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Rh long intervals of time, as calculated from the tables, and the motion as actually observed. In 1871, during the reign of the Commune, he spent more than a month at the Paris observatory, investigating old unpublished records. A great number of valuable observations, to which even those who made them did not attribute sufficient importance to have them published, were thus brought to light and when reduced were found to carry a knowledge of the exact motion of the moon back to 1670, when it had always before been supposed to begin at 1750, with the observations of Bradley at Greenwich. During his superintendency of the "Nautical Almanac" office, from 1877 to 1897, he prepared tables of the motions of the principal planets, which are now used in all the astronomical and nautical ephemerides of the world, those of France alone excepted. In connection with his purely scientific work he has published more than a hundred papers in various scientific journals; has written important books "On the Secular Variations and Mutual Relations of the Orbits of the Asteroids" (1860); "An Investigation of the Orbit of Neptune" (1874); "Researches on the Motion of the Moon" (1876); "Theory of the Inequalities in the Motion of the Moon" (1894); "Tables of Uranus: Measure of the Velocity of Light" (1884); "Uranian and Neptune System"; "Astronomical Constants"; "Eclipse and Sun Tables." His tables of the motion of the planets and of the moon are used by astronomers in all parts of the world. Among his more universally read books are: "Popular Astronomy," "School Astronomy," "Elements of Astronomy" (1900) ; "The Stars" (1901); "Astronomy for Everybody" (1903); while his series of mathematical text-books includes "Algebra for Schools," " Algebra for Colleges," "Geometry," "Analytical Geometry," "Calculus" and "Essentials of Trigonometry."

In the field of economics he has published "Our Financial Policy," "A, B, C of Finance," "A Plain Man's Talk on the Labor Question" and "Principles of Political Economy." He is also the author of an immense number of magazine articles; of a novel entitled "His Wisdom the Defender" (1900); and of "Reminiscences of an Astronomer" (1904).

The astronomer works in a field so immeasurable by the layman, that it has been found profitable to make use of the light-year—adopted by astronomers—instead of miles, in computing the distance of the stars from the earth and from each other. A light-year is the