The application of the problem of three bodies to the theory of the comet of 1759, formed the most important epoch in the life of Clairaut ; but as we have already dis cussed this subject at sufficient length both in the article ASTRONOMY and in the life of D'ALEMBERT, we Cann% resume it in this place.
Next to the lunar theory, the most important subject which then exercised the genius of mathematicians, was the improvement of the achromatic telescope. This subject occupied much of Clairaut's attention, and he published the result of his researches in three memoirs, which appeared in 1756, 1757, and 1762, and which con tain a most complete investigation of the various forms in which achromatic object glasses may be constructed. In the course of this enquiry, Clairaut discovered that the coloured spaces in equal spectra produced by substances of different dispersive powers, were not proportional, and therefore that a complete correction of colour could not be effected by two kinds of glass. This beautiful dis covery of a secondary spectrum was made about the same time by Boscovich, without any knowledge of what Clairaut had done ; and this able mathematician has shewn how a more complete correction of colour may be obtained by employing three different substances in the construction of the object-glass. This curious subject, so intimately connected with the perfection of the achro matic telescope, has been recently investigated by Dr Brewster, who has determined the relative proportions of the coloured spaces for a great variety of transparent bodies. Ile has found that the uncorrected colour gene rally increases with the difference between the dispersive powers of the two substances by which the opposite dis persions are produced ; that sulphuric acid exceeds all transparent substances in its action on the green rays, while oil of cassia exerts the least action upon them or any known substance, and that there is a tertiary spectrum which may be formed even when the opposite dispersions are produced by two prisms or lenses of the same sub stances. The application of these results to the improve ment of the achromatic telescope, will be pointed out in the article Orries."
In order to render his investigations of real utility to the practical optician, Clairaut began to reduce all his results into tables, and to compute the thickness and radii of the different lenses which were requisite to form an achromatic object-glass ; but he unfortunately did not live to finish this work. Although he had laid down a rule never to sup in Paris, yet he was on one particular occasion induced by .some of his friends to transgress it. So fatal was this rash indulgence, that he scarcely lived to repent it. Ile was attacked with indigestion and rheumatism, which baffled the skill of his physicians, and carried him off on the 17th of May 1765, in the 52d year of his age.
The following is a list of the works which he publish ed separately.
Recherches stir its courbes a double courbure. Paris, 1730, in 4to.
Elemens de Geometric. Paris, 1741, in 8vo. Elemens d'Algebre. Paris, 1746, in 8vo.
Theorie de la Figure de la Terre. Paris, 1743, in 8vo. Tables de la Lune. Paris, 1745, in 8vo.
The Memoirs which lie published in the Memoires de l'..lcademie arc the following : Observations stir un instrument par le mom) duquel on pcut prendre les Angles, et faire les calculs arithme tiques, 1727. Hist. 142.
Nouvelle maniere de trouver les formules des centres de gravite, 1731, 159.
Obs. sur les courbes quc l'on forme en eoupant tine surface courbe quelconque par un plan donne de position, 1731, p. 433.
Des epicyclo'ides spheriques, 1732, p. 289.
Maniere de trouver des courbes Algebriques et recti fiables stir la surface d'un cone, 1732, p. 385.
Solution d'un probleme de Geometric, 1732, p. 435. Ohs. sur quelques questions de maa-imis et minimis, 1733, p. 18G.
Determination Geometrique de la perpendiculiare, la mericlienne, tracee par \l. Cassini. avec: plusicurs me thodes (Pen titer la grandeur et la figure de la Terre, 17;3, p. 406, II. 59.
Solution de plusicurs problemcs, ou it s'agit de trouver des courbes dont la propriete consiste dans une certaine relation entre !curs branches, exprilnee par une equation donnee, 1734, p. 196.