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Gary,

       In order see the wood let’s remove the trees by expunging all mention of the ellipsoid and stick strictly to the sphere (special case, e=0). The attached pdf file shows the affected page of the paper. (The numbers in the example will also change slightly but let’s ignore that.) The mathematics that remains is just the familiar cosine rule and Mercator sailing formulas. Having done that we can now concentrate on the central question

How do you get a running fix on a sphere?

One possible answer is that it doesn’t matter because the graphical solution on the plane is good enough in which case there isn’t really much more to discuss. However if you agree that the question has some merit then my paper provides a simple, efficient and correct solution to the problem when other published works have been shown to be wrong. I would be interested in knowing where you stand on this and look forward to hearing from you,

Robin Stuart