NavList:

DavidP wrote

However, you quoted 'd h t   sinz = sin t cos d sec h  Bowditch  1958 p 567' . Was there no caution printed in the text surrounding this neat, plausible, and ..... manipulation of the spherical sine rule? 

"....the most common being sin Z =sin t cos d sec h

The weakness of this method is that it does not indicate whether the celestial body is  is north or south of the  prime vertical. Usually there is no question on this point , but if Z is near 90°, the quadrant may be in doubt. If this occurs, either the meridian angle or altitude when on the prime vertical can be determined  from table 25 or by computation, using th formula

cos t = tan d cot l."

Table 25   Meridian Angle and Altitude of a body on the Prime Vertical circle.

Your point is taken.

I suppose I should ask what was the purpose of the AMN? I have assumed that specialist RN navigating officers had a thorough grounding in navigation theory, much the same as Extra Masters in the merchant navy. On reflection the AMN meets the need for such officers as it includes spherical trigonometry theory written as a mathematician would probably write it. It is left up to the reader to decide what side of the triangle is co dec, what is the zenith etc. i.e there  seem to be few formulas for practical navigation.

In contrast what is the full name of Bowditch?  The Americam PRACTICAL Navigator.