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Does the Almanac still have "methods and formulae for direct
computation"? That chapter in the 1998 edition gives the dip formula
0.0293° * √h, where h is meters. I tested that against the dip table
(A2) and got perfect agreement at the extremes as well as several
intermediate eye heights

Refraction may be calculated with the formula 0.0167° / tan(H + 7.31 /
(H + 4.4)) at standard conditions of 10C and 1010 mb, according to the
same chapter. To correct for nonstandard conditions, multiply the result
of the above formula by 0.28 * P / (T + 273).

The refraction values in the Almanac are the total deflection of the ray
from the observer to the top of the atmosphere. However, in the case of
dip we are only interested in the portion of the ray from the observer
to the point where it grazes the sea.

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