The orbit of 6 Bootis computed by me in 1877 (A.N.
2 129) represented the observed angles up to 1888, but ceased to represent the distances already some time before that year. It now appears that it is possible to represent the former by orbits with very different periods, with the exception that the first two angles noted by the elder Herschel are not represented by any orbit with a period as short as I 24 years. The orbit of Bootis like the orbit of 7 Cassiopeiae is therefore fixed mainly by the measured distances.
The elements of the latter ( A . N. 3743) were calculated from Band 163. three complete observations after Klinkerfues's method, which method proved to be so very difficult of application (unless for merely adjusting an orbit the elements of which are already known with considerable accuracy) that I determined to make a trial of Thiele's method. This turned out to be so convenient, that I can recommend its use, at least in case of very eccentric orbits, which have been only partly described by the companion.
The following equations were originally given by Encke for the areas of the segments in the apparent ellipse: -3 0 -8, -100 -0.1 +o. I -0.3 +r.3 -0.3 -0.2 -0.2 +1.2 -2.5 +o. I -1.0 -0.1 -0.6 -1.6 +0.3 -0.7 -0.6 0.0 + 1.2 + 0.3 + 1 . 5