710 
then from the more remote stars we do not see those with 1/=m—e, 
but those with M= m—e—ge as stars of the magnitude m. The 
number of stars of this magnitude A’, will be 
1 ee 1 
0,6¢ — — (m—M,—p)* - 0,62 — —(m—M,—<«- Vy 
Amp tap tu % ‘ ig + f A (o) 10 ER ; ‘ de. 
These two integrals, taken between the limits + o , represent the 
numbers A, and A. If now we put 
(a? HB), — 0,3 at B* — 07 0,— B (Mo) 
ap Vat tf ap 
(a? + 8) 9, — 0,8 B" — 00, — B (m—M,—€) _ 
ap Va? +B? | oen 
1 
Ti oo 
1 1 : 
and a= [10 i= Y, D= [lof HS 
Valoge Valoge 
— 00 
Tg 
then 
Am = Yi Am + Ya Ame 
While the number 4,, is obtained from the combination of stars 
at all distances, by means of integration between oo of a function, 
proceeding according to the probability-curve, the number A’, is 
found from two such curves, belonging to 7 and m—e; from the 
first is taken a part between — oo and w, indicated by the fraction 
y, (the stars in front of the absorbing screen); of the second the 
part between x, and + oo, indicated by the fraction 7, (the stars 
behind the nebula). From the above numbers we find 
#2, = 0,220, — 1,53 — 0,132 (m—9) e,= «, + 0,132¢, 
By means of these formulae and a list of values of Am, corre- 
sponding to it, the values of A’, for different suppositions concerning 
o, and e were computed. To compare them more easily with the 
results of starcounts, we calculated from the A’, the Nien the 
total numbers of stars brighter than m + 3, and these were compared 
with the normal number Ns. The values log N—loq N', the 
logarithmic defect in starnumber, then forms the best measure for 
the influence of the absorbing nebula. These values have been united 
in the following table. 
From these values, which are graphically represented in our figure 
it appears: 
a. The influence of the absorption extends, slowly varying, over 
almost all magnitudes that are open to our investigation. This is 
especially a result of the great spreading of the luminosity-function. 
