NavList:

Artificial numbers are logarithms. Same thing. It's an old synonym which probably fell out of favor as the word "artificial" shifted in meaning in later decades. Artificial sines, cosines, tangents etc. are, of course, logarithms of the "natural" trigonometric values, as you already discovered. They added 10 to the logs (or equivalently multiplied both sides of all "natural" trigonometric equations by 10,000,000,000 before converting to logs) to eliminate negative logarithms since subtraction was avoided whenever possible. These +10 tables were absolutely standard in the era and they were used by anyone who had to work with calculations like these, not just mariners.

By the way, just a reminder: the NavList web site includes a menu at the top that says "Resources". Click on it. Then select "Bowditch and More" where the "more" includes "Moore" if you scroll down a bit. There are dozens of other interesting historical resources available for download linked there, and I would be happy to add more if anybody wants to compile additions to the list.

Frank Reed
ReedNavigation.com
Conanicut Island USA