Excerpt from On the Theory of the Moon, Vol. 10: And on the Pertubations of the Planets
M. Plana published, in 1832, his great work on the Lunar Theory, which was printed at the expense of the King of Sardinia. M. Plana made use of the method given by Laplace in vol. iii. of the Mec. Cel., which consists in employing the equations in which the true longitude is the independent variable, and the expressions for the variables, r, nt and s, being first obtained in terms of the true longitude, by the reversion of series, r, v, and s are afterwards found in terms of the mean longitude, nt. The distinguishing and important feature of M. Plana's work is, that the expressions for the coefficients are maintained to the last in a literal form: this condition gives facilities for their verification which cannot, in my opinion, be too highly appreciated.
Shortly after the publication of M. Plana's work, I began to consider this subject; and between 1834 and 1840 I published the first four parts of this work. I endeavoured to obtain the coefficients directly by means of the equations of motion, which had always been employed in determining the perturbations of the planets, and in which the time is the independent variable; still maintaining the literal development, as in M. Plana's work.
About the same time, or shortly afterwards, my friend M. de Pontecoulant began to follow in the same track, and to employ the methods which I had introduced.
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