The problem, indeed, of the moon’s motion is one of the most difficult, and has taxed the ingenuity of astronomers from an early date. Even at the present day it is impossible to predict the exact position of the moon at any one moment owing to inequalities and perturbations, the exact varying values of which are not known. The two most important theories of the motion of the moon completed towards the middle of the century were due to Hansen and Delaunay. The former’s appeared in 1838, the lunar tables being published later (1857), while the latter’s was published in 1860. Hansen’s theory had for its chief object the formation of tables; to avoid the inconvenience of using in his calculations series which slowly converge, he inserted numerical values throughout. In Hansen’s solution the problem is one actually presented by nature, allowance being made for every known cause of disturbance. There is one disadvantage, namely, that should observations demand a change in any of the constants used, there is no means of making any correction in the results. Delaunay’s theory surmounted this difficulty, but at the expense of still greater inconvenience for making an ephemeris. The slow convergence of certain series involved an immense amount of labor to give sufficiently approximate results. More recently, as the century was closing, Dr. Brown took up the subject and made a fresh attempt to calculate the motion of our satellite. It may be stated that he adopts all Delaunay’s modifications of the problem and works them out algebraically; but there are many technical differences which it would be out of place to mention here. Enough has been stated to show that there is not likely to be any breach of continuity in the treatment of this most important problem. Another attack on the moon, and, incidentally, its motion, has recently been made by another analyst, Professor George Darwin; grappling with all the consequences of tidal friction, he has been able to present to us the past and future history of our satellite. Beginning as a part of the material congeries from which subsequently some fifty million years ago both earth and moon, as separate bodies, were formed, it has ever since been extending its orbit, and so retreating farther away from its centre of motion, while the period of the earth’s rotation has been increasing at the same time, from a possible period of some three hours when the moon was born, to one of one thousand four hundred hours when the day and month will be equal, something like one hundred and fifty million years being required for the process. STELLAR EVOLUTION It was only in the 80’s, after thousands of observations of the spectra of stars, nebulæ, and comets had been secured, that the full meaning of the revelations of the spectroscope began to dawn upon the world.