Sir William Herschel discovered the planet Uranus in 1781, and subsequently found its satellites. Many star groups, double stars and nebulæ were discovered by him and he found that the solar system is traveling through space in the direction of a point in or near the constellation of Hercules. Greenwich observatory was publishing at the end of the eighteenth century the Nautical Almanac, and annual reports on star and meteorological observations as well as important astronomical monographs. Similar publications were founded in the next century in France, Germany, and Italy. The discoveries in mathematics during the eighteenth century included the differential, integral, and other forms of the calculus, differential equations, and various formulæ for dynamics, mechanics, and physical and astronomical calculations. Euler, Lagrange, Laplace, D'Alembert, and Carnot were prominent mathematical investigators. Heat in earlier times had been regarded as an imponderable substance called caloric which was supposed to be emitted by hot and absorbed by cold bodies. Thus the expansion of mercury was explained by the addition of caloric and not by the increase of distance between the molecules. Francis Bacon and the Scotch chemist Black did the preliminary work which enabled Count Rumford finally to establish the true theory of heat. Watt and Newcomen were attracted by these studies and reduced their theories to practice in the steam engine. Black described specific and latent heat and invented, and used, the calorimeter bearing his name. Hall invented an achromatic lens for telescopes in 1733, and Dollond, another English optician, improved achromatic lenses and made, in 1758, achromatic telescope objectives. The lenses were primarily designed for astronomical telescopes, but they were also applied to microscopes and other scientific instruments, resulting in improvements in our knowledge of light. The voyages of discovery, in this century, encouraged study of zoölogy and natural history subjects generally, including mineralogy and geology. Hooke, Ray, and Woodward made collections of rocks and fossils in England and advanced hypotheses to explain their origins. Lazzaro Moro suggested that fossils must have been deposited in rocks when they were being formed. He also distinguished rock formations by the characteristic fossils found in them. Hutton and Smith then made scientific studies of English rocks, fossils, and earth sculpture, and prepared the materials for the subsequent brilliant discoveries of Lyell. The first governmental school of mines was established in Freiberg, Saxony, in 1775. This institution, and others which were afterward established in different countries, led to an intensive study of the geological and metallurgical sciences, which eventuated in great advances during the nineteenth century.