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Estimates of galaxy distances based on indicators that are independent of cosmological redshift are fundamental to astrophysics. Researchers use them to establish the extragalactic distance scale, to underpin estimates of the Hubble constant, and to study peculiar velocities induced by gravitational attractions that perturb the motions of galaxies with respect to the "Hubble flow" of universal expansion. In 2006 the NASA/IPAC Extragalactic Database (NED) began making available a comprehensive compilation of redshift-independent extragalactic distance estimates. A decade later, this compendium of distances (NED-D) now contains more than 100,000 individual estimates based on primary and secondary indicators, available for more than 28,000 galaxies, and compiled from over 2000 references in the refereed astronomical literature. This paper describes the methodology, content, and use of NED-D, and addresses challenges to be overcome in compiling such distances. Currently, 75 different distance indicators are in use. We include a figure that facilitates comparison of the indicators with significant numbers of estimates in terms of the minimum, 25th percentile, median, 75th percentile, and maximum distances spanned. Brief descriptions of the indicators, including examples of their use in the database, are given in an appendix.

The Monte Carlo numerical method for obtaining statistical mechanical averages in the petite canonical ensemble has been applied to the two-dimensional triangular lattice-gas model. The Monte Carlo procedure described by Rosenbluth et al. and by Wood and Parker has been extended slightly to include the calculation of the partition function. The results are compared with the exact solutions for the two-dimensional lattice and the agreement is well within the fluctuation displayed by the numerical method. The calculations are found to be relatively insensitive to a change in the pseudo-random number sequence and to display no exceptional behavior in the region of the first-order phase transition for small lattices.

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