NavList:

Brian,
There are a few problems with your method. You do not take the change of declination between the observations into account. This will in general affect the latitude determination. In your worked example the latitude is 1.4ʹ off. But far worse is your longitude. As you ignore the difference between apparent time and mean time the result is way off. Assuming the observation date is 22 February 2022, I get a position at 36°0.8ʹN, 115°2.7ʹW, some 165 nautical miles from your result. My assumption may very well be wrong but the result will, I think, be pretty far away in all possible cases. One simple way to check the method is to calculate the altitudes at the resulting position, both altitudes should then become 40°, if the method is correct. With your resulting position I get the am altitude 38.7° and the pm altitude 41.2°.

It seems the Editor of the Journal of Navigation has difficulties nowadays finding qualified reviewers for papers relating to celestial navigation.
Lars