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Robin, Lars

Thanks.  I fear you’re correct.  I was trying to prove the impossible.  You can only make the picture look like those in the textbooks with the GC concave towards the Equator if you put a kink in the rhumb line at the equator (making not one but two rhumb lines, one from start to the Equator and one from the Equator to the finish).  The pictures of rhumb lines v great circles the textbooks never cross the Equator, so their authors never have to solve that problem.  Time to forget about this for a while methinks and come back to it in a week or so.  DaveP