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Frank, I really appreciate your taking the time to so fully explicate the 
underpinnings of Martelli in particular and time sights in general. I often 
carried Weems Secant TS as a backup. Practiced it a few times ashore, but 
fortunately my calculator never let me down asea. FWIW, and if memory serves, 
I find Martelli less tedious and am very happy to have him in a contemporary 
form thanks to Greg, Robert and Hanno.

Hewitt

Sent from my iPad

On Jan 3, 2013, at 11:39 AM, "Frank Reed"  wrote:

> Hewitt, 
> 
> Just to reiterate, FUNDAMENTALLY all of the Martelli tables are in Bowditch 
and other navigation manuals. His Table I is a table of log cosines (plus a 
constant). His Table II is a table of natural cosines (plus a constant). His 
Table III is a table of natural sines (negated, plus a constant). His table 
IV is a table of common logarithms (negated, plus a constant ...or 
equivalently, a table of "proportional logarithms" plus a constant). His 
Table V is a table of log haversines (negated, plus a constant ...or many 
other equivalent descriptions). These are all simple tables which could have 
been combined into a slim volume by anyone. But who would buy such a volume 
if they're already in Bowditch or Norie? Ahh, but mix in a little Italian 
magic and peddle it to gullible British mariners, and now you've got a 
product that sells! A big advantage of short, highly-specialized methods like 
Martelli's is that the tables can be truncated to save pages and to make 
lookups easier. For example, the range for his tables I, II, and III, is 0 to 
90 degrees. That's more convenient than making tables that cover 0 to 360 
degrees (it doesn't save pages --it saves the navigator from having to learn 
multiple entry tables). But then again, that means that they are much less 
useful for any other problem.
> 
> Incidentally, I think I've got a "good" reason now for his odd choice of 
sexagesimal (units, minutes, seconds) output from his log tables. It's easier 
to look up logs in sexagesimal tables because you can head each page with a 
certain number of "units" (call them hours or degrees, it makes no 
difference) and then head the columns with a certain number of "minutes" and 
then each row is labeled with "seconds". And as it happens a small book can 
easily display 60 rows per page. This saves space in the table of common 
logarithms (Table IV) though at the big expense of making those logarithms 
useless for any other problem. And since logarithms were so useful to a 
navigator, any navigator carrying Martelli's tables with their obfuscated 
logarithms would necessarily also have to carry a redundant normal table of 
logarithms (probably in a larger volume, like Bowditch or Norie).
> 
> -FER
> 
> 
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