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I am not sure whether I should consider myself being addressed by this inquiry or not, but now I am curious: Where is the riddle?

If one wants to interpolate a nearly linear function with slope k_t by means of a linear function with slope k_0, slightly different from k_t, then, in order to minimize the mean interpolation error, the only solution is to pivot the interpolation function on the value at the center of the interpolation interval and adjust the function values at the ends by exactly +/- half the difference between k₀ and k_t.  Naturally, this is what the HMNAO does, because it's the only thing they can do. I can't see where "proprietary" algorithms come into play here, or why HMNAO can't just publish their Fortran program that does all that; so that they may end the kabalistic tradition of keeping the "secret of the calendar", which seems slightly outdated today.

Robin Stuart wrote to Stan K.:

Can you give the details or point me toward previous posts on how the NA makes their adjustments for the GHA of the Sun? This I assume will then explain the background to Herbert's statement concerning what correct the interpolation formula should be,