NavList:

Here's an apples to apples comparison using Bowditch's Kochab example.

Compare intercept, azimuth from Pub 229 to the Law of Cosines: For Kochab, you must use AP (N 39, W 156º 43') to get an integral 307d for the LHA. Per Pub 229, this gives Hc 47º 08.4' / Zn 18.9º If you interpolate for Zn (which is not usually done) you would get Zn 18.7º . With Ho = 47º 13.6', the tabulated Hc gives an intercept of +5.2 nm.

Using the law of cosines on the triplet Dec N74º 10.6', Lat N39, LHA 307º, we find Hc 47º 08.3' / Zn 18.7º The intercepts are within 0.1 nm of each other.

Or, if you like, you can adjust the Pub 229 intercept using I_new = I - delta*cos(Lat)*sin(Zn), where delta is the number of nautical miles to move the assumed longitude. delta is negative to move west. So to move from W 156º 43' (required by Pub 229) to the DR W 157º 08', we find I_new = 5.2+ 25*cos(39)*sin(18.7) = +11.4 nm, which matches (to within 0.1') the law of cosines result, using the AP (N39º, W157º 08').

I would say Pub229 is matching within its claimed 0.2' for altitudes less than 86º (mostly due to rounding errors introduced when using the interpolation tables to adjust for the non-integral declinations.)
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