Studies in Stellar Statistics 



37 



C, 



^4 



BD 



1st Coir. 



2(t Corr. 



■III 



Ai:m) 



BD 



1st Corr. 



2(1 Corr. 



m 



A[m) 



5"' .9 



9 .2 

 c dit C. 

 13 .89 



+ 0"'.05 

 -|- 0 .05 



— Ü^.OS 

 + 0 .37 



5"'. 87 

 9 .62 



13 .89 



52 

 3 289 



74 045 



5"'.9 

 9 .2 

 c du C. 

 13 .89 



+ 0"'.05 

 + 0 .05 



— O'-'.Sl 

 -f- 0 .04 



5"'.64 

 9 .29 



13 .89 



56 

 8180 



716 832 



The » second corr.» is taken from tab. 3. The correction for 9.2 is the mean 

 of the corrections for 9.1, 9.2 and 9.3. 



The equation (66) for determining N hence runs as follows: 



(66*; 



0 = 4.27 Err 1 



104' 



~N 



In 



8.02 Err 1 



In 



6578\ , ^ /, 148 090 

 + 3.75 Err 1 — 



N 



/ 112\ „ ^ /, 16 360\ , „ /, 1 433 664\ 

 (60**) 0 = 4 60 Err 1 1 — — 8.2.^ Err ^1 ^ j + 3.65 Err ( 1 ^ j. 



Giving to N successively the values 10^ 10^ 10^ 10^ 10" etc. we find that 

 these equations probably have two roots. The higher root, exceeding 10 '^ — if 

 it exists — cannot be reached with the help of our table of the Error-function. 

 As to the lower root it is found that it lies, for C,, between 10^ and lO*' and for 

 .between 10^ and 10^ Diminishing the interval ten times we obtain the following 

 values of the right member of the equations (66*) and (66**) which we denote 

 with f{N) 



N 10" 

 f{N) — 3.170 



10^ 10» 10" 10" lO'i 



+ 0.48 + 0.67 + 0.91 + 0.86 + 0.69 



10" 10'» 10" 



- 0.49 + 0.59 (+ 0.43) 



5.10^ 6.10^ 7.10' 8.10' 9.10' 10« 



— 0.261 —0.048 + 0 100 + 0.168 + 0.189 + 0.196 



N W 2.10' 4jo' 7.10' 10« 



/(J\^) — 0.51 — 0.14 + 0.11 + 0.19 + 0.25 



Through graphical interpolation I obtained from these values of f{N) : 

 In (7, : N= 630 000 and in (7, : N= 30 000 000. 



With these values of IV the corresponding values of k and were easily 

 obtained from (65*). I give here all the details of the calculations for : 

 2A, : iV= 0.000 165; Err(l — : iV) = + 3.769 5.87«/ = a.'— 1.890 ■.• x = + 5.669 



2J : 0.010 439 Err (1 — 2^2 ■ N) = ^ 2.565 



X- 



9.62 y ^ 



X- 



■3.096 X' .-= + 5.661 



2^3: iV= 0.235 019 Err(i — 2A3:i\^)= + 1.188 = a;— 13.89 = X — 4.470 x = + 5.658 

 The value of ?/, obtained from the first and the third equation is // = + 0.3218. 

 The corresponding values of x are given in the last column. The agreement be- 



