eighteen years, for the purpose of improving the lunar theory, a problem which had long occupied much of his attention. He had the satisfaction of completing this eighteen-year task before his death, which occurred in 1742, his age being eighty-five.
Soon after the development of Newton's method, Halley set to work with the application to comets' orbits. Certain terms were tabulated in order to facilitate the application, but even with this aid Halley himself, who delighted in large undertakings, seems to have been greatly impressed with the magnitude of this one. The undertaking consisted in computing the parabolic orbits of all comets where sufficient data existed for this purpose, but, although the appearance of some four hundred of these bodies had been noted during historic times, only twelve had been sufficiently observed to give much hope of success. To this first twelve were afterwards added twelve more. The final results of this long investigation were not published until 1749, when it appeared with the title, "Synopsis Astronomiæ Cometæ." In these days, with improved methods of attacking the problem, such a task
