H 4

This is the one of the most important inventions of all time:  a clock sufficiently accurate for a navigator to determine his ship's longitude, or distance west or east of Greenwich, England (zero degrees longitude).

The determination of latitude is simple; in less than an hour anyone can be taught how to use a sextant to measure the sun's height above the horizon in degrees at "high noon" (local apparent noon), and how to correct that "altitude" for time of year (declination), height of eye, refraction, and error of sextant. The result of this "noon sight" is latitude, accurate to a mile or so if the sextant work is good, and no clock needed.

Latitude is very good, but's just one line of position (LOP), and that's not a fix. By measuring the altitude in degrees of a navigational body at a known time, a line of position perpendicular to the body's azimuth ("direction" from the navigator to the body) can be determined, which, when crossed with a noon sight advanced along the ship's track, or with a sun, moon, star or planet sight, gives a fix. In short, an LOP developed other than by noon sight (ok, or a sight on Polaris, which of course also can give only latitude) requires time, and a second of error can equal a mile on the chart.

In 1714 the British government offered 20,000 pounds (around $4.5 million, in 2009 dollars) to the first person to develop an accurate means of determining longitude at sea. Others focused on cumbersome methods of determining time by reference to the movement of heavenly bodies, but watchmaker John Harrison worked for thirty-four years to perfect a clock accurate at sea. His masterpiece, the H4, lost but 4 seconds on a trip from England to Jamaica, an error corresponding to less than two nautical miles. I saw this instrument, on a pilgrimage to Greenwich in 2007. It is about seven inches across. These clocks initially cost roughly one-quarter as much as a merchant ship might.