Recent discussions regarding the possibility that the SOS position sent by the Titanic was incorrect due to mistakes made in applying the traverse tables make interesting reading.
Traverse tables have been used for about 200 years to solve the mathematical problems involved in short distance sailing. The tables simply tabulate the results of relevant trigonometric calculations and would have been extremely useful to navigators in the days before electronic calculators became available. However, it should be noted that, although traverse tables are reasonably accurate for short distance sailing, they are not accurate over long distances (over 600 nautical miles). This is because data in the traverse tables is calculated using ‘straight line’ trigonometry which cannot be applied to long distance, great circle sailing involving the use of ‘spherical trigonometry’.
An exposition of the use of the traverse tables is given in my book ‘Astro Navigation Demystified’.
Astro Navigation Demystified 
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