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. [Illustration: 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. Halley’s brilliant conjecture was thus justified; a new member was added to the solar system, and hopes were raised—to be afterwards amply fulfilled—that in other cases also the motions of comets might be reduced to rule, and calculated according to the same principles as those of less erratic bodies. The superstitions attached to comets were of course at the same time still further shaken. Clairaut appears to have had great personal charm and to have been a conspicuous figure in Paris society. Unfortunately his strength was not equal to the combined claims of social and scientific labours, and he died in 1765 at an age when much might still have been hoped from his extraordinary abilities.[133]