6 A NEW METHOD OF DETERMINING 
Stérungen der kleinen Planeten, undoubtedly marks a great advance in the determina- 
tion of the general perturbations of the heavenly bodies. 
The value of the work is greatly enhanced by an application of the method to a 
numerical example in which are given the perturbations of Egeria produced by the 
action of Jupiter, Mars, and Saturn. And yet, notwithstanding the many exceptional 
features of the work commending it to attention, astronomers seem to have been de- 
terred by the refined analysis and laborious computations from anything like a general 
use of the method; and they still adhere to the method of special perturbations devel- 
oped by Lacraner. HaANsEN himself seems to have felt the force of the objections 
to his method, since in a posthumous memoir published in 1875, entitled Ueber die 
Stérungen der grossen Planeten, insbesondere des Jupiters, his former positive views 
relative to the convergence of series, and the proper angles to be used in the argu- 
ments, are greatly modified. 
Hint, in his work, A New Theory of Jupiter and Saturn, forming Vol. IV of 
the Astronomical Papers of the American Ephemeris, has employed HAwnsEn’s 
method in a modified form. In this work the author has given formule and devel- 
opments of great utility when applied to calculations relating to the minor planets, and 
free use has been made of them in the present treatise. With respect to modifica- 
tions in HAwsen’s original method made by that author himself, by Hit and others, 
it is to be noted that they have been made mainly, if not entirely, with reference to 
their employment in finding the general perturbations of the major planets. 
The first use made of the method here given was for the purpose of comparing the 
values of the reciprocal of the distance and its odd powers as determined by the pro- 
cess of this paper, with the same quantities as derived according to HANSEN’s 
method. Upon comparison of the results it was found that the agreement was prac- 
tically complete. ‘To illustrate the application of his formule, Hansen used Egeria 
whose eccentricity is comparatively small, being about ;4;. The planet first chosen 
to test the method of this paper has an eccentricity of nearly +. And although 
the eccentricity in the latter planet was considerably larger, the convergence of the 
series in both methods was practically the same. It was then decided to test the 
adaptability of the method to the remaining steps of the problem, and the result of the 
work has been the preparation of the present paper. 
HAnsEN first expresses the odd powers of the reciprocal of the distance between 
the planets in series in which the angles employed are both eccentric anomalies. He 
then transforms the series into others in which one of the angles is the mean anomaly 
of the disturbing body. He makes still another transformation of his series so as to 
be able to integrate them. 
