It may be well before attempting to obtain a glimpse of recent progress that we should try to grasp the state of the science at the time when the nineteenth century was about to dawn, and this, perhaps, can be best accomplished by seeing what men were working at this period, at which the greatest activity was to be found in Germany; there was no permanent observatory in the southern hemisphere or in the United States. First and foremost among the workers—he has, in fact, been described as “the greatest of modern astronomers”—was William Herschel, a German domiciled in England. In the year 1773 he hired a telescope, and with this small instrument he obtained his first glimpses of the rich fields of exploration open in the skies. From that time onward he had one fixed purpose in his mind, which was to obtain as intimate knowledge as possible of the construction of the heavens. To do this, of course, great optical power was necessary, and such was his energy that, as large instruments were not to be obtained at any price, he set to work and made them himself. Herschel presented the beginning of the nineteenth century not only with a definite idea of the constitution of the stellar system, based on a connected body of facts and deductions from facts, as gleaned through his telescopes, but observations without number in many fields. He discovered a new planet, Uranus, and several satellites of the planets; published catalogues of nebulæ; established the gravitational bond between many “double stars,” and carried on observations of the sun, then supposed to be a habitable globe. What Herschel did for observational astronomy and deductions therefrom, Laplace did for the furtherance of our knowledge concerning the exact motions of the bodies comprising the solar system. Newton had long before announced that gravitation was universal, and Laplace brought together investigations undertaken to determine the validity of this law. These were given to the world in his wonderful book on _Celestial Mechanics_, the first volumes of which appeared in 1799. A survey of the work of these two great astronomers gives one an idea of what was going on in observational and mathematical astronomy at the beginning of the century. The study was now destined to make rapid strides, as not only were new optical instruments—some designed for special purposes—introduced, new mathematical processes applied, fresh fields for research opened up, but the number of workers was considerably augmented by the increased means available; so much so, indeed, that the first astronomical periodical was founded by Von Zach in 1800 to facilitate intercommunications between the observers.