A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 May 11, 08:40 -0700
They were simply called logarithms, and this trick of adding ten to logs of trig functions to avoid negative values (both because subtraction is difficult and also because it's easier to tabulate and print all positive values) was just "normal work" with "common logarithms". You had titled this thread "19th Century Logarithms". I changed it because this practice of adding ten to log trig tables was common and standard right through the end of the era, even in the 1960s.
You don't need more obfuscatory jargon. They're logarithms. Plain and simple. Even some of the "named" logarithms, like the infamous "proportional logarithms" which have confused and needlessly obsessed so many students of lunars, are merely logarithms with un-necessary jargon labels attached. Jargon doesn't help. :)
PS: You wrote: "adding 10 to a log is adding 10^10 or 10,000,000,000 to the common number". Obviously you merely mis-spoke there, but in case anyone with less background in this old-timey logarithmic math is puzzled here, adding 10 to a logarithm is equivalent to multiplying the original number by 1010 (or ten billion). It's a handy trick.