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--- Begin Message ---Hi Steve, all, Yes, the ’10-trick’ was so common because it made things very easy – well, comparatively speaking. But I see I have not been entirely clear: I forgot to mention the big trick, because to me it is so obvious – the user doesn’t have to do any adjusting, because the tables list everything ready-made. For instance, the sines table would not tabulate sines, nor would it tabulate the log of sines: it would tabulate the ten plus the log of the sine. All the computer (the person doing the computing!) had to do was look up the angle – say, 31° 25’ from the example – and get the number 9.71705 directly from the SIN table. Likewise, 45° 05’ will give you 9.84885 in the COS table. The addition of ‘minus ten’ in the example below was just to make it clear to me, the student, what was happening. In actual practice it was never written down. And going the other way, still in the example below, you could just search for ‘9.88400’ in the log-sin table and find the corresponding angle 49° 57’ 36”. (Unfortunately, there is a printer’s error in the example here: the number should really be 9.88400 , not 0.88400.) Of course, interpolation was most always required; there were handy small lists for that in the margins of the table pages. A sight reduction form was a marvel of efficiency. Just take your sextant-read altitudes, determine all necessary corrections (you must do all that even today), and enter all on the form. Then, just proceed line by line: adding, sometimes subtracting, and looking up in tables; and you end up with a star fix. Later, we got the HO-249 (and similar) publications, reducing the work even further. I bet that old first mate could work out a fix just as fast as anyone can today on an iPad. And if we dropped our HO-249, the worst that could happen was that we cracked the spine (not that it ever happened); compare that to the drama that a falling iPad might engender! Rudolf Van: sundial <[email protected]> Namens Steve Lelievre Verzonden: dinsdag 9 augustus 2022 17:43 Aan: [email protected] Onderwerp: Re: Computing hour lines for horizontal sundials Ooof! Did the method of adjusting all the logs by +10 really make the task easier? Merely negating the log seems better to me.... or simply learning to do arithmetic on negatives. Steve
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