The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field. II.

In this paper the theory recently developed by the writer for the analysis of counts of the extra- galactic nebulae in terms of a fluctuating density field has been applied to the counts obtained by Shane and Wirtanen at the Lick Observatory. The observational data have been reduced to the forms required for this analysis, and the corresponding theoretical functions have been obtained for several sets of values for the parameters involved. The comparison of the theory with the observations indicates that the effects of fluctuations in the absorption within our own Galaxy can be neglected in a first approximation; further, the theoretical expectations for the case in which there is a dispersion of 2 mag. in the absolute magnitudes of the nebulae are found to be in best accord with the observations. The mean square of the deviations in the space density of the nebulae from the mean is found to be about twenty-five times the square of the mean density. The value for the microscale, ro, characterixing the "eddy" distribution of the nebulae and the value for the mean density of the nebulae in space, p, are both dependent upon the particular values used for the limiting apparent magnitude of the counts, rn , the mean absolute magnitude of the nebulae, M1, and the optical half-thickness of the galaxy, ri/1 for given values of these quantities it is shown how the corresponding values of r and p can be deduced on the basis of the theory. From a straightforward analysis of the counts as they are given, the value ri/I = 0.76 is obtained. If this value is taken as that which is appropriate to the observational material and if the best available values for rn'1 and M1 are used, it is found that r = 3.0 X 106 parsecs and p = 6.0 X 10-19 nebulae per cubic parsec.