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 Stan,

I think the reason for the different, compact methods was that the standard books of tables; Bowditch, Tables Requiest, and even the Almanac were the product of mathamatians and astronmors.  The compact tables and methods seem to be the product of navagators or at least someone who talked to navigators.

Look at the 1846 Bowditch.  It is about 825 pages long.  The table XXIV is a table of natural sine and cosine.  Three tables later there is a table of log sine, tangents and secants.  There are over 50 tables in this Bowditch including Lat. and Long. of the fixed stars.  What navigator in 1846 needed a table of fixed stars?

To do the law of cosine formula one would need to look up the log sin of Lat. and Dec. then add them then go to another table to get the sine of that sum.  Then go to another table to get the log cosine of Lat., Dec., and T, add them up then go to another table to get the cosine of that sum etc. etc. etc.  No one, that I could find, printed a table of sin, log sine log cosine, and cosine on one line for every minute of every degree.  So easy to use but no one seemes to have printed one.

Same for the Almanac - published by astronomers for astronmers.  A navigator only need a short table - maby two pages long with the Dec. of the sun and the equation of time for each day of the year.  A perminent table of increments for Dec. and EOT would be bought once.  Such tables were sold and were used but again seem to be the product of sea -fairing men.

The compact methods all seem to put the few tables needed into one small book.  Why no one thought of one short table with sin, log sin, log cos, cos is a great mystery to me.  Why did the New World not have the wheel?

John H.