The double-reflecting octant
A sea instrument for measuring angles in which the ship's motion does not spoil the accuracy: both the target and the reference direction fall into the same field of view. Every earlier instrument had to be held level, and a deck is never level, and the error from rocking ate the very accuracy the instrument was picked up for.
The octant defeats that motion by double reflection. A small mirror catches the body and throws it onto a second mirror silvered over half its surface; through the clear half the observer sees the horizon, or a second body, at the same time. Both images fall into one field of view and rock together, so the alignment stays true aboard a moving ship, and the reading on the arc gives twice the angle the mirror turns through, which is why an eighth of a circle measures ninety degrees.
The Englishman John Hadley communicated the instrument to the Royal Society on 13 May 1731. Almost simultaneously and independently Thomas Godfrey built the same thing in Philadelphia; Hadley's version went into production. In 1757 Captain Campbell's sextant grew out of the octant, with the arc of one hundred and twenty degrees needed for the large angles between Moon and star.
Why this date
exact: the instrument was communicated to the Royal Society on 13 May 1731 and described in the Philosophical Transactions, vol. 37 (1731-1732). Thomas Godfrey's independent invention of the same instrument in Philadelphia is dated 1730. The page numbers of Hadley's paper could not be verified and are therefore not given.
What grew out of it
-
The Nautical Almanac and the lunar-distance method in the mariner's hands
prerequisite for · Confidence: high
A lunar distance is the angle between the Moon and a star, which has to be taken from a rocking deck to within minutes of arc. Hadley's double reflection yields exactly such a measurement, and Campbell's sextant, grown out of the octant with its arc of 120 degrees, was made to the requirements of this method. Tables are useless without an instrument able to deliver an observed angle of the needed accuracy.
Dispute: The historians put it more mildly than a hard dependence requires: Falk says 'particularly useful', Higgitt 'greatly facilitated'. None of those quoted asserts strict physical impossibility outright, and the link is called a hard one on the substance of the accuracy requirement rather than on the letter of the quotations. What argues for it is the chronology: the lunar-distance method itself was described in print by Werner in 1514, more than two centuries before the octant, and through all that time it did not work at sea.
Link sources
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
Hadley's octant and the sextants that later incorporated Hadley's innovations were particularly useful for the precise measurements required in the lunar-distance method, and in any case it is hardly surprising that the NMM curators chose to place them on the right hand side of the gallery, where they help Mayer's maps and Maskelyne's tables to stand a chance of attracting attention away from Harrison's shiny clocks.
- Rebekah Higgitt, «Longitude», Encyclopedia of the History of Science, vol. 4, issue 1 (April 2021) (2021) Verified 20 Sep 2026
Timekeepers were tested alongside the lunar-distance method, supported by predictive tables and newly developed double-reflection observing instruments – octants, sextants and circles – that greatly facilitated ship-board observations by using mirrors to align objects and produce a reading of their angular distance.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
his measuring device was brushed aside in favour of the sextant, which is a development of Hadley's octant, conceived by Capt. Campbell, meeting the requirements of high accuracy and large angles set by the lunar distance method.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.
- Seb Falk, «Ships, Clocks & Stars: The Quest for Longitude», Science Museum Group Journal, Autumn 2014 (2014) Verified 20 Sep 2026
Node sources
- John Hadley, «The Description of a New Instrument for Taking Angles», Philosophical Transactions, vol. 37 (1731-1732), JSTOR 104076 (1731)
The Description of a New Instrument for Taking Angles. By John Hadley, Esq; Vice-Pr. R. S. Communicated to the Society on May 13. 1731
- William B. Ashworth, Jr., «John Hadley», Scientist of the Day, Linda Hall Library Verified 20 Sep 2026
In 1731, Hadley presented a second instrument to the Royal Society, this one a reflecting octant for measuring the altitude of the Sun or a star.
- William B. Ashworth, Jr., «John Hadley», Scientist of the Day, Linda Hall Library Verified 20 Sep 2026
His octant had a small mirror that reflected the light of the Sun, or a star, onto another flat mirror that was half-silvered (as we would now describe it), meaning that one half was reflective, and the other transparent.
- William B. Ashworth, Jr., «John Hadley», Scientist of the Day, Linda Hall Library Verified 20 Sep 2026
The octant (sometimes called a quadrant, because it could measure an angular difference of a quarter of a circle) was invented independently and nearly simultaneously by the Pennsylvania mathematician Thomas Godfrey, but it was Hadley's version that was put into production.
- William B. Ashworth, Jr., «John Hadley», Scientist of the Day, Linda Hall Library Verified 20 Sep 2026
Both instruments could also be used for determining longitude using the lunar distance method that was proposed in the 1740s.
- Steven Wepster, «Precomputed lunar distances», (Universiteit Utrecht) Verified 20 Sep 2026
his measuring device was brushed aside in favour of the sextant, which is a development of Hadley's octant, conceived by Capt. Campbell, meeting the requirements of high accuracy and large angles set by the lunar distance method.
"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.