74 
ASTRONOMY: A. 0. LEUSCHNER 
The close commensurability of the mean motion with twice Jupiter's mean 
motion made it apparent that a satisfactory determination of the perturba- 
tions of this planet by Hansen's method was entirely out of the question, in 
fact impossible. After the revision of von Zeipel's tables for the Hecuba 
group, to which I have already made reference, this, our most difficult and 
striking case of the Hecuba group, was selected as a test case for our tables. 
After applying our perturbations, the least squares correction was based on 
ten oppositions from 1894 to 1907 with eminently satisfactory results, not 
only for these thirteen years but also for the 1877 oppositions, seventeen years 
before, and for a subsequent opposition in 1911. According to Miss Sophia 
H. Levy's computations, the perturbations of this planet are the largest we 
have experienced, the coefficient of the largest term in the perturbation of the 
mean anomaly reaching nearly 30°. For the 1877 opposition the perburba- 
tion in the mean anomaly is 24°. These amounts generally produce double 
the displacement in geocentric position at opposition and yet an approximate 
right ascension and declination published by Wolf in 1911 is represented by 
our theory to within 4' of arc in right ascension and less than 1' in declina- 
tion. A further very slight revision of the theory is contemplated before 
publication to include some terms of higher degree depending on the very 
large eccentricity of 20°. This revision will make this representation still 
more satisfactory, although the larger part of all outstanding differences is 
due to perturbations by Saturn. 
Even then our representation is much closer than was to be expected. 
Another approximate position has recently been published by Wolf for Jan- 
uary 16, 1914. This is equally well represented, showing that the theory 
has definitely been verified by observation. The importance of this result 
lies in the fact, that with the most difficult case of the Hecuba type con- 
quered, the revised tables of von Zeipel now provide a ready and accurate 
means of representing the motions of all planets of this type at present known. 
Confirmation of this statement is afforded by our subsequent work on (104) 
Clymene, (106) Dione, and (168) Sybilla of the same group with mean motions 
of 634", 629'', and 572". 
But this planet has another striking significance. To prevent its loss, 
pending the computation of its theory under the Watson Fund, Berberich of 
the Kgl. Rechensinstitut, Berlin, has applied the laborious process of special 
perturbations by Jupiter and Saturn for the determination of osculating ele- 
ments. The extent of his unpublished work was not known to me, until 
some years ago I addressed an inquiry to Berlin in regard to any unpublished 
data, particularly the Saturn perturbations. 
Among the unpublished data are osculating elements for epochs in 1877, 
1892 and from then on for practically every year until 1910. According to 
these elements the mean motion in 1877 was 617".7. In 1892, fourteen and 
a half years later, it was 614". For three and a half years it oscillated about 
this figure and then in another fourteen and a half years to 1910 gradually 
