Quote of the Day
If you want to live a happy life, tie it to a goal, not to people or objects.
— Albert Einstein
Introduction
Figure 1: Pitcairn Island As Seen from the
International Space Station (Source).
I liked reading the book Longitude by Dava Sobel, and I also enjoyed the television movie version. I was recently doing some reading about the Bounty mutiny when I realized that the problem of measuring longitude played a role in that tale as well.
The story of longitude is one of technology and obsession. While mariners had been able to measure their latitude accurately for centuries, measuring one's longitude required the development of accurate timepieces. Longitude is the story of the development of the marine chronometer. In essence, our modern GPS systems are extremely accurate clocks that provide the ultimate realization of the longitude goal.
While escaping from Captain Bligh, the Bounty mutineers stumbled upon Pitcairn Island, an island with an actual position that was significantly different than shown on their charts. This error provided the mutineers with an opportunity – the error was so large (181 nautical miles) that their pursuers could only find the island by accident. They decide to make Pitcairn their home and hope that they would remain undiscovered. Their instincts proved to be correct as the Royal Navy would not land on Pitcairn until 1814, which was 25 years after the 1789 mutiny. By then, all but one of the mutineers were dead.
The error was not made by the map's cartographers, but simply reflects the fact that the original discovers did not have an accurate measurement of the island's longitude. Here is an excerpt from log of Captain Pipon of the HMS Tagus, one of two Royal Navy warships that stumbled onto Pitcairn on September of 1814.
On the 17 Sep'r 1811 [1814] at about half past 2 o'clock in the Morning, to my surprise & astonishment, Land was discovered both by the Briton & Tagus & nearly at the same moment. The Ships were hove too, in hailing the Briton, it was determined to continue in that situation until day light in the morning; to ascertain the exact position of the Land in view, & according to circumstances, to reconnoitre it, if necessary. We were then by our reckoning in the Latitude of about 24°..40′ South & Longitude 130°.24W. the Land bearing SSE 5 or 6 leagues. As in all the Charts in our possession there was no Land laid down in, or near this Longitude, we were extremely puzzled to make out what Island it could be; for Pitcairn Island being by all accounts in the Longitude of 133° 24 W . we could not possibly imagine so great an error could have crept in our Charts, with respect to its situation.
This quote shows that the longitude error was over 3° while the latitude error was ~24 arcminutes. Errors of this magnitude were common prior to the development of accurate timepieces. Note that the latitude measurement is much more accurate than the longitude measurement.
Let's examine the charted position versus the actual position (from the Wikipedia) and determine the errors. To keep things simple, I just computed a Euclidean distance, which is close enough for short-ranges on Earth.
Figure 2: My Rough Calculations for the Pitcairn's Charted Position Error.
Trying to find a tiny island (18 square miles) when you have a position error of nearly 200 nautical miles is a daunting task.