A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Robert Pearson
Date: 2017 Mar 30, 10:57 -0700
The delta value at 0° appears to me to be adjusted so a better value for the cosine can be calculated between angle of 0° and 0°.5. You can calculate a delta value for 0.25° which to 1 decimal is 0.1 x10e-5. and maybe that's what he used. In any case I think this recognizes that a delta of 0.0 while correct for 0° does not provisde a way to calculate a "good" value for angles between 0° and 0°.5.
At 0°.5 I calculate a delta of 0.3 (0.2581) and from Doniol I read 0.2. This might imply he used some value between 0°.25 and 0°.5 to calculate the delta. Again without comparing values calculated using the table against more accurate values I can't say whether this provides better interpolated values under some metric. But the purpose of the delta is to facilitate interpolation within the table and to that end using a delta value based exactly on the entry value is not appropriate at angles near 0° for the cosine (or near 90° for the sine).
The rest of the tabular values agree very well with calculations I made in open office calc. To you comment about values at 61°, I read a value of 0.48481 (looks more like 0.48181 at 1st glance but obviously a problem with scanning) for the cosine and for the delta 25.4, both values match the values I calculated in the spreadsheet I set up.
I do agree a better scanned copy might help here.