# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Index Card for Trig/Log Table**

**From:**George Huxtable

**Date:**2009 Sep 10, 20:31 +0100

A few comments about Greg's posting [9697]. He wrote- "I choose to drop the characteristics on the index card then keep track of the decimal by approximation." Fair enough. That's a perfectly valid way to do the job, though it adds quite a lot of complication; which he didn't mention when introducing us to his procedure. That explains why he had to look up, and note down, the cosines of the three angles, as well as the log-cosines, which would otherwise have been sufficient. Then he can multiply them together, to get a rough idea of the product. Simply estimating the product in-his-head should suffice. That then allows him to put the decimal point in the right place when the antilog gives the precise product-of-cosines. But isn't that a bit long-winded and unnecessary, when it can be bypassed, simply by working the log calculations to include the integer before the decimal place? That calls for writing down fully the log-cosines of the three angles, as 9.91772, 9.99804, and 8.94030, as he has done below, summing them to give 28.85606, as he has done below. Then discarding two tens from the result, to arrive at 8.85606 (not 2.85060, as he has shown). Then the next step is to use inverse logs, of 8.85606, to arrive at 0.07179, automatically. It's just what such logs were invented for. For LHA 85� : appx(.07) appx(.05) Log Cos Log Cos Sin (by slide rule) Lat 34� 10' 9.91772 91772 .8274 .5616 Dec 5� 26' 9.99804 99804 .9955 .0947 MA 85� 00' 8.94030 94052 .0872 +.0532 28.85606 2.85628 ............. .0718 Inv Log .07179 .07183 .1250 Inv Sin Hc 7� 11' =============================== Then the next step is to add to that the product of sines of lat and dec. In this case, it can be seen that the two terms in this sum are of similar magnitude, so a 1 in 1000 error (if that's accepted as reasonable, from a slide rule) ends up as 1 in 2500 error in the sum, which would create an overall error of well over a minute in the result, from that cause alone. It's why slide rules are not really acceptable for such calculations. Instead of multiplying those sines by a side rule, log sines could be extracted instead, added, then the result found by an inverse log (antilog) table. Then that has to be summed with the product-of-cosines, found previously, and then the inverse sine obtained as before. Those log sin calculations could be completed in the time saved by not having to work, and multiply, those cosines. And the result would not have lost any of its precision. What I'm trying to point out is that in this case the old ways were the best, and Greg hasn't saved time, but has lost precision, by doing it differently. Of course, better ways of working that calculation, by logs, were developed to avoid that awkward addition. 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. --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---