The autocorrelation function of the North Pole dust

The angular scales on which local interstellar dust is distributed are so far rather unknown as are the geometrical shapes of the dust features. From the about 5000 color excesses resulting from a north polar survey with 4 to 5 stars per square degree the two-point autocorrelation function is derived for separations ranging from 10 min to 3 deg. For intercloud lines of sight, -0.020 is less than E(b - y) is less than -0.010 mag, the average cross products (E sub 1 x E sub 2)(sub theta) show no variation with separation theta(1,2) whereas products of cloud column densities, 0.030 is less than E(b - y) is less than 0.040 mag, seem to prefer discrete separations either less than 20 min, around 75 min, or finally at about 150 min. Surprisingly the two point autocorrelation function omega(sub E) = E(sub 1) x E(sub 2)/E squared - 1 equals 0 except for any separation except theta = 0. Omega(sub E)(theta)'s absence of variation is unexpected because omega(sub H)(theta) is known to vary exponentially above b = 40 deg for separations less than 3 deg. Atomic hydrogen and dust may thus not be entirely mixed or the moments (E sub 1 x E sub 2)(sub theta) may not characterize the dust distribution.