Chapter 6: Empirical Curves
Research workbench, not a finished commentary page.
This page is generated from processed source text and candidate catalogs. It exists to help researchers decide what to verify, promote, and deeply decode next.
Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Engineering Mathematics: A Series of Lectures Delivered at Union College |
| Year | 1911 |
| Section ID | engineering-mathematics-chapter-05 |
| Location | lines 16483-21988 |
| Status | candidate |
| Word Count | 7171 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER VI. EMPIRICAL CURVES. A. General. 142. The results of observation or tests usually are plotted in a curve. Such curves, for instance, are given by the core loss of an electric generator, as function of the voltage; or, the current in a circuit, as function of the time, etc. When plotting from numerical observations, the curves are empirical, and the first and most important problem which has to be solved to make such curves useful is to find equations for the same, that is, find a function, y=f{x), which represents the curve. As long as the equation of the curve is not known its utihty is very limited. While numerical values can be taken from the plotted curve, no general conclusions can be derived from it, no general investigations based on it regarding theSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Magnetism
Section titled “Magnetism”... While numerical values can be taken from the plotted curve, no general conclusions can be derived from it, no general investigations based on it regarding the conditions of efficiency, output, etc. An illustration hereof is afforded by the comparison of the electric and the magnetic circuit. In the electric circuit, the relation between e.m.f. and e current is given by Ohm's law, i = -, and calculations are uni- versally and easily made. In the magnetic circuit, however, the term corresponding to the resistance, the reluctance, is not a constant, and ...Waves / transmission lines
Section titled “Waves / transmission lines”... II, and the methods of resolution and arrangements devised to carry out the work rapidly have also been dis- cussed in Chapter III. The resolution of a periodic function thus consists in the determination of the higher harmonics, which are super- imposed on the fundamental wave. As periodic curves are of the greatest importance in elec- trical engineering, in the theory of alternating-current phe- nomena, a familiarity with the wave shapes produced by the different harmonics is desirable. This familiarity should be sufficient to enable one to jud ...Radiation / light
Section titled “Radiation / light”... ata below magnetic saturation would be used for deriving the theoretical equations, and the effect of magnetic saturation treated as secondary phenomenon. Or, for instance, when studying the excitation current of an induction motor, that is, the current consumed when running light, at low voltage the current may increase again with decreasing voltage, 212 ENGIN^EERING MATHEMATICS. instead of decreasing, as result of the friction load, when the voltage is so low that the mechanical friction constitutes an appreciable part of the motor output. Thus, ...Ether references
Section titled “Ether references”... 0, but must equal the mechanical friction, and an expression like y = Axf^ cannot represent the observations, but the equation must contain a constant term. Thus, first, from the nature of the phenomenon, which is represented by the empirical curve, it is determined (a) Whether the curve is periodic or non-periodic. (6) Whether the equation contains constant terms, that is, for x = 0, 2/7^0, and inversely, or whether the curve passes through the origin: that is, y = 0 for a: = 0, or whether it is h3^erbolic ; that is, y= 00 for x = 0, or x = 00 fo ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Ether | 10 | seeded |
| Frequency | 10 | seeded |
| Radiation | 4 | seeded |
| Light | 1 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| ether | 10 | seeded |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
| No chapter-local candidates yet | - | - |
Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
| No chapter-local candidates yet | - | - |
Hidden-Gem Quote Candidates
Section titled “Hidden-Gem Quote Candidates”| Candidate ID | Candidate Passage | Source Location |
|---|---|---|
| No chapter-local candidates yet | - | - |
Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
- Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
- Ether references: Verify exact wording before drawing conclusions. Ether language must be separated from later interpretive systems.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
- Waves / transmission lines: Standing/traveling wave passages may support richer field interpretations; the page keeps those readings separate from verified Steinmetz wording.
- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
- Ether references: If Steinmetz mentions ether, quote only the verified source words first; any broader ether-field synthesis belongs in a labeled interpretive layer.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
- Promote exact quotations only after checking the source image.
- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
- Move diagram candidates into the diagram archive only after image extraction, crop verification, and manifest creation.
- Keep Steinmetz wording, modern translation, and ether-field interpretation in separate labeled layers.