Newton, Opticks (1730, fourth edition): the fits, their interval, and the corpuscular queries

Companion source

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: eleven passages (three added 2026-09-22, one on 2026-09-23, one on 2026-09-29) 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.
The interval times the momentum is a refraction invariant. Prop. XVII, “manifest by the 10th Observation”, makes the intervals of the fits in two mediums as the sine of incidence to the sine of refraction, so the interval is shorter in the denser medium by the refractive ratio; Prop. X’s hypothesis makes the ray faster there by the same ratio. Together they make \(\Lambda v\), and so \(\Lambda p\), the same in every medium, which is the Newton-age form of a phase advancing at a rate proportional to momentum (polygon-lift note, §5). Added 2026-09-22.
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.
Permanent least bodies, for the sake of lasting natures. Query 31 posits hard primitive particles that no ordinary power divides, so that natures stay the same in all ages: the atoms that Leibniz’s Pacidius names as the only escape for leaps, used in the continuity note, §4c.

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. 10	4627–4639	Plates of water and air at like rings “as about three to four”; the general rule by the sines
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. XI	6303–6306	Light “is propagated from luminous Bodies in time, and spends about seven or eight Minutes of an Hour in passing from the Sun to the Earth”
Book II, Part III, Prop. X	6124–6128	Light “swifter in Bodies than in Vacuo, in the proportion of the Sines”
Book II, Part III, Prop. XVII	6489–6495	Intervals of the fits in two mediums “as the Sine of Incidence to the Sine of Refraction”
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	8479–8533	Rays are small bodies of different sizes, put into fits by vibrations they “stir up” that “overtake them”
Book III, Query 31	9179–9197	Primitive particles “so very hard, as never to wear or break in pieces; no ordinary Power being able to divide what God himself made one in the first Creation”, so that bodies keep “one and the same Nature and Texture in all Ages”

Coverage and limits

Reading level passage for the ten 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.