The scale of distance, as previously mentioned, is the essential clue to the. interpretation of explorations in the realm of the nebulae. The significance of surveys, for instance, depends upon the characteristics of the average, or normal, nebula. From a study of the relative frequencies of various types we know that the average nebula is an intermediate type spiral. We know, further, that it is about 85 million times as bright as the sun, and perhaps 1,000 million times as massive. The conspicuous portion, called the main body, is a highly flattened, lens-shaped figure, about 8,000 light-years in diameter. Very faint exterior regions can be traced by delicate photometric methods out to a diameter of about double that of the main body. The nebula is a stellar system whose contents are rather similar to those of the galactic system. The very brightest stars are blue super-giants which are most numerous in the outer regions of the spiral arms. The integrated light from the main body is very similar to sunlight.
Surveys, in general, deal with nebulae so distant that practically all their characteristics are lost from view except their total luminosities. The surviving characteristic assumes unusual importance, and requires further discussion involving a rather technical point. Nebulae in a given volume of space, or those in a great cluster, average about 85 million times as bright as the sun. However, nebulae of a given apparent faintness average about 2.5 times brighter, or about 210 million suns. This curious relation arises from the dispersion in luminosities together with the more or less uniform distribution of nebulae. A group of nebulae which appear equally faint contains giants, normal nebulae, and dwarfs. The giants are more distant than the dwarfs, and, consequently, are scattered through a larger volume of space. Therefore, the giants greatly outnumber the dwarfs, and the average for the entire group is evidently brighter than normal.
In either case - nebulae in a given volume of space or nebulae of a given apparent faintness - the percentage deviations from the mean luminosity are scattered at random, and the numerical value of the dispersion is known. Therefore, when we assume that all the nebulae have the same average luminosity, we can assign the numerical values of the uncertainties. In the case of a single nebula the chances are about equal that the error is greater than, or less than, 50 per cent. For the mean of groups of nebulae the probable. error diminishes as the size of the group increases. The probable error in the mean luminosity of a group of a hundred nebulae, selected at random, is about 5 per cent.
These examples illustrate one of the advantages of statistical methods which deal with large numbers of individual objects. Accidental errors, random deviations from normal, tend to cancel out. The major source of uncertainty in the results arises from the possibility of systematic errors. In the surveys, for instance, the effects of dispersion in luminosities can be accurately calculated; relative distances of nebulae are known rather precisely. Consequently, results which depend upon relative distances only, and which are derived from logarithms of distances, are quite reliable. Uncertainties arise when actual distances are introduced, because the unit of distance may be wrong. The most likely source of error, as previously mentioned, is the step from Cepheids to brightest stars. A careful examination of this and other possible sources of error suggests that the unit of distance is probably correct to within 25 per cent. However, the main results of the surveys, and those that will be discussed in these lectures, would not be materially altered if the unit of distance were in error by as much as 50 per cent.