The first successful attempt to measure the heating power of moonlight was made in 1846 on Mount Vesuvius by _Melloni_, an Italian physicist, whose results were confirmed four years later by _Zantedeschi_, another Italian. The most important work in this direction was accomplished by the present _Earl of Rosse_ (born in 1840), who in the years 1869-72 believed himself to have measured the lunar heat; but these conclusions were not altogether confirmed by the observations of Dr _Otto Boeddicker_ (Lord Rosse’s astronomer), during the total lunar eclipse of October 4, 1884. Further investigations on this subject were afterwards made by _Samuel Pierpont Langley_ (1834-1906), of Alleghany, and by his assistant, _Frank Very_. The motion of the Moon and its perturbations were made the subject of deep study by the famous _Pierre Simon Laplace_ (1749-1827), the contemporary of Herschel, and the worthy successor of Newton. He devoted much attention to the secular acceleration of the Moon’s mean motion, a problem which had baffled the greatest mathematicians. After a profound discussion he found, in 1787, that the average distance of the Earth and Moon from the Sun had been slowly increasing for several centuries, the result being an increase in the Moon’s velocity. In the third volume of the ‘Mécanique Céleste’ Laplace worked out the lunar theory in great detail, although he calculated no lunar tables. After his death the subject was taken up by _Charles Theodore Damoiseau_ (1768-1846), and the most important advance was made by _Giovanni Antonio Amadeo Plana_ (1781-1864), the director of the Turin Observatory, who published in 1832 a very complete lunar theory. The work of Plana was followed by that of _Peter Andreas Hansen_ (1795-1874), whose lunar tables were used for the Nautical Almanac, and whom Professor Simon Newcomb considers to be the greatest master of celestial mechanics since Laplace. The theory of the Moon’s motion was worked out in detail by the famous astronomer _Charles Eugene Delaunay_ (1816-1872), who from 1870 till 1872 occupied the post of director of the Paris Observatory. Delaunay was about to work out the lunar tables when, in 1872, he was accidentally drowned by the capsizing of a pleasure-boat at Cherbourg. The work accomplished in this direction by _Simon Newcomb_ (born 1835) is of great importance, particularly in his correction of Hansen’s tables. _John Couch Adams_ (1819-1892), one of the discoverers of Neptune, while at work on the lunar theory, had occasion to correct Laplace’s supposed solution of the acceleration of the lunar motion. On going over the calculation Adams found that several quantities, omitted by Laplace as unimportant, showed that the Moon has a minute increase of speed for which the theory of gravitation will not account,—a conclusion opposed by Plana, Hansen, and Pontécoulant, but fully confirmed by Delaunay. Delaunay suggested in 1865 that the minute apparent increase was due to the retardation of the