Distribution of Nebulae in Depth
The large-scale uniformity emerges from all surveys to faint limits, when local obscuration has been corrected and the limits have been carefully determined. Each survey can be specified in numerical terms. To a particular limit of apparent faintness, say to stellar magnitude m, there are, on the average, a certain number of nebulae per square degree; say Nm.
This method of describing the data leads to the second problem of nebular distribution, namely, the distribution in depth. When several surveys are made to different limits of apparent faintness, each survey, although it represents the examination of many thousands of nebulae and requires months or years for its completion, may be summarized by the single symbol, Nm. The symbol may be interpreted in various, equivalent ways, because the limiting faintness, m, represents a specific distance and a definite volume of space. For instance, we may compare the various surveys in order to determine how the numbers of nebulae increase with the volumes of space they occupy. If the numbers are strictly proportional to the volumes, and N = V × constant, we know that the distribution of nebulae in depth is uniform. If the factor of proportionality is not constant, we know that the distribution departs from uniformity, and the departures become very significant features of our sample.
The first counts were made hurriedly - a rapid reconnaissance for the purpose of planning the accurate surveys that followed. The result of the surveys will be discussed later, after certain corrections required by red-shifts in nebular spectra have been explained. At the moment we will consider only the preliminary counts. They demonstrated that the large-scale distribution in depth is roughly uniform. Within the uncertainties of the data, the numbers of nebulae were found to be a constant multiple of the volumes of space they occupy. There was no evidence of a thinning out with distance. The observable region, our sample of the universe, is approximately homogeneous as well as isotropic; everywhere and in all directions, it is very much the same.