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'Octant' is a measuring instrument similar to a sextant. Its scale is 1/8 of a circle (45°) rather than the sextant's 1/6.
In 1767 the first edition of the Nautical Almanac tabulated lunar distances, enabling navigators to find the current time from the angle between the sun and the moon. This angle is sometimes larger than 90°, and thus not possible to measure with an octant.
Newton's octant, used by Halley, was most likely an anticipation of the principle described by Hadley ^[1] but Newton's instrument ^[2] was not described (owing to Halley's death) until 1742. It was a major advancement over all previous designs and is still the basic design of the modern sextant. It was truly a "point and shoot" device. The observer looked at one place - the straight line of the horizon sighted through the horizon glass alongside the reflected image of the star. The sight was easy to align because the horizon and the star seemed to move together as the ship pitched and rolled. By the time of the publication in 1758 of Edward Stone's translation of Bion's Mathematical Instruments, Hadley's instrument was beginning to be widely employed in place of the earlier Davis quadrant.

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References

References

1. Hadley, “Hadley’s Octant.” Philosophical Transactions of the Royal Society, vol. 37, p. 147, 1731.
2. Newton, I., “Newton’s Octant” (posthumous description), Philosophical Transactions of the Royal Society, vol. 42, p. 155, 1742