Next message: Bruce Stark: "Re: Proportional logs, etc."
Henry H wrote:
"how to calculate these logs, please give me a shout. These things seem to
have passed into antiquity without so much as an obituary, as respects
navigation"
In case it hasn't been said yet in this discussion, the definition of normal
proportional logs is simply
P.L.(x) = log(3/x)
which is of course equivalent to log(3) - log(x) so the lack of a
proportional log table saves only a single subtraction. Because the practice of lunars
invariably involved interpolation between two predicted lunar distances
separated by three hours, saving a subtraction here and there added up in the long
term.
By the way, if x is in seconds (or time or arc), then the "3" will be
replaced by 3*3600 or 10800. So as an example, the proportional log of 500 seconds
should be given by
P.L.(500") = log(10800") - log(500") = 1.33445.
Because proportional logs are a sort of "upside-down" logarithm, converting a
modern calculation to proportional logs generally involves inverting it. For
example, if I want to calculate the Moon's parallax, I would calculate
p = HP*cos(h).
Converting to ordinary logarithms this would be
log(p) = log(HP) + logcos(h)
but with proportional log tables the calculation would be
PL(p) = PL(HP) + logsec(h).
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
