A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Roger W. Sinnott
Date: 2018 Dec 3, 16:38 -0500
Your haversine table looks quite nice, with no wasted white space!
However, one problem, as it stands, is that 4 decimal places isn’t enough to preserve significant digits in very small angles. So, for example, when you look up the haversine of 0° 48ʹ, the answer you get from the table is zero (not very useful).
Some time back I made a set of 3-place tables, each the size of a business card and laminated, that I keep in my wallet. I haven’t made one for haversines (yet), but I encountered a similar problem with significant digits in my 3-place sine table (picture attached). My solution was to invent a new notation, where a negative exponent precedes the decimal value, so that the sine of 1° is
given as -1.175 and means the same as 0.175 x 10-1, or 0.0175. (I hope the superscripts I’ve typed survive this transmission by email!)
Note that this exponent could be anywhere from -1 up to -9 and not take up any more space in the table, so even a number like 0.000000000397 could be accommodated in a 3-place table.