The sextant is essentially a refinement of the octant in which the arc of the instrument is increased from one eighth of a circle (45°) up to one sixth of a circle (60°). Mirrors are used to double the angle that can be measured in exactly the same way they are in the octant, increasing the size of the largest angle that can be measured from ninety degrees (90°) to one hundred and twenty (120°) degrees. The development of the sextant as a replacement for the octant is largely due to the efforts of the Scottish Royal Navy officer and navigational expert John Campbell 1720-1790), whose experiences of using the Hadley octant led him to suggest increasing the arc of the instrument from forty-five to sixty degrees and replacing the wooden frame (which had a tendency to warp and split) with one of brass.
A US Navy midshipman taking a sextant reading as part of his training
Octants continued to be popular, mainly because they were easily manufactured, and because they were lighter and cheaper than the sextant, but the sextant became the instrument of choice for many navigators. The By the late eighteenth century, octants and sextants had essentially replaced all other navigational instruments. In fact, up until the end of the nineteenth century it was quite common to find both of these instruments in use on the same vessel. The octant would typically be used for routine daily measurement of the Sun's altitude, while the sextant (which was more accurate but heavier) was used for the measurement of the angular distances between objects in the night sky. In order to use these instruments to find one's geographical position, however, something else is required.
It had been possible for centuries for navigators to find their latitude (i.e. their distance north or south of the equator) by measuring the angular height of the Sun at mid-day. Navigators would measure their latitude when they left port on a voyage. For the return journey, they would sail north or south until they attained that latitude, then turn left or right as appropriate, and simply sail along the line of latitude until they reached their home port once more. What such measurements cannot reveal is the longitude of the observer, which is essentially a measure of how far east or west they are from a particular point (in modern navigational systems, longitude is a measure of how far east or west you are from the prime meridian, which is an imaginary line that runs from pole to pole via Greenwich, England).
In order to be able to calculate your exact position on the Earth's surface, you must have reliable maps and charts. You must also be able to measure both your latitude and your longitude. By the eighteenth century, thanks to centuries of meticulous astronomical observation and record keeping and the availability of mathematical techniques such as spherical trigonometry, astronomers were able to accurately calculate the relative positions in the night sky of the Sun, Moon, stars, and planets at different times throughout the year. This information was carefully recorded and compiled into tables which, together with the fact of the Moon's relatively rapid transit across the night sky, provided navigators with a means of finding their longitude from anywhere in the world.
Because the moon is in orbit around the Earth, and because it is much closer to the Earth than any other celestial body, it travels across the night sky relatively quickly by comparison with the stars and planets. Using the observational data collected, astronomers were able to perform the calculations required to predict where the Moon would be in relation to a particular star or planet, i.e. the angular distance between them, at any time of the night or day. In fact, they could predict these "lunar distances", as they called them, for several years in advance. At any given moment, the angle measured between the Moon and a particular star or planet (or, indeed, the Sun) would be the same, regardless of the observer's location on the Earth's surface. Complete tables of these lunar distances were compiled into publications called nautical almanacs.
Most importantly, the time at which a particular lunar distance would occur was calculated using Greenwich time (i.e. the local time at the Greenwich observatory in London, England). This meant that an observer could measure a lunar distance (using a sextant) and consult their almanac in order to determine the current time at the Greenwich observatory. In order to calculate their longitude, the observer need only determine the difference between the time in Greenwich and the local time. A difference of one hour represented an angular distance of fifteen degrees from the Greenwich meridian. Of course, there was also the small matter of correctly determining the local time. This could be established fairly easily, however, by measuring the height of the Sun or a suitable star.
Although the above description probably makes the task of establishing longitude sound relatively easy, in reality things were a lot more complicated. The Moon is a relatively large object in the night sky, and may appear larger or smaller depending on latitude and the precise distance of the Moon from the Earth at any given time. Furthermore, because the Moon is relatively close to the Earth (by comparison with the stars and planets), its position as measured by an observer can vary by anything up to a whole degree of arc, depending on precisely where the observer is. There were of course mathematical methods available to navigators to allow them to compensate for such factors and eliminate errors, but they were time consuming and tedious. Navigation became easier once reliable and accurate marine chronometers, synchronized to the time in Greenwich, became available.
The available of GPS technology for commercial use has meant that a sextant is no longer needed for navigation. The use of a sextant is nevertheless still part of the training undertaken by navigators, and still features in navigational exams. The reason for this is simple; navigational aids based on GPS technology are dependent on both the availability of electrical power and the continued presence of a functional GPS satellite network. Given the possibility that either or both of these resources could be compromised, however unlikely that may seem the availability of a sextant, and the knowledge required to use it, ensures that navigators will still be able to find their location.