NavList:

Frank and Homer, is the PN (Polar North) my mis label?   I think so!  Why did I draw a picture?  Frank didn't understand my question so I thought I'd draw a picture and hoped that the picture would do a better job of describing my Law of Cosines question.  For the drawing, I used Keynote (Apple's version of PowerPoint) and just drew it.  It's a pretty simple drawing tool.  The text boxes are actually 1x1 tables for Law of Cosines formula....You can do drawings in Microsoft's PowerPoint also.  I know that there is an app that will do the drawing in a more generally.  I was looking at it the other day.   Stellarium is a little bit too complex for me since I'm only an occasional use of it.

Back to my original question.  I was originally thinking of using LOC to calculate Longitude based on the derived UTC from Lunars observation and the Ho (observed altitude of one of the bodies after all of the corrections).  I didn't think of it at the time, but now think it is simpler and just as accurate to just calculate Longitude Change starting from the Assumed Longitude (the DR Longitude) using 15 degrees per hour earth rotation and the UTC time difference between the Assumed UTC and the Lunars derived UTC.  Frank, is that the correct way?

Regarding my Davis Mark25.  I was happy enough with it for Altitude sights.  But with Lunars, my Mark 25 shades in front of the horizon mirror looks like a Venn diagram (the horizon shades used to protect my eyes from the rising Sun; the Moon is "ahead" of the Sun by a few hours.  Which Sun image touches the Moon Limb?!  On the other hand, the shades in front of the index mirror are tighter and I don't get that Venn diagram.  So, altitude sights are good enough.  Do you have the same issue with your Davis Mark 25?