How to Find the Longitude with a Chronometer?

"Long by Chron"

Someone on the ship makes an observation of the position of the sun, say at noon. Because the earth rotates, points on the surface at different longitudes will face the sun at different times of the day. The chronometer is set to show the time in a standard location (such as Greenwich), and to keep time very accurately and precisely. When the ship is away from Greenwich, then when it is noon with respect to the ship, it is not noon at Greenwich. The amount of difference of time, as shown by the chronometer, translates into how far away the ship is from Greenwich. Or in other word how far around the earth the ship is from Greenwich.


Suppose that the ship observes noon when the chronometer shows 3 pm. Then the earth has rotated (away) three hours from Greenwich's noon. That is  3/24 = 1/8 of the way eastward since it was noon at Greenwich. The circumference of the earth is computed according to the latitude (which is easy to determine with an instrument such as a sextant). 1/8 of the circumference of the circle at that latitude is then the distance west of Greenwich. On the equator this would be 40'075/8 = 5'009,4 km


If the chronometer shows some time in the morning when it is noon at the ship's position, then the ship is some distance east of Greenwich, the longitude is computed in the same way as before.

(Source: based on yahoo answers)

Impact of the accuracy of a Marine Chronometer

In 24 hours the earth rotates once around its axis. During this period the earth covers the Distance of 40'075 km if you take a point on the equator. If you look at this in seconds:

24 hours = 86'400 seconds => per second the earth advances by 0.463 km (40'075/86'400).

If you travel for one month and your watch is accurate within 1 second you will be able to find your position with a precision of about 500 m. (to be exact: if you move away from the equator this figure changes). Now let's calculate the same thing with a normal quartz watch which is accurate to 30 seconds. 30x500m = 15'000m=15km. You are able to find your position within 15 km. Because it is difficult to determine the exact local noon with the sextant, the precision is lower than we calculated here on a theoretical base. With the method "Long by Chron" you can count to find your position within 10 nautical miles (see Wikipedia). Sum up this inaccuracy with the one from a not so accurate watch and the precision gets unacceptable to the extend that navigating becomes difficult if not dangerous.

Be autonomous!

Only with a good marine chronometer (and some more traditional instruments such as a sextant) you can autonomously find your position within an acceptable precision. Of course, today we use GPS and radio controlled watches, both give better results. But they could fail and you depend on third parties. If you want to rely only on the instruments on board, you must have a marine chronometer.