Euler’s first contribution to astronomy was an essay on the tides which obtained a share of the Academy prize for 1740 already referred to, Daniel Bernouilli and Maclaurin (chapter X., [§ 196]) being the other two Newtonians. The problem of the tides was, however, by no means solved by any of the three writers.
He gave two distinct solutions of the problem of three bodies in a form suitable for the lunar theory, and made a number of extremely important and suggestive though incomplete contributions to planetary theory. In both subjects his work was so closely connected with that of Clairaut and D’Alembert that it is more convenient to discuss it in connection with theirs.
231. Alexis Claude Clairaut, born at Paris in 1713, belongs to the class of precocious geniuses. He read the Infinitesimal Calculus and Conic Sections at the age of ten, presented a scientific memoir to the Academy of Sciences before he was 13, and published a book containing some important contributions to geometry when he was 18, thereby winning his admission to the Academy.
Shortly afterwards he took part in Maupertuis’ expedition to Lapland (chapter X., [§ 221]), and after publishing several papers of minor importance produced in 1743 his classical work on the figure of the earth. In this he discussed in a far more complete form than either Newton or Maclaurin the form which a rotating body like the earth assumes under the influence of the mutual gravitation of its parts, certain hypotheses of a very general nature being made as to the variations of density in the interior; and deduced formulae for the changes in different latitudes of the acceleration due to gravity, which are in satisfactory agreement with the results of pendulum experiments.
Although the subject has since been more elaborately and more generally treated by later writers, and a good many additions have been made, few if any results of fundamental importance have been added to those contained in Clairaut’s book.
He next turned his attention to the problem of three bodies, obtained a solution suitable for the moon, and made some progress in planetary theory.
Fig. 80.—The path of Halley’s comet.
Halley’s comet (chapter X., [§ 200]) was “due” about 1758; as the time approached Clairaut took up the task of computing the perturbations which it would probably have experienced since its last appearance, owing to the influence of the two great planets, Jupiter and Saturn, close to both of which it would have passed. An extremely laborious calculation shewed that the comet would have been retarded about 100 days by Saturn and about 518 days by Jupiter, and he accordingly announced to the Academy towards the end of 1758 that the comet might be expected to pass its perihelion (the point of its orbit nearest the sun, P in fig. 80) about April 13th of the following year, though owing to various defects in his calculation there might be an error of a month either way. The comet was anxiously watched for by the astronomical world, and was actually discovered by an amateur, George Palitzsch (1723-1788) of Saxony, on Christmas Day, 1758; it passed its perihelion just a month and a day before the time assigned by Clairaut.