709 
if the small density is caused by absorbing matter, the screen cannot 
be at a great distance, say not more than 200 or 300 parsecs at 
most.” (l.c. page 6). However, as the P. M. of the stars up to the 
9th magnitude in the dark regions are found to be no higher than 
elsewhere, so that no larger average distance is pointed out, this 
conclusion again becomes uncertain. For the present investigation, 
which proposes to ascertain more accurately the distance of these 
absorbing nebulae, the chart of star-counts adjoined to their treatise 
proved to be most useful. 
§ 2. In order to deduce from the star-densities the distance of 
an absorbing nebula, we must first theoretically investigate what is 
the influence of an absorbing screen on the number of stars of 
different magnitude. We suppose that the luminosity-function is 
known according to the formula of Kaprryn; for the logarithm of 
the star-density as function of the distance we likewise, according 
to the empirical data, assume a quadratic formula. We call 1 the 
magnitude, M/ the absolute magnitude of the stars, and introduce as 
modulus of the distance o —= 5 logr, where 9 =O for 7=0'1 is 
taken’): then 
1 1 
log p (M) = Const — —(M—M,)’ log A (e) = Const — ree)" 
at 
The number of stars of magnitude mm will be 
ys a 0,6 9 Se (m—My—p)? Aa 0,6 p — ED (m— My —p)? SRA ip 
A(m) =i A (o) 10 at do = fio a gr do 
1 
or log A (m) = Const — — pn — (0, + M, + 0,38°)} 
a? + B? 
| 1 
For the luminosity-function = eS ae and M,—9 was 
a 
assumed. For the zone between 6 = 20° and 40°, in which the 
Taurus-regions are situated, the following formula was deduced from 
the numbers of van RHIJN 
1 
log A(m) = Const +-0,630 m — 0,0118 m?= Const — ae (m— 27)? 
which is met by the values «*-+ 6? = 86, fp" —= 52, M,+ 0, = 11, 
o,— 2. These values will be used in the following calculations. 
If at the distance o, there is a screen, absorbing ¢ magnitudes, 
NS 1 
1) If we call absolute magnitude M the magnitude for zr =1.”"0, all p in this 
article should be increased by 5 and all M diminished by the same number. 
46* 
