718 
Separately considered these values represented on our figure by 
crosses, especially if supplemented by the value for 9,4 of field A, 
can well be harmonized. with a curve for o, = 7,5 (in which case 
the decrease of 15m to 16™ is not real). But the result (d) is utterly 
opposed to the result (6); the numbers of stars in the S.A. demon- 
strate, that the defect in stars for 9,4 and 15,9 cannot be about 
equal, cannot have a maximum at 12" and afterwards decline. 
The contradiction does not lie simply in a difference between the 
FRANKLIN-ADAMS plates and the Selected Areas. The S.A. 47 com- 
prises only 1 square degree of strong absorption, in which the counts 
on the F.A. plate give a defect of 0,71, about the same therefore — 
and this is only natural, the limiting magnitude employed, viz. 15,9, 
having been deduced from these Selected Areas themselves. The 
case might be explained by the fact that there is a real difference 
in structure between S.A. 47 and region A on the one side, (the 
small values for A from 6,5 to 9,4 ie. the slight defect in B.D. 
stars would then be considered as real) and the other regions of 
absorption on the other side; that therefore A is caused by another 
nebula at a far greater distance. It may be questioned, however, 
whether the data are accurate enough to allow of such a conclusion. 
The values for the B.D. in A are based on a moderate number of 
stars only; the numbers of stars 12—14 in S.A. 47 are very small, 
so that accidental irregularities in the distribution play a great part; 
and the taking of averages for the F.A. plates from the irregularly 
distributed density-numbers is somewhat uncertain also. This proves 
once more, that as yet we dispose of much too small a number of 
data concerning the star-density for the fainter stars 10™—16™ over 
sufficiently extensive regions. 
Now, according to § 2, the determination of the distance of ab- 
sorbing nebulae depends mainly on the bright stars; the uncertainty 
in the numbers of the weaker magnitudes is of very little importance 
here. It is upon the data of the B.D. therefore that this determina- 
tion must almost exclusively be based. To avoid accidental mistakes, 
we will therefore unite these 8 fields 2 by 2 into groups, in the 
order of the NV’ (15,9). 
Also now the accidental uncertainties still give an irregular course. 
Between the three first groups A—F no marked difference presents 
itself for these magnitudes; therefore these have still been combined 
to a general average, to which the values in the last column apply 
and which are represented in the figure by-dots. The slight depend- 
ence on the absorption e can be taken into account in such a way, 
that corrections are introduced to reduce them to the limiting value 
