unwritten customs (so to speak), at any rate to its fundamental laws. Their movements, in short, were demonstrated by the most unanswerable of all arguments--that of verified calculation--to be _calculable_, and their investigation was erected into a legitimate department of astronomical science. This notable advance was the chief _result_ obtained in the field of inquiry just now under consideration during the eighteenth century. But before it closed, its cultivation had received a powerful stimulus through the invention of an improved _method_. The name of Olbers has already been brought prominently before our readers in connection with asteroidal discoveries; these, however, were but chance excursions from the path of cometary research which he steadily pursued through life. An early predilection for the heavens was fixed in this particular direction by one of the happy inspirations of genius. As he was watching, one night in the year 1779, by the sick-bed of a fellow-student in medicine at Göttingen, an important simplification in the mode of computing the paths of comets occurred to him. Although not made public until 1797, "Olbers's method" was then universally adopted, and is still regarded as the most expeditious and convenient in cases where absolute rigour is not required. By its introduction, not only many a toilsome and thankless hour was spared, but workers were multiplied, and encouraged in the prosecution of labours more useful than attractive. The career of Heinrich Olbers is a brilliant example of what may be done by an amateur in astronomy. He at no time did regular work in an observatory; he was never the possessor of a transit or any other fixed instrument; moreover, all the best years of his life were absorbed in the assiduous exercise of a toilsome profession. Born in 1758 at the village of Arbergen, where his father was pastor, he settled in 1781 as a physician in the neighbouring town of Bremen, and continued in active practice there for over forty years. It was thus only the hours which his robust constitution enabled him to spare from sleep that were available for his intellectual pleasures. Yet his recreation was, as Von Zach remarked,[241] no less prolific of useful results than the severest work of other men. The upper part of his house in the Sandgasse was fitted up with such instruments and appliances as restrictions of space permitted, and there, night after night during half a century and upwards, he discovered, calculated, or observed the cometary visitants of northern skies. Almost as effective in promoting the interests of science as the valuable work actually done by him, was the influence of his genial personality. He engaged confidence by his ready and discerning sympathy; he inspired affection by his benevolent disinterestedness; he quickened thought and awakened zeal by the suggestions of a lively and inventive spirit, animated with the warmest enthusiasm for the advancement of knowledge.