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David Birch's N(x) table is quite nifty, but it starts to have problems with interpolating for small angles.  It occurred to me that if you're reduced to using his Emergency Navigation Card you're probably also using an improvised way to measure altitudes, which get their best precision with small altidues or small hour angles.  I've found workarounds.

Strictly speaking, linear interpolation of the N(x) table breaks down for angles smaller than 16°; second difference errors become significant if you're trying to interpolate to, say, 1' precision.  However, if you keep your precision to no smaller than 0.1° (reasonable when using a kamal), then linear interpolation works fine for angles as small as 4°. 

For angles smaller than 2° there's a trick available that relies on the following:

sin(2x) = 2sin(x)cos(x)

N(90°-x) = 0 when x < 1.9°

sin(30°) = 1/2

Long story short:

When x<2.0°, N(x) = N(2x) + N(30.0°)

Between 2.0° and 4.0°, a reverse lookup can cause errors greater than 0.05° near 2.5° and near 3.5°.  It's likely negligible, but if you really want, the exact expression for all angles is:

N(x) = N(2x) + N(30°) - N(90°-x).

The expression "N(90°-x)" rolls over from 1 to 2 when x>3.1°.

Extrapolating, x should be treated as 0.0° when N(x)>7043

(As an aside, if your working precision is 0.1°, interpolating the Emergency Almanac for the Sun that comes attached to the N(x) Table becomes much easier!)