ASTRONOMY: A. 0. LEU SC FINER 
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set of directions for the application of von Zeipel's theory for the Hecuba 
Group and has illustrated the same with full numerical details for his example, 
10 Hygiea, for the guidance of computers. 
The work to which I have just referred serves to indicate how the original 
program of routine computation to the first order of mass with respect to 
Jupiter by Hansen's established formulae was completely changed to include 
extensive theoretical investigations. 
Although Hansen's and Bohlin's methods — the latter extended by von 
Zeipel and ourselves, and also by D. F. Wilson, to provide tables for groups 
1/2, and 5/2 in addition to group 1/3 — were entirely sufficient to master the 
Watson planets, for which, however, the group 5/2 was not applied, an ex- 
tensive theoretical analysis has also been made of Brendel's recent methods 
based on the researches of Gylden. These methods appeared while our work 
was well under way. In passing I might state that all this theoretical work 
was done independently of the Watson funds. 
Aside from these purely theoretical problems the Watson work naturally 
falls under two heads: 
(1) The investigation of the causes of the failure of the earlier work as 
referred to by Newcomb. 
(2) The application of the most suitable methods to the planets on which 
work had not been undertaken. 
In addition the ultimate investigation of the cause of the loss of (132) 
Aethra was constantly kept in mind. 
Under the first head I wish to make especial reference to the work done by 
Eichelberger on (93) Minerva. Professor Newcomb naturally suspected an 
error of computation on account of an apparent motion of the node indicated 
by the outstanding discrepancies in the representation of the observations. 
Newcomb himself attempted to correct Eichelberger's investigations by 
further computations at Washington. But later I found the whole trouble 
to be due to the fact that too much had been expected from first order per- 
turbations by Jupiter, that is, perturbations involving only the first power 
of the mass. I suggested that a repetition of the work on Minerva to only 
four or five places would accomplish as much as the previous investigation to 
seven figures and that the residuals of the observations would reveal the same 
implied motion of the node; that the latter was of a higher order; and that it 
could be determined empirically either from our own or Eichelberger's out- 
standing residuals. Professor Newcomb welcomed this test and all of Eichel- 
berger's ■ work was repeated under the plan proposed, but on the basis of 
mean instead of Eichelberger's osculating elements and with the mean instead 
of the eccentric anomaly as independent variable, with the result that the 
suspected cause of the trouble was fully substantiated. The outstanding 
discrepancies which were really negligible under the original program but 
appeared large because of the great accuracy with which Eichelberger had 
computed, were then removed by an empirical determination of the still 
remaining motion of the node. 
