Mathematics of Steinmetz

The mathematics section preserves original equations, historical notation, modern notation, derivations, worked examples, and physical meaning.

Mathematics At A Glance

3,845

Formula candidates

Source-routed OCR/PDF-text candidates awaiting scan and notation review.

2,528

Reviewable relations

Relations with enough structure to be sorted into mathematical families.

1,330

Strong formula candidates

High-priority mathematical strings for transcription, variable mapping, and derivation work.

10

Equation families

AC symbolic method, impedance, transients, waves, apparatus, energy, magnetism, and engineering math.

Open the Equation AtlasThe corpus-level map of formula candidates by mathematical family, source, and review status.Open Source Formula MapsThe same mathematical evidence split by source, with source text, workbench, and diagram routes.Open the First Canonical SetThe small promoted seed set where notation, meaning, modern form, and verification status are kept together.Open Equation VerificationThe scholarly queue for scan checking, mathematical transcription, variable definitions, and notation review.Open Visual Topic GalleriesUse diagrams when the mathematics is geometric: phasors, waves, line constants, transients, hysteresis loops, and field storage.Open Interactive ToolsWave, phasor, impedance, power-factor, hysteresis, transient RLC, and surge explorers.

Seeded Equation Pages

• First Canonical Equation Set
• Equation Atlas
• Source Formula Maps
• Velocity, Frequency, and Wavelength
• Symbolic Rectangular Components
• Symbolic Operator j
• Inductive and Condensive Reactance
• Impedance and Reactance
• Admittance, Conductance, Susceptance
• Power Factor and Effective Resistance
• Capacity Susceptance
• Steinmetz Hysteresis Law
• Permanent Term and Transient Term
• RLC Oscillation Frequency and Damping
• Condenser Oscillation Frequency and Decrement
• Synchronizing Power in the Commonwealth Edison Report

Canonical Equation Data

The archive now has two mathematical layers:

• processed/canonical_equations.json preserves the first small promoted equation seed set.
• processed/equation_atlas.json exposes the full source-routed candidate formula layer for review.
• processed/crosslinked_research_surfaces.json links formula families back into source-level visual maps and concept pages.

The first promoted equation set is stored as:

processed/canonical_equations.json

This file is a review-control artifact. It records source location, modern notation, public page link, and current verification status for the first twelve equations.

The generated equation atlas currently routes 3,845 equation and formula candidates from 15 processed sources into families such as symbolic AC, impedance/admittance, transients, waves/radiation, magnetism/hysteresis, power/energy, engineering mathematics, and apparatus systems. It is intentionally labeled as OCR/PDF-text candidate material until each formula is scan-verified.

The source formula maps split that same mathematical layer book by book. Use them when the question is not “what family does this formula belong to?” but “what math has this source contributed so far, and where do I read it beside the diagrams and source text?”

Open Source Formula MapsEvery processed source gets a formula map with family counts, top candidates, source text, workbench, and matching visual routes.Open Source Visual MapsRead the diagram side of the same source-by-source evidence layer.

Working Mathematical Strands

Radiation Scale

The first source uses velocity, frequency, and wavelength to place electric waves, visible light, ultraviolet, and X-rays on one continuous scale. The archive keeps Steinmetz’s historical notation visible, then translates the relation into modern SI units.

Symbolic Alternating-Current Method

The AC sources move from time-varying quantities into symbolic calculation. The first promoted equation pages now cover rectangular components, impedance, reactance, admittance, conductance, and susceptance.

Hysteresis and Core Loss

The AC and engineering-mathematics sources give the empirical 1.6-power law that made magnetic hysteresis loss calculable. The archive now keeps this as a candidate equation page until exact source units are verified.

Transients and Natural Terms

The transient books require a separate mathematical layer: permanent terms, transient terms, exponential decay, condenser charge, oscillatory discharge, decrement, line reflections, and distributed constants.

Synchronous System Stability

The Commonwealth Edison report adds a practical appendix on station sections out of phase or out of frequency, connecting impedance, reactance, synchronizing current, power exchange, and critical slip.

Visual Mathematical Guides

Impedance geometry

Resistance, reactance, impedance magnitude, and phase angle.

Transient response

Permanent term, natural term, damping, and oscillatory exchange.

Admittance plane

Conductance, susceptance, reciprocal impedance, and symbolic AC calculation.

Distributed line constants

Line inductance, capacity, leakage, resistance, and traveling disturbances.

Candidate Catalogs

The first OCR pass produced candidate equations in:

processed/radiation-light-and-illumination/equations.json
processed/elementary-lectures-electric-discharges-waves-impulses/equations.json
processed/engineering-mathematics/equations.json
processed/theory-calculation-alternating-current-phenomena/equations.json
processed/theory-calculation-transient-electric-phenomena-oscillations/equations.json
processed/commonwealth-edison-generating-system-trouble/equations.json

Those candidates require scan verification before becoming canonical.

The broader generated atlas is the next working surface:

Open the Equation Atlas