Whole-sky Statistics of Celestial Objects

The advantages of statistical representations based on only those celestial objects with greatest apparent brightness have been enumerated. The system of observations and results that has been devised can be applied to almost any recognizable category of celestial object. The observable parameters are $${m}_{\nabla}(10),q,\,\bar{M},\,{\sigma} _{M}\,\text{and}\,\bar{b}$$ , representing respectively magnitude of the tenth object, change of number with magnitude, absolute magnitude and its dispersion, and mean galactic latitude. The equations and numerical data are given for conversion of these (in most cases) into the descriptive quantities $${M}_{0},\,\sigma,\,{D}_{0}\,\text{and}\,\gamma$$ , representing respectively the absolute magnitude and its dispersion, the space density and scale height perpendicular to the galactic plane. Some alternatives to $${M}_{0},\,{D}_{0}\,\text{and}\,\gamma $$ are given which are not so sensitive to the evaluation of σ. The mean absorption coefficient and optical thickness of the galaxy must be known. The analysis has been exemplified by application to Wolf-Rayet stars, O stars, flare stars, all stars, white dwarfs, globular clusters, open clusters, extra-galactic nebulae, novae and A stars.