NavList:

Hello Sam, you wrote:
"I am familiar with using the Mer Pass or Polaris to establish latitude, and also with the traditional method of using position lines, but is there a similar, relatively simple technique to establish one's longitude?"

When you say 'similar', I take it you mean similar to a Sun meridian sight in terms of simplicity? There's nothing THAT simple, but there are some methods that come close. Could you explain more why you're asking? For example, are you trying to put together an introductory, basic version of celestial navigation for students? What age group, if that's the case? From land, the best approach is to find the time when the Sun is exactly due South (or due North if you're south of the "underSun" location). When that occurs, the Local Apparent Time is exactly 12:00:00. If there's no surveyed line to find due South, you can do the next best thing by observing the Sun's altitude an hour before Noon and then again about an hour after when it returns to exactly the same altitude (+/- as much as a couple of minutes of arc due to changes in Declination). Then just split the difference. Record the GMT of each sight, and average them. Note that no altitude corrections are required. That middle GMT is the time of Local Apparent Noon or, in other words, the time was exactly 12:00:00 Local Apparent Time. Then you look up the "equation of time" for that date (probably interpolating based on the GMT) and add or subtract that to 12:00. This gives Local Mean Time. LMT and GMT differ by your longitude in time units. So subtract them and convert to degrees at the usual rate of 15°/hour. And you're done.

You also asked:
"I understand that this might be done by shooting the sun when it bears directly east or west but I am uncertain as to how."

You measure the altitude and record the GMT at that instant. Then you do the usual altitude corrections, work up a standard spherical trig calculation (solving for hour angle, given Lat, Dec, and observed altitude), consult the almanac for the equation of time, and the result is "Local Mean Time". You subtract that from GMT and the difference is longitude (as above). Note that this "time sight" is usually described for the case where the Sun is due east or due west but it's not essential. Even 45° away from the Prime Vertical is just fine. This process is not as alien as it sounds. It's equivalent to a line of position, and the work to produce a longitude from it is about the same. Clearly there's more math work then the "equal altitude splitting" teachnique I described above, but it was primary historical method at sea for about 150 years.

As Antoine has already mentioned, none of this works without a clock reading accurate absolute time (GMT). Without that, you cannot get longitude.

-FER

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