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Terry you wrote: I'm not familiar with "arc error" or the "Q or P in A". One of them must be Altitude:  Semi-Diameter/Parallax tho I'm assuming that would be the arc error? The P being atmospheric pressure? I haven't even a guess for the Q or A. I am really trying to learn this the right way and am very glad to have your time and help. Your previous answer has already helped me greatly.

Terry. Sorry if I made my answer overly complicated.  I’m no expert with a marine sextant myself, but as I understand it:

Index Correction:  This is when the measurement of the horizon or a distant object measured against itself doesn’t quite read zero on the arc.  It might be the order of a couple of minutes of arc.  It is then applied to all readings as if the calibration of the sextant arc itself was perfect for all angles.

Arc Error:  However, depending upon the quality of the sextant, the age of the cutting machine etc, the arc may not be perfect.  There should be a certificate in the top of the sextant box giving further tiny corrections at 30, 60, 90, and 120, degrees.  They are the order of seconds of arc.  My 1941 Hughes Mates Three Circle sextant claims 0” on all four angles, but I’ve seen a 1970s model of the same sextant that had values in the order of 1 or 2 seconds of arc when released from the factory.

Q:  This is a correction to allow for the fact that the declination of Polaris isn’t exactly 90 degrees, so Polaris actually travels around the pole in a tiny circle throughout 24 hours.  It is only applied to Polaris sights.

Parallax in Altitude (P in A): This is a correction usually applied to Moon shots only. Because the Moon is so relatively close to the Earth, you have to allow for the difference in altitude measured at the surface compared to that which would have been measured from the centre of the Earth (if that were possible), because that’s where Hc is calculated from.  DaveP