The octant (sometimes known as the reflecting quadrant) is primarily a navigational instrument. As the name suggests, the octant has a shape that is one-eighth of a circle. The instrument relies on mirrors that reflect light along a path to the observer. The mirrors are arranged in such a way that they double the size of the angle that can be measured from one-eighth of a circle to one-quarter of a circle (i.e. a quadrant), or ninety degrees (90°). The octant is believed to have been invented by the English physicist and mathematician Isaac Newton (1643-1727) in around 1699, although a full description of Newton's instrument, which he passed on to the English astronomer and physicist Edmund Halley (1656-1742), was not published until after Halley's death (this was the same Edmund Halley, incidentally, after whom Halley's comet is named).
By default, therefore, the credit for the invention of the octant is generally attributed jointly to English mathematician John Hadley (1682-1744) and American inventor and optician Thomas Godfrey (1704-1749), who invented similar instruments independently in around 1730. Hadley generally gets the lion's share of the credit, probably because most of the significant developments relating to the development of scientific instruments during the eighteenth century were taking place in London under the auspices of the Royal Society. It is therefore Hadley's version of the octant on which we will focus our attention here. The drawing below shows Hadley's second version of the octant. This design will be far more recognisable to those interested in the history of navigation, since it is similar to that of the sextant (which we will discuss in due course).
A drawing of John Hadley's octant © The Royal Society
From the drawing, you can probably see that the main frame of the instrument spans an angle of forty-five degrees (45°). A moveable arm (called the index arm) is mounted on the frame so that it can pivot around the apex of the frame. A narrow sighting telescope is mounted at the top of the instrument, near its apex (note that in use, the octant is held upright, with the telescope at the top). A mirror (known as the index mirror) is mounted on the index arm between the telescope and the apex of the frame, and moves with the arm. In the drawing you can see two smaller mirrors, one of which is directly in line of sight with the telescope, and the other to the right of it. These smaller mirrors are called horizon mirrors.
The horizon mirror in line of sight with the telescope reflects light from the index mirror through the telescope. The horizon mirror is small enough to allow the observer to see the horizon through the telescope (past the mirror) at the same time. Thus, the observer can see both the horizon and the object reflected in the index mirror (usually the sun or a known star) at the same time, without having to change the position of their eye. The index arm is rotated until the object being used for navigational purposes (which can lie anything up to ninety degrees from the line of sight) aligns with the horizon. The angle is then read off on a graduated scale, marked along the lower arc of the octant, through an aperture in the index arm. You can see a very nice demonstration of how the octant would have been used by navigators here.
The second horizon mirror, mounted perpendicular to the first, was intended for use with the telescope (which was detachable) mounted on the other side of the frame. The user could adjust the position of the telescope in order to see either horizon, as well as the object reflected in the index mirror. This allowed them to measure angles of up to ninety degrees from each horizon, giving a total coverage of up to one hundred and eighty degrees (180°), and enabling them to calculate the height of any object in the sky. Notice the shade mounted on the top of the octant. This was used to reduce the glare from reflected sunlight, but could be removed when measuring the height of objects in the night sky.
The octant became a popular instrument with navigators because of its relatively small size, light weight, and versatility. The ability to view both the horizon and the object whose height was being measured at the same time reduced the likelihood of errors. It was relatively easy to align the horizon and the reflected image, even if the ship experiencing significant movement due to pitch and roll, since from the observer's point of view they would appear to move together. An octant could be half the size of an equivalent cross-staff or back staff, with no accompanying loss of accuracy. It was constructed primarily of wood. Typically, the frame was made of mahogany or ebony, with the scale engraved on an ivory panel. Metal fittings were usually made of brass. On early versions, the mirrors were of polished metal. These were later replaced with silvered glass mirrors, once the technology for producing glass mirrors of sufficient quality had evolved.