Newton, Opticks (1730, fourth edition): the fits, their interval, and the corpuscular queries
Source: Project Gutenberg eBook #33504, release date 23 August 2010, which prints the fourth edition; local verbatim excerpt
.txt; retrieved 2026-09-17. Metadata: Isaac Newton, Opticks: or, a Treatise of the Reflections, Refractions, Inflections and Colours of Light, the fourth edition, corrected (London: William Innys, 1730). Extraction: six passages copied verbatim from the plain-text file, with its line numbers recorded in each heading. Underscores mark the original italics, as in that file. Rights: public domain text; Project Gutenberg transcription. Limit: a transcription of the fourth edition, not a critical edition. The paper drafted from it must cite the 1730 printing itself, and Shapiro’s edition and commentary for the textual history of the fits.
What it supplies
The two factors of the mark cost \(\kappa=\delta\Delta\) of the mark-cost note, in Newton’s own quantities and with one of them measured.
- A least length, measured. The interval of the fits is defined as a length the ray traverses, and Prop. XVIII gives it as the \(1/89000\)th part of an inch for the yellow–orange confine, about \(0.285\,\mu\)m. This is the corpuscle’s transverse position scale \(\Lambda\) in premise M3 of the mark-floor note.
- A least impulse, posited. Query 29 makes the rays small bodies, which carries a transverse momentum scale \(p\); Newton has no way to measure it.
- The determinism that blocks the premise. Prop. XII states the fits as a transient Constitution or State of the ray which returns at equal Intervals and disposes the Ray at every return to be transmitted. The disposition is a determinate periodic property of the ray, so the outcome at a surface is fixed by the ray’s phase. M3 is the denial of exactly that, and in modern terms it is Robertson’s inequality for the corpuscle’s transverse position and momentum.
- Colour dependence, measured. Obs. 13 puts the ratio of the red to the violet interval at 14 to 9, bracketed between 3 to 2 and 13 to 8, so \(\Lambda\) varies across the spectrum by about half. Query 29 makes the violet corpuscles the least and the red the biggest. A universal value of \(\Lambda p\) is therefore beyond Newton-age data, which is what Planck’s constant later supplies.
- Action at a distance on light. Query 1 asks whether bodies bend the rays by acting at a distance, most strongly at the least distance, which is the inflexion that limits a mark’s resolution when the beam is narrowed.
Passage anchors
All line numbers refer to the Gutenberg plain-text file and are recorded again in the excerpt.
| Passage | Lines | What it gives |
|---|---|---|
| Book II, Part I, Obs. 13 | 4662–4690 | Red-to-violet interval ratio “as 14 to 9” |
| Book II, Part III, Prop. XII | 6325–6332 | Transient constitution returning at equal intervals |
| Book II, Part III, Definition | 6404–6410 | “the space it passes between every return and the next return, the Interval of its Fits” |
| Book II, Part III, Prop. XVIII | 6498–6506 | “the 1/89000th part of an Inch” |
| Book III, Query 1 | 7717–7720 | Bodies act on light at a distance and bend its rays |
| Book III, Query 29 | 8479–8530 | Rays are small bodies of different sizes, put into fits |
Coverage and limits
Reading level passage for the six anchors;
metadata for the rest of the work. The historiography is
not covered here and is an open obligation of the paper: Shapiro’s
Fits, Passions, and Paroxysms (1993) for the theory of fits and
its development, Sabra’s Theories of Light from Descartes to
Newton (1981) for the optical context, and Guicciardini’s
Reading the Principia (1999) for the limit arguments that the
Principia side of the comparison uses.