194 
hardly mention that I commenced the calculations for it with little 
hope of success. 
For the reduction to apparent place I found: 
in «a: +5s.112 in d: + 9."75 
and as correction for parallax : 
in a: — 08.247 in d: + 0".72 
The observed apparent place thus becomes: 
1906 Dec. 7.273046 : a = 3°38" 55.275 d = 4 51°17'3".17 
Time of aberration: 0.011279 day. 
This observation has further been treated in exactly the same way 
as the three preceding ones in my communication of Nov. 1906. 
As starting-elements I again adopted those given in my paper of 
January 1906, p. 677, after increasing M with 50". I obtained as 
differences Obs.— Comp. : 
1906 Dec. 7.27: Aa=+ 18.065 A d= - 15".53 
For the derivation of the differential quotients of @ and d with 
respect to M, 7 and §% the computed places were then derived 1. with 
AM —-+ 40" (instead of +50"); 2. with A= +10"; 3. with 
AQ=+10". Thus this fourth place yielded the two following 
equations of condition: 
From a: + 0.2288 AM — 0.0372 Ai— 0.0114 AN =+ 18.065 
From d: + 0.426 AM+1.374 Ai4+ 0.083 AS =+ 15".58. 
The first equation was again multiplied by 15 cos d and just as 
ASb ya 
before sae was introduced as unknown quantity instead of Af; 
moreover I gave half weight to both equations. Thus I obtained 2 
new equations, in addition to the former six, given in my paper 
Researches IV (Nov. 1906): 
from the R. A.: 
A 
0.18128 AM + 9.39236, At + 9.87872, a = 0.84917 
from the declination : 
9.47889 AM + 9.98747 Ai + 9.36799 a — 1.04067 
in which all co-efficients are logarithmic. 
From the total of 8 equations of condition there follow the normal 
equations: 
