  We present theoretically-established values of the CO-to-H2 and C-to-H2
conversion factors that may be used to estimate the gas masses of external
galaxies. We consider four distinct galaxy types, represented by M51, NGC 6946,
M82 and SMC N27. The physical parameters that best represent the conditions
within the molecular clouds in each of the galaxy types are estimated using a
chi^2 analysis of several observed atomic fine structure and CO rotational
lines. This analysis is explored over a wide range of density, radiation field,
extinction, and other relevant parameters. Using these estimated physical
conditions in methods that we have previously established, CO-to-H2 conversion
factors are then computed for CO transitions up to J=9-8. For the conventional
CO(1-0) transition, the computed conversion factor varies significantly below
and above the canonical value for the Milky Way in the four galaxy types
considered. Since atomic carbon emission is now frequently used as a probe of
external galaxies, we also present, for the first time, the C-to-H2 conversion
factor for this emission in the four galaxy types considered.
