  Solid particles with the composition of interstellar dust and power-law size
distribution dn/da propto a^{-p} for a < a_max with a_{max} > 3 lambda and 3 <
p < 4 will have submm opacity spectral index beta(lambda) = dln(kappa)/dln(nu)
approx (p-3) beta_{ism}, where beta_{ism} approx 1.7 is the opacity spectral
index of interstellar dust material in the Rayleigh limit. For the power-law
index p approx 3.5 that characterizes interstellar dust, and that appears
likely for particles growing by agglomeration in protoplanetary disks, grain
growth to sizes a > 3 mm will result in beta(1 mm) < ~1. Grain growth can
naturally account for beta approx 1 observed for protoplanetary disks, provided
that a_{max} > ~ 3 lambda.
