Beyond 12.0 mag. the lists quickly lose their aspect of completeness and cannot be used for the present purpose. There are available, however, the counts by Fath[24] of nebulae found on plates of Selected Areas made with the 60-inch reflector at Mount Wilson. The exposures were uniformly 60 minutes on fast plates and cover the Areas in the northern sky down to and including the –15° zone. The limiting photographic magnitudes for stars average about 18.5. The counts have been carefully revised by Seares[25] and are the basis for his estimate of 300,000 nebulae in the entire sky down to this limit.
Approximate limiting total magnitudes for the nebulae in two of the richest fields, S.A. 56 and 80, have been determined from extra-focal exposures with the 100-inch reflector. The results are 17.7 in each case, and this, corrected by the normal color-index of such objects, gives a limiting visual magnitude of about 16.7, which can be used for comparison with the counts of the brighter nebulae.
The various data are collected in [Table XVIII], where the observed numbers of extra-galactic nebulae to different limits of visual magnitude are compared with those computed on the assumption of uniform distribution of objects having a constant absolute luminosity. The formula used for the computation is
| (10) |
where the constant is the value of log N for mT = 0. The value —4.45 is found to fit the observational data fairly well.
The agreement between the observed and computed log N over a range of more than 8 mag. is consistent with the double assumption of uniform luminosity and uniform distribution or, more generally, indicates that the density function is independent of the distance.
The systematic decrease in the residuals O – C with decreasing luminosity is probably within the observational errors, but it may also be explained as due to a clustering of nebulae in the vicinity of the galactic system. The cluster in Virgo alone accounts for an appreciable part. This is a second-order effect in the distribution, however, and will be discussed at length in a later paper.
TABLE XVIII
Numbers of Nebulae to Various Limits
| mT | log N* | O – C | log D† | |
|---|---|---|---|---|
| O | C | |||
| 8.5 | 0.85 | 0.65 | +0.20 | 5.74 |
| 9.0 | 1.08 | 0.95 | .13 | 5.84 |
| 9.5 | 1.45 | 1.25 | .20 | 5.94 |
| 10.0 | 1.73 | 1.55 | .18 | 6.04 |
| 10.5 | 1.95 | 1.85 | .10 | 6.14 |
| 11.0 | 2.17 | 2.15 | + .02 | 6.24 |
| 11.5 | 2.43 | 2.45 | – .02 | 6.34 |
| 12.0 | 2.70 | 2.75 | .05 | 6.44 |
| 16.7 | 5.48 | 5.57 | –0.09 | 7.38 |
| (18.0) | (6.35) | (7.64) | ||
* Log N = 0.6 mT – 4.45.