reduced to the form : 
rat Ts HT Ta 
= (: Tae ZE 
This equation is satisfied by the real places of the objeet when 
we neglect a residual of the 5% order with respect to the intervals 
of time. This signifies little, however, when compared with the 
accuracy of the places calculated after Gipps’ method, which rigo- 
rously satisfy them; for each set of vector corrections A ZP,, 4 ZP, 
and A ZP does not lessen the agreement below the 5' order with 
respect to the intervals of time, provided they satisfy the condition 
NZE AZ AZE 
1 T 8 2 
Ts, 2 
and are not below the 38'¢ order with respect to those intervals. 
Because in GiBBs’ method the relations 7, and 2, contain errors 
of the 4t" order, it would follow from this that the places computed 
after this method are inaccurate in the 4" order also. But thanks to 
the circumstance that GiBBs’ method includes for n, +, the terms 
of the 4 order in all cases, its results are yet correct in terms of 
the 4% order. 
This special feature of Gipps’ method has been pointed out by 
K. Weiss *). 
In order to obtain for n, and ”, expressions including in all cases 
the 4 order of the intervals of time and containing besides them 
1 1 
only ——=2,, — =, and a I have used the relation derived 
ve 
1 2 3 
i) 1 = 
on p. 754 K,= =O Ker 
Starting from the development 
n= Krt + Kyr? + Krt‘ + K,t° + remainder of the 5 order 
I can make use of the following relations between the coefficients 
k, the quantities z,, z,, 2, and n,. 
NEE en a ec WGC Nes UA a ie ij 
1= K, Ts ir K, Tan =i K, ts Si kK, Ts. zl Hy 
+ 6K,t, + 12K, 7,2 + 20K, t° +f, 
GK. Ie OK ORE ME 
0 = K,z,+ 6K, 
ne 
1) E. Weiss, Ueber die Bestimmung der Bahn eines Himmelskörpers aus drei 
Beobachtungen. Denkschriften der Mathem. Naturw. Classe der Wiener Akademie. 
Bd. LX (1893). 
