#30Theory and Calculation of Alternating Current PhenomenaChapter 9: Kbsistanci: And Kbactance Of Transmission Iine8- line 6819
Priority OCR formula candidatea maximum for dP^j db = 0, that is, according to § 61, if -
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#31Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1290
Priority OCR formula candidatee.m.f., e = EQ sin 6.
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#32Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1035
Priority OCR formula candidatew=j*pdt, (10)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#33Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1232
Priority OCR formula candidatef = j (13)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#34Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1339
Priority OCR formula candidateK = j^; (21)
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#35Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1440
Priority OCR formula candidate(B = -j =/z JClinespercm2.
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

#36Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1446
Priority OCR formula candidate7 = -j = yG am-
Why this is not rendered automatically

This line is OCR/PDF-derived candidate text. Treat it as a pointer to the source scan, not as a verified mathematical transcription.

Source-Level Math Coverage

Section titled “Source-Level Math Coverage”
SourceYearAll CandidatesReviewable RelationsSection-LinkedOpen
Engineering Mathematics: A Series of Lectures Delivered at Union College1911300254300source - research review
Theory and Calculation of Transient Electric Phenomena and Oscillations1909300169300source - research review
Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients1911300182300source - research review
Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients1914300202300source - research review
Theoretical Elements of Electrical Engineering1915300213287source - research review
Theory and Calculation of Alternating Current Phenomena1916300203300source - research review
Theory and Calculation of Alternating Current Phenomena1900300194300source - research review
Theory and Calculation of Electric Apparatus1917300241300source - research review
Theory and Calculation of Alternating Current Phenomena1897300200300source - research review
Radiation, Light and Illumination1909300146300source - research review
Theory and Calculation of Electric Circuits1917300201300source - research review
Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.1919220173220source - research review
Four Lectures on Relativity and Space192317091170source - research review
General Lectures on Electrical Engineering190813445134source - research review
America and the New Epoch1916211421source - research review

Promotion Standard

Section titled “Promotion Standard”
  1. Open the source text and workbench.
  2. Check the scan or source PDF for exact typography.
  3. Preserve Steinmetz’s original notation before translating it.
  4. Define every variable.
  5. Add the modern equivalent only as a labeled translation.
  6. Add a worked example only after the formula is mathematically reviewed.