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Dave Walden wrote, about correcting amplitudes for apparent horizon rather 
than true horizon-

"Isn't it really much easier to find the change in A with alt:

d A = d ALT * sin lat/sqrt [(cos lat) ^2 - (sin dec) ^2]

(at ALT = 90 deg)"

He later corrected that to ALT = 0º.

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Yes, of course, that's true now, but Dave should remember that those tables 
were produced for an era when mariners had no calculators or computers, and 
all such calculations had be done using trig tables, log-trig tables, and 
log tables. So mariners were accustomed to using tables of all sorts to 
short-cut such calculations.

It's quite true, though, that the producers of that table could (and 
should) have used the formula presented by Dave when compiling it, rather 
than looking for small differences between computed amplitudes. If they had 
done so, those unphysical numerical jumps of 0.1º would have been avoided.

But the purpose of those corrections was in connection with finding compass 
error, at sea, in the days before chronometers were carried. In which case, 
a possible error of 0.05º either way was immaterial. Nobody reads a compass 
to that precision. And the vagaries of refraction, near the horizon, 
introduce uncertainties that are much greater.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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