70 
ASTRONOMY: A. O. LEUSCENER 
powers of the eccentricities of the disturbed and disturbing planets and of 
the mutual inclination of their orbit planes. In order to avoid unmanageable 
expressions Bohlin had to confine himself to terms of the second and some- ' 
times third degree in these quantities, while Hansen's method with the aid 
of Bessel's functions for the eccentricities imposes no restrictions in this 
respect. 
Bohlin's method otherwise closely resembles Hansen's in the treatment of 
the perturbations, the only other distinctive feature being that for planets 
with mean motion nearly commensurable with Jupiter's, the perturbations 
are developed by Taylor's theorem in ascending powers of a quantity w which 
depends on the difference between a multiple of a planet's actual mean motion 
and a multiple of Jupiter's so that ultimately series within series progress 
according to powers of the mass of the disturbing body, of the eccentricities 
of the disturbed and disturbing bodies, of the mutual inclination of their 
orbit planes, and of the quantity w. 
Now several of the Watson planets belong to the Hecuba Group or Group 
1/2, having a mean motion of nearly 600" or about twice that of Jupiter, 
and as no theory then existed for this group it was decided to develop the 
theory and tables for this group 1/2 on Bohlin's plan for the group 1/3. But 
owing to the great complexity of the problem and the intricate transforma- 
tions involved it was thought wise first of all to assure ourselves of an exact 
understanding of Bohlin's method by reproducing selected values of his tables 
for the group 1/3. In this we failed in many instances. After much fruit- 
less search for the cause of the discrepancies these were called to the atten- 
tion of Bohlin, who promptly replied that he had become aware of inaccu- 
racies in his theory and tables and that he had already completed a revision 
of his work, sending at the same time advance proof sheets, verifying our 
conclusions. We now felt safe in attacking the mathematical theory of- group 
1/2 and after another year's work on the theory and tables of group 1/2 
preparatory to the application of Bohlin's method to the Watson planets of 
that group, we learned from Bohlin that von Zeipel was engaged in the same 
task. A little later we received von Zeipel's printed tables. These we at 
once compared with our own, many transformations from one to the other 
being necessary on account of the difference of developments used, but to 
our dismay we discovered many disagreements. By correspondence these 
have practically all been cleared up and thanks to the careful system of checks 
adopted in our work we found it unnecessary to change any of our results. 
In some minor respects we still differ, but the expressions on which the num- 
bers in question are based are so complicated that von Zeipel doubts whether 
he can remember how he has obtained his values. We are thus abiding by 
our own results, which have been fully verified as I shall show a little later. 
The mathematical and numerical work involved in the revision of von 
Zeipel's theory has been performed under my direction by Miss Anna Estelle 
Glancy and Miss Sophia H. Levy. The former has also prepared a complete 
