REPORT ON ASTRONOMY. 
159 
Pound’s observations of the elongations of Jupiter’s satellites), 
or that given by Bouvard (from the perturbations of Saturn), 
differing little from the other. Now Nicolai stated, that the 
observations of Juno at 15 oppositions required an increase of 
about gTjth in the mass of Jupiter; but that even then the ob¬ 
servations could not be well represented ; and that he conceived 
Xhe absolute attraction of Jupiter on Juno, must be different from 
that upon the Sun. The last conclusion, attacking one of the 
most important principles in the theory of gravitation, required 
further examination. In the Berlin Memoirs 1826, Encke dis¬ 
cussed all the observed oppositions (fourteen) of Vesta, sepa¬ 
rating the perturbations produced by Jupiter into two parts, 
one being Jupiter’s attraction on the Sun, and the other, Jupi¬ 
ter’s attraction on Vesta, and considering the assumed mass of 
Jupiter in these two attractions, as liable to two separate errors. 
The result was, that the absolute attraction of Jupiter on Vesta 
did not differ from that on the Sun, by more than two o' °f the 
whole, and that Nicolai’s mass ought to be increased about tw 
of the whole. Encke remarks however, that Nicolai’s mass 
will represent the observations very nearly as well; and Gauss 
has found the same for Pallas. Nicolai’s mass is generally 
adopted by the German astronomers.—In the last-mentioned 
paper, and in the Berlin Ephemeris 1827, the reader will find 
an account of the method of quadratures used by the Germans 
(to which I intend to refer hereafter). In the Astronomische 
Nachrichten No. 165, Heiligenstein has given the outlines of 
the calculation of the perturbations of Ceres for the opposition 
of 1880. 
The methods of determining from observations the orbits of 
comets may be divided into those which assume parabolic mo¬ 
tion, and those which do not: of the former, at the beginning 
of the century, Olbers’s was best known on the Continent, and 
Lagrange’s and Boscovich’s in this country: of the latter, 
Laplace’s was the only received one. In the Berlin Mem. 
1801, is a method by Trembley. In 1806, Legendre published 
his methods, (the last Supplement appeared in 1820,) which be¬ 
gan without the parabolic assumption, but finally adopted it. 
It is curious that the only two examples which he has taken for 
the parabolic orbit, are comets now known to move in very 
short ellipses, and in which the preference of an elliptic to a 
parabolic orbit was shown, at the time, by Gauss and Bessel. 
This is a striking instance of the danger of making our calcu¬ 
lations on too restricted suppositions. In 1809 appeared Gauss’s 
Theoria Motus , still considered in Germany the classical work 
on this subject. Of the variety and contrivance in the methods 
given there, it is impossible to give any idea: parabolic motion 
