The first evening of the nineteenth century (January 1, 1801) augured well for progress. It had long been thought that all the members of the solar system had not as yet been discovered, and there was a very notable gap between the planets Mars and Jupiter, indicated by Bode’s law. Observers were organized to make a thorough search for the missing planet, portions of the sky being divided between them for minute examination. It fell to the Italian observer, Piazzi, to discover a small body which was moving in an orbit between these two planets on the date named. The century thus began with a sensation, and because the new body, which was named “Ceres,” was not of sufficient size to be accepted as the “missing planet,” the idea was suggested that perhaps it was a fragment of a larger planet that had been blown to pieces in the past. An opportunity here arose for mathematical astronomy to come to the help of the observer, for Ceres soon was lost in the solar rays, and in order to rediscover it, after it had passed conjunction, an approximate knowledge of its path and future position was necessary. With the then existing methods of computation of orbits it was imperative to have numerous measured positions to use as data for the calculation. The scanty data available in the case of Ceres were not sufficient for the application of the method. The occasion discovered a man, one of the greatest mathematicians of the nineteenth century, Karl Frederick Gauss, who, although only twenty-five years of age, undertook the solution of the problem by employing a system which he had devised, known as “the method of least squares,” which enabled him to obtain a most probable result from a given set of observations. This, with a more general method of orbit computation, also elaborated by himself, was sufficient to enable him to calculate future positions of Ceres, and on the anniversary of the original discovery, Olbers, another great pioneer in orbit calculations, found the planet in very nearly the position assigned by Gauss. So great was the curiosity regarding the other portions of the planet, which was supposed to have been shattered, that numerous observers at once commenced to search after other fragments. These were the _actualities_ of 1801 and thereabouts; but the seed of much future work was sown. Kant and Laplace had already occupied themselves with theories as to the world formation, and spectrum analysis as applied to the heavenly bodies may be said to have been started by Wollaston’s observations of dark lines in the solar spectrum in 1802. Fraunhofer was then a boy at school. In the same year the first photographic prints were produced by Wedgewood and Davy. OBSERVATORIES