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I had never looked at Frank Reed's methods when I decided to try a lunar in 1992 on my voyage to Hawaii, and I tried to figure out myself how to do it. If you had the lunar distance, sun and moon altitudes all measured simultaneously, it would be pretty straightforward. I remember reading in one of the Hornblower books that it took three midshipmen observing together to do a lunar, but that was clearly not how Slocum did it. 

When I observed for my lunar, I measured a series of Lunar Distances, sun altitudes and the time between those measurements, but I couldn't get the moon altitude because the horizon under it was obscured. I took the data home and despaired of a solution, until I realized that longitude, time and lunar distance were linked, and a lunar distance along with any other celestial observation was enough to determine the solution. The iterative method allowed me to calculate the solution, and then I realized it had some other advantages as well. The iterative method allows one to focus on careful observations and let the calculations handle the other complications. You don't need three midshipmen. I think it would be pretty tedious to do this calculation with logarithms, but with a cheap calculator it is reasonable. I eventually programmed a hand calculator to do all the celestial calculations, including lunars using this iterative method. 

The main advantage of this method is that you don't have to try to determine a lunar distance and sun and moon altitudes simultaneously, something that I think is observationally awkward. 

I believe the StarPath calculator they sell - which is the only one I know, except mine, which does lunars - uses this iterative method as well, based on some correspondence I had with them. 

I would be glad for any comments: I can be reached at wendel.brunner@gmail.com.