(759) 
relations and the results of GriBBs’ expressions for this example I 
borrow from P. Harzer’s Bestimmung und Verbesserung der Bahnen von 
Himmelskirpern nach drei Beobachtungen p. 8. *) 
The heliocentric motion of the planet Pallas was from the 1st to 
the 3¢ observation 22°33’. 
logt, = 9.8362703 logt, = 0.0854631 logt, = 9.7255594 
log 7, = 03630906 logr, = 0.5507163 log r, = 0.3369508 
These values for log r are also taken from Harzer and differ a 
little from those according to Gauss. 
Results for log n, and for log n, 
GIBBS 9.7572961 GrBBs 9.6480108 
formula IT 9.7572928 formula I 9.6480167 
rigorous 9.7572923 rigorous 9.6480201. 
Formula III yields: log 2298907237: 
n, 
With the given logarithms agree the following values: 
n, Ns eesti: 
rigorous = 0.5718654 0.4446518 07775491 
Gak 0.5718641 f.l 04446484 f. II] 0.7775418 
differences _ — 0.0000007 + 0.00000384 + 0.0000075 
From the expressions given for the remainders of the 5 order 
I calculated that they are in the ratio of — 9, + 72 and + 140. If we 
compare these numbers. with the residuals, it appears that for our 
example they would vanish to the 7" decimal if we succeeded 
in including also the terms of the 5 order in the expressions. 
As to the calculation of the quantities A and 6 dependent on 
Tt, and t,, I remark that it may be performed quickly if we modify 
these forms in the following way : 
ve cae G Eaves =] aes hes Se Fg (stat 
ONT raze I) (EA ea i 
mn BEATE) maa EE ret) 
Az = — 56 = ES =) 136} == 45 = eee ee) 
Moe BEE) syns Bll ated 
dn) meme ere 
mmh) mri oA) 
1) Publication der Sternwarte in Kiel, XI. 
