58 
the solution becomes impossible; this points to discontinuities in the 
stardensities, (voids in the star masses, influence of distant starclouds) 
which we will not consider at this moment. 
uh 
By applying the above-mentioned formulae, in the following research 
we have tried to determine the shape of our local starsystem. The 
galactic zone between + 20° latitude was divided into 12 sectors 
of nearly 30° longitude. The only sources giving sufficient data 
on the numbers of stars are the Durchmusterung Catalogues; we 
have used the counts of STRATONOFF *), giving the density per square 
degree for fields of 5° square according to the Bonner Durchmusterung 
(to O° decl.), the Südliche Durchmusterung of SCcHÖNFELD (to —20° 
decl.) and the Cape Photographic Durchmusterung. As class 9.1—9.5 
in all these catalogues is incomplete, only the numbers up to 
magnitude 6.5, 8.0 and 9.0 were used in our computations. The 
details of the extensive researches that were necessary to find the 
relation between these empirical scales and the photometric magni- 
tudes will be given elsewhere; the resulting limiting magnitudes are 
for the different zones of declination of the N. hemisphere: 
Decl. 0°—10° 10°—20° 20° — 40° 40°—60° 60°—80° 80°—90° 
6.55DM =6.37 6.69 6.72 6.75 6.75 6.62 
8105) ac MOT BS 0 28.26 A 85204 Bios MED Lak 0005 (D==15) 
Bast oss dors | Vous. ota) "O24 625 Kr 0401215) 
For the Südliche Durchmusterung we found 
6 48 —0.014(D—15); 8.14—0,018 (D—15) ; 9.39— 0.025 (D—15) 
where D denotes the number of stars per square degree up to 9.5 
(not up to 10). To reduce these magnitudes to the scale, adopted 
in our computations, viz. the scale of Groningen Public. 18, corrected 
by the values, given by Van Rayn in Groningen Publications 27 
(G.P. 18 ce), we must still add to our results the values — 0,17, 
— 0,08, + 0,02 for the three limiting magnitudes. For the C.P.D. 
for the galactic zone the values 
5,76 7,86 and 9,46 (scale G.P. 18 c.), 
were adopted; but these are much more uncertain than for the 
catalogues of Bonn. 
From these N(m), the number of stars from the brightest to the 
limiting magnitude m, the numbers A (m), running nearly parallel 
1) W. SrRATONOFF. Etudes sur la structure de l’univers. Publications de Tach- 
kent. Nr. 2 et 3. (1900, 1901). 
