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, 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.

processed sources with mathematical records.

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 Formula Candidates

#1Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3090

(Let A = a(\cos a+j \sin a) be divided by J5 = 6(\cos ,5+y \sin /5),)

OCR source line

Let A = a(cos a+j sin a) be divided by J5 = 6(cos ,5+y sin /5),

#2Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3131

(If, A=ai +ja2 = a (\cos a+j \sin a), then)

OCR source line

If, A=ai +ja2 = a (cos a+j sin a), then

#3Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3525

(At the moment 0 = 0, let the \mathrm{e.m.f.} e = E \cos (0 - 00) be)

OCR source line

At the moment 0 = 0, let the e.m.f. e = E cos (0 - 00) be

#4Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3660

(i = io \cos (0 - 7) = io \cos 7 \cos <j> + i0 \sin 7 \sin)

OCR source line

i = io cos (0 - 7) = io cos 7 cos <j> + i0 sin 7 sin

#5Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 4573

(e = 2;oCe-”’ \sin (0 =F co - 7) j)

OCR source line

e = 2;oCe-”’ sin (0 =F co - 7) j

#6Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 7: Line Oscillations- line 5086

(i = e~ ”’ J ai \cos </) \cos co + 6i \sin cf) \cos co + Ci \cos 0 \sin co)

OCR source line

i = e~ ”’ J ai cos </) cos co + 6i sin cf) cos co + Ci cos 0 sin co

#7Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2398

(and ai + ja2 = a (\cos 6 + j \sin d) ;)

OCR source line

and ai + ja2 = a (cos 6 + j sin d) ;

#8Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2400

(or ai —ja2 = A(\cos 0+j \sin 6).)

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or ai -\-ja2 = A(cos 0+j sin 6).

#9Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2414

(and A ==5 (\cos 37 ^\circ H-j \sin 37 ^\circ).)

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and A ==5 (cos 37 deg. H-j sin 37 deg).

#10Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2844

(C = AB = ah (\cos a+j \sin a) (\cos /?+ / \sin /5))

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C = AB = ah (cos a+j sin a) (cos /?+ / sin /5)

#11Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 3115

(A = ai +ja2 = a(\cos a+j \sin a),)

OCR source line

A = ai +ja2 = a(cos a+j sin a),

#12Theoretical Elements of Electrical EngineeringTheory Section 3: Generation of E.m.f.- line 1101

(e = 2 7r/n$ \sin r the instantaneous generated \mathrm{e.m.f.})

OCR source line

e = 2 7r/n$ sin r the instantaneous generated e.m.f.

#13Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 3242

(B = 6’ + jh” = 6(\cos 13 + j \sin /3))

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B = 6’ + jh” = 6(cos 13 + j sin /3)

#14Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4185

(is r - j (x -f x0} = r = .6, x + x0 = 0, and \tan S>0 = 0 ;)

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is r - j (x -f x0} = r = .6, x + x0 = 0, and tan S>0 = 0 ;

#15Theory and Calculation of Alternating Current PhenomenaChapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance- line 5453

(is r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and \tan do = 0; that)

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is r - j {x + Xo) = r = 0.6, x -{- Xo = 0, and tan do = 0; that

#16Theory and Calculation of Electric ApparatusChapter 1: Speed Control Of Induction Motors- line 1689

(= - J = (\tan a - j) (7))

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= - J = (tan a - j) (7)

#17Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3545

(Since e = E \cos (0 - 00) = impressed \mathrm{e.m.f.},)

OCR source line

Since e = E cos (0 - 00) = impressed e.m.f.,

#18Theory and Calculation of Transient Electric Phenomena and OscillationsChapter 4: Inductance And Resistance In Alternating Current Circuits- line 3661

(i = -z | \cos (I? - 00- 0J- i~x° \cos (00 + OJ j (9))

OCR source line

i = -z | cos (I? - 00- 0J- i~x° cos (00 + OJ j (9)

#19Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 6: Double-Energy Transients- line 3943

(if = 140 \cos 0.2 1 - 80 \sin 0.2 1,)

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if = 140 cos 0.2 1 - 80 sin 0.2 1,

#20Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2282

(20. If ai+y6i=6+2.5 J is represented by the point \pi;)

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20. If ai+y6i=6+2.5 J is represented by the point Pi;

#21Engineering Mathematics: A Series of Lectures Delivered at Union CollegeChapter 1: The General Number- line 2284

(and the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-)

OCR source line

and the vertical distance 6i=2.5. If a2+jb2 = S+4:j is repre-

#22Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1257

(If an alternating current i = I0 \sin 6 passes through a resist-)

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If an alternating current i = I0 sin 6 passes through a resist-

#23Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 976

(1.) Ohm’s law : i = e j r, where r, the resistance, is a)

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1.) Ohm’s law : i = e j r, where r, the resistance, is a

#24Theory and Calculation of Alternating Current PhenomenaChapter 1: Introduction- line 1237

(1.) Ohm’s law : i = e j r, where r, the resistance, is a)

OCR source line

1.) Ohm’s law : i = e j r, where r, the resistance, is a

#25Theory and Calculation of Alternating Current PhenomenaChapter 5: Symbolic Method- line 2645

(or, if E = e —je’ is the impressed \mathrm{e.m.f.}, and 7 = i ’ — ji’)

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or, if E = e -\-je’ is the impressed E.M.F., and 7 = i ’ -\- ji’

#26Theory and Calculation of Alternating Current PhenomenaChapter 6: Topographic Method- line 3017

(\mathrm{e.m.f.} of the generator OE°, where Z0 = r0 - jx0 = inter-)

OCR source line

E.M.F. of the generator OE°, where Z0 = r0 - jx0 = inter-

#27Theory and Calculation of Alternating Current PhenomenaChapter 7: Polar Coordinates And Polar Diagrams- line 3818

(/, upon the \mathrm{e.m.f.}, or by IE \cos d, where 9 = angle of time-)

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/, upon the e.m.f., or by IE cos d, where 9 = angle of time-

#28Theory and Calculation of Alternating Current PhenomenaChapter 8: Capacity- line 4264

(but E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,)

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but E = E^y I^E^j z. If x^ > - 2,t-, it raises, if ;r < - 2 jr,

#29Theory and Calculation of Alternating Current PhenomenaChapter 8: Circuits Containing Resistance, Inductance, And Capacity- line 4580

(Then, if E0 = impressed \mathrm{e.m.f.},-)

OCR source line

Then, if E0 = impressed E.M.F.,-

#30Theory and Calculation of Alternating Current PhenomenaChapter 9: Kbsistanci: And Kbactance Of Transmission Iine8- line 6819

(a maximum for dP^j db = 0, that is, according to § 61, if -)

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a maximum for dP^j db = 0, that is, according to § 61, if -

#31Theoretical Elements of Electrical EngineeringTheory Section 4: Power and Effective Values- line 1290

(\mathrm{e.m.f.}, e = EQ \sin 6.)

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e.m.f., e = EQ sin 6.

#32Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1035

(w=j*pdt, (10))

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w=j*pdt, (10)

#33Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1232

(f = j (13))

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f = j (13)

#34Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1339

(K = j^; (21))

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K = j^; (21)

#35Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1440

((B = -j =/z JClinespercm2.)

OCR source line

(B = -j =/z JClinespercm2.

#36Elementary Lectures on Electric Discharges, Waves and Impulses, and Other TransientsLecture 2: The Electric Field- line 1446

(7 = -j = yG am-)

OCR source line

7 = -j = yG am-

Source-Level Math Coverage

Source	Year	All Candidates	Reviewable Relations	Section-Linked	Open
Engineering Mathematics: A Series of Lectures Delivered at Union College	1911	300	254	300	source - research review
Theory and Calculation of Transient Electric Phenomena and Oscillations	1909	300	169	300	source - research review
Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients	1911	300	182	300	source - research review
Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients	1914	300	202	300	source - research review
Theoretical Elements of Electrical Engineering	1915	300	213	287	source - research review
Theory and Calculation of Alternating Current Phenomena	1916	300	203	300	source - research review
Theory and Calculation of Alternating Current Phenomena	1900	300	194	300	source - research review
Theory and Calculation of Electric Apparatus	1917	300	241	300	source - research review
Theory and Calculation of Alternating Current Phenomena	1897	300	200	300	source - research review
Radiation, Light and Illumination	1909	300	146	300	source - research review
Theory and Calculation of Electric Circuits	1917	300	201	300	source - research review
Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.	1919	220	173	220	source - research review
Four Lectures on Relativity and Space	1923	170	91	170	source - research review
General Lectures on Electrical Engineering	1908	134	45	134	source - research review
America and the New Epoch	1916	21	14	21	source - research review

Promotion Standard

Open the source text and workbench.
Check the scan or source PDF for exact typography.
Preserve Steinmetz’s original notation before translating it.
Define every variable.
Add the modern equivalent only as a labeled translation.
Add a worked example only after the formula is mathematically reviewed.