(12) 
Moreover it is a fact that the personal error often varies greatly with 
the angle of position itself, especially when the latter, as is the 
case with Sirius, gradually falls from 90° to 0°, so that the con- 
necting line passes from the horizontal to the vertical position. 
However I did not feel at liberty to pass over the entire question ; 
the indications of systematic differences were often too clear for 
doing so. 
With regard to the last three normal positions I have still to 
remark that to the 24-inch refractor of Lowell Observatory the same 
weight 4 is assigned as to the 36-inch of Mt. Hamilton. The diffe- 
rences A @ have been laid down in the following diagram and have 
been joined by right lines. 
That the remaining errors might vanish as nearly as possible the 
differential relations were derived between the differences in the 
angle of position @ and the several elements. Without difficulty 
we find: 
sin t ‘4 
R\<2 
ee ee an cosi AA + 
7 
cot w + tg w cos? 
a 
r 
: 2 
+ (=) sin Beos i(2— & — eco EA y + ( ) cosicos p A Mo + 
5 
= (=) costcosp(t—T,)Au. 
r 
In this expression 
w indicates the distance from the node, measured in the plane of 
the orbit, 
E the excentric anomaly, 
> the apparent, and 7 the true distance of the companion, 
p the angle of excentricity. 
The epoch Z,, for which M, stands, may be chosen arbitrarily ; I 
bave placed it somewhere in the middle of the period of observation 
namely at 1880.0. 
The equations of errors obtained were treated in the well known 
manner according to the rules of the method of the least squares; 
to make the coefficients less unequal the following substitutions were 
made (logarithmically) : 
2r=06A db; y= OK € VN AE HAES ANS 
pd AS w=0.5 A Mo; n= 0.7 degrees. 
