In order to make every step of my argument clearly intelligible to all educated readers, it will be necessary to refer continually to the marvellous extension of our knowledge of the universe obtained during the last half-century, and constituting what is termed the New Astronomy. The next chapter will therefore be devoted to a popular exposition of the new methods of research, so that the results reached, which will have to be referred to in succeeding chapters, may be not only accepted, but clearly understood. CHAPTER III THE NEW ASTRONOMY During the latter half of the nineteenth century discoveries were made which extended the powers of astronomical research into entirely new and unexpected regions, comparable to those which were opened up by the discovery of the telescope more than two centuries before. The older astronomy for more than two thousand years was purely mechanical and mathematical, being limited to observation and measurement of the apparent motions of the heavenly bodies, and the attempts to deduce, from these apparent motions, their real motions, and thus determine the actual structure of the solar system. This was first done when Kepler established his three celebrated laws: and later, when Newton showed that these laws were necessary consequences of the one law of gravitation, and when succeeding observers and mathematicians proved that each fresh irregularity in the motions of the planets was explicable by a more thorough and minute application of the same laws, this branch of astronomy reached its highest point of efficiency and left very little more to be desired. Then, as the telescope became successively improved, the centre of interest was shifted to the surfaces of the planets and their satellites, which were watched and scrutinised with the greatest assiduity in order if possible to attain some amount of knowledge of their physical constitution and past history. A similar minute scrutiny was given to the stars and nebulæ, their distribution and grouping, and the whole heavens were mapped out, and elaborate catalogues constructed by enthusiastic astronomers in every part of the world. Others devoted themselves to the immensely difficult problem of determining the distances of the stars, and by the middle of the century a few such distances had been satisfactorily measured.