158 
SECOND REPORT - 1832 . 
of Juno and Vesta, and I find that they are rather more accu¬ 
rate than those of Venus. 
Of the successive steps in the theories of these planets, the 
following are the principal. 
In the Milan Epliemeris 1803, Oriani gave formulas for the 
perturbations of Ceres, on two suppositions of the value of the 
major axis; also for the perturbations of Pallas, as far as the 
third power of the inclination, and the second dimension of the 
eccentricity and its combination with the inclination. In the 
Berlin Epliemeris 1805, Schubert gave expressions for the 
perturbations of Ceres by Jupiter; and in the volume for 1809, 
Pfaff gave similar expressions for the effect of Saturn. In the 
Monatliche Correspondents , vol. 7, Gauss gave Tables for the 
perturbations of Ceres. In tom. 1. of the Gottingen Transactions, 
the same writer discussed the elements of the orbit of Pallas, 
taking no account of perturbations. In the Memorie della 
Societa Italiana for 1810, Santini gave Vesta’s secular variations 
and formulae for her periodic inequalities to the first order of 
small quantities, on two hypotheses of the value of the major 
axis. In the Milan Epliemeris 1815, Carlini gave Tables for the 
equation of the centre and the reduction of Ceres ; in 1816, ex¬ 
pressions for the equation of the centre of Vesta. Lindenau 
remarked in vol. 1. of the Zeitschrift, that Carlini’s Tables for the 
equation of the centre would be of little use, because the enor¬ 
mous perturbations produced by Jupiter would alter the eccen¬ 
tricity so much that the term depending on a given variation of 
the eccentricity, would soon be found inaccurate. In the Milan 
Epliemeris 1819, Carlini gave the equation of the centre for 
Pallas and Juno, with two values of the eccentricity, together 
with the alteration for each depending on alteration of eccen¬ 
tricity. In the Monatliche Correspondents , vol. 28, Burckhardt 
had given formulae for the perturbations of Vesta, on two sup¬ 
positions as to the magnitude of its semi-major axis ; in the 
Mem . della Soc. Italiana, Santini gave elements deduced from 
observations, and complete Tables, including those for the per¬ 
turbations to the first order of small quantities. In the Con - 
naissance des Temps for 1818 and 1820, Daussy gave very 
complete Tables for the perturbations of Vesta, including 40 
equations. These are still considered standard, except that 
the Germans prefer calculating the perturbations produced by 
Jupiter, by the method of quadratures. In the Berlin Ephe- 
meris 1826, Nicolai gave a short paper containing results of 
great importance deduced from the discussion of observations 
on Juno. In all the calculations hitherto made, the mass adopt¬ 
ed for Jupiter was either that assumed by Laplace (founded on 
