NavList:

Thanks all for the replies.  Frank, you are pretty much dead on.  Yes I attempted the solution using splitting a great circle into two right triangles thinking it might be a practical alternate "procedure", not realizing it in itself can be a fair mathamatical challenge. 

I typically use the spherical law of cosines, until I get close enough so mercator errors are inconsequential, but was wondering if a non-calculator log solution to the GC was practical using Napier's rules by splitting the triangle into two right triangles, simply because several tables do variations of this for the nav triangle.

Honestly I was contemplating a practical logarithm based math solution to great circle problems that was not adding more esoteric mathamatical derivational futzing.  I suppose normally if I threw the calculator overboard, and wanted to do GC's, I would revert to the various tables as all the tools for great circles are really there as basically catalouged solutions to spherical triangles. 

I understand that historically Haversines are more log friendly in many cases, and I will look at those formulas with curious interest after I print them out. 

in the end, ...i suppose the worth of all this must be balanced agianst mother nature anyway....my own experience is she has a lot of her own ideas on surface navigation which aren't GC's.

As much as anything, I am just trying to understand all of the different approaches, reasons, etc., till I feel a comfort I understand what is going on, and could always think my way out of a corner if one of my normal tools is missing. Historically its of interest as well. The complexity and historical efforts of entire nations to solve navigation are astounding.  

When I first started this crazy journey..my goal was simply being able to find my way around...once i found out i could do that pretty readily......  Then i wanted to find my way around when I broke my watch  LOL.....thus (lunars)....

So really I am trying to understand how we got to where we are..as I always learned once you really understand a subject, you can think for yourself without the cookbooks available and come up with whatever solutions are best with whatever tools are at hand. I also find for me that purely hypothetical futzing really cements understanding of the hands on stuff, because it forces me to understand it better.

One thing i have discovered is the subject is beyond fantastically complex if you wish to get into historical and theoretical approaches.  

BTW,  I do very much hope to see you in march for the historical celestial course in mystic.

Agian, thanks all for the replies, I have a lot to digest. The haversine stuff intrigues me.