A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 May 13, 19:12 -0700
In the local time portion of this, you wondered about the corrections in the calculation of the Declination, which you numbered as lines 2 and 4. We can see that this is an interpolation of the Dec, but it's odd, right? In the modern world, we would interpolate based on the hours of UT. If the change in 24 hours is, for example, 12', and the UT is 4h, then since that's one-sixth of a day, the change in the Dec in those four hours would be 2'. Back then they did it a little differently, and you'll still see this difference ven today in various tools in "manual" observational astronomy. Back then they corrected for longitude and then for local time. It's hard to be sure, given the handwriting, but I believe the labels here are "Corr Long" and "Corr Noon" (could be something else, but the sense of this would be a correction for the elapsed hours since local noon). Interpolating for UT at this level of precision is essentially identical to interpolating first for longitude difference and then for local time. This is really a pre-chronometer way of looking at things, but old habits die slowly in navigation.
In that same section, when the navigator writes down 90°, he labels it as "Rad...". You have identified this as "Radian". Another possibility is that he wrote "Radius". The term radius, in English-navigation at least, was reserved for the base scale of trig tables (that's my loose description of it ...maybe someone else can describe it better), which is apparently why we refer to half the diameter of the Sun (which really should be a "radius") as a Semi-Diameter... The word radius was already spoken for.
You also wondered about the net correction for the Sun's altitude here. This navigator is using 10', and, as you suspected, it's the sum of dip, maybe a minute of arc for refraction, and SD: -5-1+16. A few decades earlier, +12 for LL and -20 for UL was the popular standard (you can see the -20 for UL in the lunar portion of this later) for both Moon and Sun sights, but navigators were aware it was a bit lazy, a bit inaccurate. It was better to have a tailor-made correction for the vessel and circumstances, and it appears that this navigator preferred +10 for Sun LL sights.