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Finding Longitude At Sea

 

The problem relates not so much to finding longitude, but to finding position at sea!

Much has been written on the development of the marine watch or chronometer, but unless the navigator can find his (and so his ship's) local apparent time (LAT) precisely, the time at Greenwich (GMT) as shown by the corrected chronometer time is largely meaningless!

Most authors say that apparent noon at sea can be found easily from the maximum altitude or "culmination" of the sun. That is, at time of culmination the local apparent time (or LAT) is 12:00 precisely. Comparing instantly with the GMT (from the corrected chronometer time) yields longitude. Hey Presto! QED!

Unfortunately, that statement contains one error of principal and several difficulties!

The error of principal is because the sun's culmination yields a Local Apparent Time of noon (i.e. LAT = 12:00) but this is not comparable directly with Local Mean Time:

GMT difference LAT <> Longitude

GMT difference LMT = Longitude

The reason for this is that the sun is not a perfect time-keeper! Throughout the year the sun crosses the prime meridian at Greenwich, or any other meridian for that matter, at a slightly different clock time each day. This time difference waxes and wanes to a maximum and minimum (approximately sixteen minutes difference) in a well known and predictable way.

This time difference is known as The Equation Of Time. Tables of these values were calculated early in the 17th Century and were available to clocksmiths and sundial users to enable them to adjust domestic and church clocks accurately, before good watches were available. The table of values were of little use to mariners of the period for the same reason - however, once a good sea watch was aboard our ship, we can now re-write the equation above as:

GMT difference LAT. Eq. of T. = Longitude

The above statement is generalised - since GMT is measured as 0 to 24 hours and longitude is in fact measured as 0-180W or 0-180E, there isn't a simple difference between the two quantities (or even an mathematical one) but it will suffice for the time being!

The several difficulties referred to above may be broadly described as operational:

Firstly, it is difficult to measure the precise point of the sun's culmination! With a low sun - winter noon or ships in higher latitudes - the sun climbs in altitude slowly, hangs in altitude for several minutes, and then declines slowly. It is only after several minutes of sextant observation that the navigator decides that he has witnessed the passing of maximum altitude (i.e. L.A.T. 12:00) and every minute of time represents a (i.e. 15 minutes) of longitude error - remember that this error is one minute of time. Therefore the navigator, from this difficulty alone, and assuming that it is only one minute would not know his longitude with 30 minutes, or in mid-latitudes within 20 nautical miles or so at least.

Culmination point is further compounded by the vessel's course and speed - sailing at 10 knots (well within the capability of 18th century craft)  - sail west and the max altitude or culmination will occur actually after 1200 L.A.T. Sailing due East it will be before. Courses with some Northing or Southing will decrease or increase the altitude erroneously.

Some authors explain away this problem of deciding when local noon occurs by saying the altitude is taken when the sun bears due south (or north) i.e. on the observer's meridian! This is sheer deception - marine compasses could not show bearing to this accuracy and a 2 or 3 error of bearing would be worse than 2 or 3 minutes of time!

 

If you find this interesting prepare for some spherical geometry and some Celestial Navigation in the next monograph.

 

- 5th January 1999

 

 

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