With reference to theory published earlier, formulas are given for the estimation of (i) abundances of morphological types among field galaxies, (ii) of selection probabilities, and (iii) of ‘space luminosity functions’. Strictly, the theory applies to ‘homogeneous classes’ of galaxies. This term designates a category of galaxies, say C, so finely defined that the probability, say Φ(m | C), that a galaxy of category C will be included in the catalogue depends on its photographic apparent magnitude m and on nothing else. The practical use of the theory is illustrated on data in the HMS Catalogue. It appears that certain combinations of the Hubble morphological types satisfy the definition of a homogeneous class. Such, for example, is the case for combinations of ellipticals E0–E3 and, separately, of spirals Sc, Scp, SBc. However, the combination of these two categories is not a homogeneous class.
In order to validate the theory empirically, calculations were performed to predict the abundances of eight combinations of morphological types among cluster galaxies listed in the HMS Catalogue, each combination being treated as a distinct homogeneous class. Additional hypotheses underlying these calculations are: (a) abundances of morphological types, (b) luminosity functions of these types, and (c) selection probabilities for cluster galaxies coincide with those for field galaxies. A comparison with the observations, reaching the value of z = 0.07, is satisfactory. This tends to validate the combination of formulas (i), (ii), (iii) with the additional hypotheses (a), (b) and (c). Incidentally, the result tends to support the steady state cosmology.