59 
with them, may be got by the relation A om) = N (m). 
Putting . 
N(m) = 10*+Amtrm we get A (m) = "/loge (B + 2ym) LOstAmtm*, ov 
log A (m) =a + Bm + ym? — log loge + log 3 + log (: + a mn) thus 
2y? 
B 
2 
a= a — logy loge + log B; b= B+ loge: c= — y+ log e. 
For the mean magnitude m, was taken 8.0. 
Further data are given by the Selected Areas of Kaprryn; for 
each of the 6 Northern sectors the mean was taken of all selected 
areas lying in it. The numbers per half magnitude from 11,0 to 14,5 
‚(for the greater part after the counts of van RHyN, kindly commu- 
nicated to me), were doubled in order to represent the values A (m) 
for m=11,25 to 14,25. They could be represented by linear 
formulae without perceptible curvature. In these formulae /og A (m’) 
=a’ + b’ (m’—12,75) the m’ denote photographic magnitudes; as 
for these faint classes the reduction of photographic to visual magnitude 
may be represented by m—m’ = —0,62 —0.05 (m’—12,75), we have 
log A(m) =a + b(m—12,13), where aa’, b=*%,, 8. 
LE: 
Tbe results of the Durchmusterung catalogues are collected in the 
next table, where the first column gives the mean galactic longitude 
of each sector and ” the number of fields of STRATONOFF of 23 square 
degrees on the average. 
long. n a b c 0, h k l 
15° 49 0.236 0.478 + 0.0086 12.23 9.812 —0.122 +0.011 
45 57 351 510 + 0059 12.70 857 — 090 + 007 
75 48 ale 480 + O171 12.26 971 — 120 + 034 
105 52 198 475 + 0121 12.19 810 — 125 + 018 
135 56 147 446 + 0212 11.77 932 — 154 + 055 
165 49 182 548 — 0126 13.29 540 — 052 — 009 
190 38 246 556 — 0246 13.36 548 — 044 — 014 
225) 68: 303 "488 ‚—, 0017, 12.38 | 193) —~ “tia a. 002 
255 48 264 481 + 0030 12 „27 793 — 119 + 003 
285 52 272 503 + 0032 12.59 9.767 — 097 + 004 
315 68 277 440 + 0271 11.68 0.204 — 160 + 127 
350 37 102 466 + 0049 12.06 9.771 — 134 + 006 
