xlvi Mr. Pickering’s Eulogy on 
In the same chapter, he notices the method adopted by La Place, 
of combining the observations, with a view to the greatest accuracy 
in the theory of a comet; and he considers the method to be liable 
to some objections. He then, in a subsequent note, proposes a 
valuable improvement in the mode of correcting the elements by a 
method of his own. * 
We have, in the same Book (ch. 6, § 49), an example of his own 
skill in finding the last terms of the series there in question, by 
an original method, which he had discovered and used before he 
had ever seen the work of La Place, where the same method is 
adopted. 
In the subsequent chapter of the same Book, he considers the 
great and interesting question of the permanency of the Solar System, 
which La Place believed he had there fully established. Dr. Bow- 
ditch, however, found it necessary to make a very important limita- 
tion in La Place’s celebrated equations of condition, from which that 
author had inferred, that the orbits of the planets will for ever remain 
nearly circular and in the same plane; and he then shows, that 
however just the inference may be, that the orbits of the three exte- 
rior planets, Jupiter, Saturn, and Uranus, can never be very eccen- 
trical or deviate much from the same plane, yet it does not follow, 
from the same equations, that the orbits of the smaller planets will 
always be nearly circular and in the plane of the ecliptic; for the 
orbits of these might be very eccentric, and even parabolic, and the 
planes of them be perpendicular to each other, and yet the equation 
be satisfied. Dr. Bowditch had discussed this point many years 
before, and published a paper upon it in the Memoirs of the Ameri- 
ean Academy, which I have already mentioned. t 
* Bowditch’s La Place, Vol. I. pp. 463, 470. 
f Mem. Amer. Acad. Vol. IV. p. 74. 
