  We consider the effect of optical depth of the 2 ^{3}S level on the nebular
recombination spectrum of He I for a spherically symmetric nebula with no
systematic velocity gradients. These calculations, using many improvements in
atomic data, can be used in place of the earlier calculations of Robbins. We
give representative Case B line fluxes for UV, optical, and IR emission lines
over a range of physical conditions: T=5000-20000 K, n_{e}=1-10^{8} cm^{-3},
and tau_{3889}=0-100. A FORTRAN program for calculating emissivities for all
lines arising from quantum levels with n < 11 is also available from the
authors.
  We present a special set of fitting formulae for the physical conditions
relevant to low metallicity extragalactic H II regions: T=12,000-20,000 K,
n_{e}=1-300 cm^{-3}, and tau_{3889} < 2.0. For this range of physical
conditions, the Case B line fluxes of the bright optical lines 4471 A, 5876 A,
and 6678 A, are changed less than 1%, in agreement with previous studies.
However, the 7065 A corrections are much smaller than those calculated by
Izotov & Thuan based on the earlier calculations by Robbins. This means that
the 7065 A line is a better density diagnostic than previously thought. Two
corrections to the fitting functions calculated in our previous work are also
given.
