HISTOKY OF PHYSICAL ASTEOXOMY.
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Laplace did not undertake tlie excessive labour of calculating its maximumvalue. Burg, however, selected it for the purpose of representing theerrors of the tables, applying to it an empiric coefficient equal to 15"In 1812 Burcliardt obtained corrections of Burg’s elements, which he em-ployed in the calculation of new tables. He rejected the equation oflong period depending on the action of the sun, and substituted instead ofit, the equation which Laplace attributed to the difference between thetwo hemispheres of the earth. This equation was not calculated anymore than the other; Burchardt merely endeavoured to satisfy the ob-servations by applying to it an empiric coefficient equal to 12".5.
The lunar tables were hitherto principally indebted to observation forthe details as well as the groundwork of their construction, since the ar-guments alone of the equations were derived from theory. As this cir-cumstance was considered derogatory to the dignity of Physical Astro-nomy, the French Institute in 1821 proposed as the subject of a prize,a theory of the moon’s motion which should only exact from observationthe data required to determine the six fundamental elements. Two me-moirs were deemed worthy of being crowned; one by Damoiseau, theother by Plana and Carlini. The former of these has been published inthe third volume of the “Memoires des Savans Etrangers the latterhas not been given to the world, hut an elaborate work on the same sub-ject, and avowedly executed upon the same plan, was published by Plana,in 1832*. Damoiseau has used Laplace’s method of investigation; but hehas carried the approximation to a much greater extent than that illus-trious geometer has done. His memoir has been much admired for theclearness which pervades its vast expansion, and the beautiful symmetrywhich distinguishes the arrangement of the terms. He calculated tablesof the moon solely by the aid of his theory, which have been regarded asat least equal to any of those in previous use. The method of Planaagrees essentially with that pursued by Clairaut and his successors; buthe has introduced into it several ingenious modifications. The entireresearches of this distinguished geometer exhibit the most commandingmastery of his subject. It is impossible to repress a feeling of sympathyfor the author, when he informs us that throughout all the immense calcu-lations of this work, he had not the benefit of a single assistantf.
Damoiseau, as well as Plana and Carlini, found reason to believe that theequations of long period, suggested by Laplace, did not possess sensiblevalues. Laplace, who always had strong misgivings respecting the mag-nitude of these equations, concurred in this opinion, and it was now ge-nerally admitted that the errors in the moon’s epoch could not be ac-counted for by an equation of any known form. Carlini in 1824 sug-gested four equations for the purpose of reconciling the tables with ob-servation. Some of these he considered to be preferable to Laplace’s, buthe maintained that the errors were best represented by a term dependingon the square of the time. The admission of this explanation would havebeen tantamount to an abandonment of the question; hut such a coursewould have been a reproach to the advanced state of Physical Astronomy,and could not on any account he sanctioned.
* Theorie du Mouvement de la Lune, 3 tomes 4to, Turin , 1832.
+ “ Je n’ai pu me faire aider par personue; j’ai du traverser seul, cette longue ebainede caleuls, et il n’est pas dormant si par inadvertence, j’ai omis quelques termes qu’il fa.il-lait considerer pour me conformer a la rigueur de mes propres principes.”—DiscoursPreliminaire, p. xii.