Monday, October 3, 2011

Longitude

Orientation—whether in the physical, social, or metaphysical dimension—is the absolute beginning of knowledge. You’ve got to know where you are. That very word, orientation, is derived from the physical. It comes from the Latin oriri, to rise, and the rising something indicated by the word was the sun, therefore the east. East-west orientation, therefore, was relatively easy for humanity. You simply had to observe the sun. It rose in the east and set in the west.

Paradoxically, however, traveling by sea, humanity’s first effective orientations using the sun told people where they were in the north-south dimension. After we were certain that the earth was a ball, that it travelled around the sun—and at a tilt to the sun’s own rotation around its axis—we learned to use an astrolabe, thus an instrument able to measure the angle of the sun to the horizon at noon, thus at its highest point. Knowing this angle and the time of year, the astrolabe (and later the sextant) could tell us how far north or south we were of the equator at any time of year. That technique dates to 150 BC. I’ve summarized the process on this blog earlier; the link is below.

To know where we were in the east-west dimension took much, much longer. It required the development of very accurate clocks—able to operate at sea. That achievement finally came in the eighteenth century, thanks to the achievements of an English clockmaker called John Harrison (1693-1776). That story is told most eloquently by Dava Sobel in her 1995 book, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. It’s short, suspenseful, entertaining, has pictures, and is must reading to anyone who’d like to know this story in detail. Harrison labored to win a £20,000 prize set by the British Parliament to solve the intractable problem of longitude. That prize in today’s dollars would be $4.47 million.

Why such a huge prize? Ships, cargo, entire fleets—and all the people on them—were routinely lost at sea in those days because they had miscalculated, by so-called dead reckoning, just where they were in an east-west direction from their intended landing place. Dead reckoning used estimated measurement of speed and time, over a set course (measurable by latitude), and thus calculating distance. But especially in stormy weather, speed-measurement, indeed course calculation, was extremely chancy. Therefore dead reckoning, while it worked reasonably well, was extremely chancy. After such a period, getting a hard fix on longitude was impossible out on the open sea.

So how do clocks come into this? In brief, as observed from the earth, the sun moves 15 degrees of longitude in the space of an hour. If you know your own time accurately, and also know what time it is at another fixed point on the earth, you can use the difference in time to calculate with great accuracy how far you are from that fixed point.

The illustration shows the geometrical basis of lines of longitude calculated as angles from the Prime Meridian. The Prime Meridian here is the “fixed point”—or rather the fixed line—from which the navigator calculates his or her distance east or west. The Prime Meridian these days runs right through the Royal Observatory of Greenwich, England. That line begins at the north and ends at the south pole. If the navigator sailed west and measured time locally and it was noon, the other clock, running on universal (call it Greenwich time) said 2:00 pm, the navigator knew that he or she was 30°W longitude from Greenwich, which is at 0° longitude. Conversely, if your local time is noon, but Greenwich time is 10:00 am, where are you then? 30°E longitude. One degree is 60 nautical and 69 statue miles or 111 kilometers—that’s at the equator. More on this later.

Now more illustrations:



This one shows the longitude over the United States. Our longitudes are all west. Longitudes are further subdivided into 60 minutes, each minute into 60 seconds. My own location in Detroit is 83° 05’—although I note that not all of my sources agree about the minutes. When you see longitude or latitude figures, the fractions may also be rendered into hundreds, so that Detroit’s longitude may be shown as 83.08 and mean the same thing as above. The above courtesy of Tutapoint.com (link).


Herewith longitudes overlaying a map of the world. This graphic, of course, does not do justice to a crucial fact. The distance between longitudes is not uniform all around the world. It is greatest at the equator, 69 miles, and zero at the poles. At 40° latitude, north or south, the distance between lines of latitude shrinks to 53 miles. Therefore accurate calculations of longitude require additional lookups to adjust for the latitude where the navigator takes his or her readings. The illustration is from Jacksonville State University (link).


Herewith the big picture, showing the whole world again, as presented by Wikipedia (link).

This post is the third, and last, on the subject of the astrolabe. The others are here (first, second). The astrolabe is meaningfully connected to this subject for two reasons. A good clock measuring Greenwich time and an astrolabe would still suffice today to navigate accurately on the oceans. The astrolabe was useful for determining the exact local time, thus noon—which has always been the time for seafarers to find out where they were

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