'In GPS we trust' seems to be the mantra for many yachtsmen and boat owners but even the most sophisticated digital navigational devices aren't fail-safe. Indeed, the more sophisticated they are, the more chance there is of finding yourself all at sea.
The rest is trigonometry
What's needed is a back-up system. Something that doesn't rely on satellites, electronics or even batteries. Cue the sextant. Essentially this is an instrument that measures the angle between two objects. The name is derived from the length of its scale - one sixth of a circle or 60°. Sir Isaac Newton (1643-1727) invented a version with a quarter of a circle scale but never published it. Incredible isn't it? To dream up something as brilliant as a sextant and not bother to tell anyone. And around 1730 John Hadley, an English mathematician and a glazier from Philadelphia called Thomas Godfrey, independently developed an octant-based system. So reassuringly, the basic idea is a sound one and has stood the test of time.
It's all done with mirrors
The way it works is relatively simple. Rather like an inversion of the range-finder. That pinpoints the location of objects in relation to yourself. The sextant enables you to establish your location in relation to objects - a celestial body and the horizon. The basic principle relies on two mirrors. One - mirror A - is half-silvered, half-transparent so it both reflects an image and allows some light to pass through. This is the mirror through which you view the horizon. The second, mirror B, is used to reflect the sun - or at night a specific star. Mirror B is mounted on a moveable arm which can be adjusted so the reflected image of the sun is also reflected on mirror A. When the image of sun is superimposed on the horizon, the angle between the two can be read off the scale. And it's surprisingly accurate measuring an angle to within 1/3,600th of a degree.
Out in the midday sun
Straightforward so far? Well now things become a little more complicated. In order to find your location you first need to find your latitude. This is done by measuring the angle between the sun and the horizon at mid-day, i.e. when the sun's at its highest. Now refer to your navigation tables (more about these in a moment). They'll tell you the line of latitude the sun will be above on any particular day. For instance, on December 21st the sun is directly over the Tropic of Capricorn meaning your latitude is 23.5° south.
Now for longitude. Every hour the earth spins through 15° in its orbit. So if the sun is above 0° longitude at noon, by 1500 hours it will be above 45° longitude west. But absolute accuracy in time-measurement is essential. You'll need a watch made to chronometer standards because an error of just 4 seconds equates to a discrepancy of one nautical mile.
Turning the tables
At any precise moment, a celestial body - sun, moon, navigational star Spica - will be directly above a particular geographic position on earth. This is known as the sub-point and its location (latitude and longitude) can be determined by the tables in a nautical or aeronautical almanac.
Ignorance is bliss?
Of course this blog only sketches in rough outline the principle of the sextant. A thumbnail of the theory. To become proficient in practice requires... well, practice - like so many nautical skills. And it's also worth remembering that epic sea voyages - Magellan's circumnavigation of the world for example - were achieved without the aid of this instrument.
The Vikings made it to Newfoundland by way of Iceland, Greenland and even discovered the Faroes (they're hard enough to find in an atlas never mind the North Atlantic) without a sextant. And Columbus died 14 years after reaching the Caribbean... convinced he'd discovered a short cut to the East Indies.