Chapter 5: Methods Of Approximation
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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-04 |
| Location | lines 15156-16482 |
| Status | candidate |
| Word Count | 3828 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER V. METHODS OF APPROXIMATION. 124. The investigation even of apparently simple engineer- ing problems frequently leads to expressions which are so complicated as to make the numerical calculations of a series of values very cumbersonme and almost impossible in practical work. Fortunately in many such cases of engineering prob- lems, and especially in the field of electrical engineering, the different quantities which enter into the problem are of very different magnitude. Many apparently compHcated expres- sions can frequently be greatly simplified, to such an extent as to permit a quick calculation of numerical values, by neglect- ing terms which are so small that their omission has no appre- ciable effect on the accuracy of the result; that is, leaves the result correct within the limits of accuracy required in engineer- ing, which usually, dependingSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Impedance / reactance
Section titled “Impedance / reactance”... _b/ s\ (14) QTj^wli^ a greater exactness is required, by taking in the second term, ■^V T±s--ai}^-a^-^ '15) 128. Example. AVhat is the current input to an induction motor, at impressed voltage eo and slip s (given as fraction of synchronous speed) if ro — jxo is the impedance of the primary circuit of the motor, and ri — jxi the impedance of the secondary circuit of the motor at full frequency, and the exciting current of the motor is neglected; assuming s to be a small quantity; that is, the motor running at full speed? Let E be the e.m.f. gen ...Complex quantities
Section titled “Complex quantities”... a small quantity by s, and where several occur, by Si, S2, S3 . . . the following expression may be written: / (,0±Sl)(l±S2)=l±S]±S2±SlS2, ; and, since S1S2 is small compared with the small quantities Si and S2, or, as usually expressed, S1S2 is a small quantity of r* fjj higher order (in this case of second order), it may be neglectod, '-^ f and the expression written: X (l±Si)(l±S2)=l±Si±S2 (1) This is one of the most useful simplifications : the multiplica- tion of terms containing small quantities is replaced by the simple addition of ...Radiation / light
Section titled “Radiation / light”... l compared with h. For instance. METHODS OF APPROXIMATION. 189 in astronomical calculations the mass of the earth (which absolutely can certainly not be considered a small quantity) is neglected as small quantity compared with the mass of the sun. Also in the effect of a lightning stroke on a primary distribution circuit, the normal line voltage of 2200 may be neglected as small compared with the voltage impressed by lightning, etc. 126. Example. In a direct-current shunt motor, the im- pressed voltage is eo = 125 volts; the armature resistance ...Field language
Section titled “Field language”... ineer- ing problems frequently leads to expressions which are so complicated as to make the numerical calculations of a series of values very cumbersonme and almost impossible in practical work. Fortunately in many such cases of engineering prob- lems, and especially in the field of electrical engineering, the different quantities which enter into the problem are of very different magnitude. Many apparently compHcated expres- sions can frequently be greatly simplified, to such an extent as to permit a quick calculation of numerical values, by neglect ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Frequency | 4 | seeded |
| Light | 2 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| effective resistance | 1 | source-located candidate |
Equation Candidates
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Figure Candidates
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Hidden-Gem Quote Candidates
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- Radiation / light: Compare the chapter’s radiation vocabulary with modern electromagnetic radiation, spectral frequency, wavelength, absorption, and illumination engineering.
- Field language: Read for whether field language is mechanical, geometrical, causal, descriptive, or simply a convenient engineering model.
- Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Radiation / light: Radiation and wave language can invite ether-field comparison, but source wording, modern radiation theory, and speculative synthesis must stay separated.
- Field language: Field-pressure or field-gradient interpretations can be explored here only after the explicit source passage and modern engineering translation are kept distinct.
- Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
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.