_The Recent Progress of Astronomy_, by ELIAS LOOMIS (Harper and Brothers), exhibits the most important astronomical discoveries made within the last ten years, with special reference to the condition of the science in the United States. Among the topics treated in detail, are the discovery of the planet Neptune, the addition to our knowledge of comets, with a full account of Miss Mitchell’s comet, the new stars and nebulae, the determination of longitude by the electric telegraph, the manufacture of telescopes in the United States, and others of equal interest both to men of science and the intelligent reader in general. Professor LOOMIS displays a singularly happy talent in bringing the results of scientific investigation to the level of the common mind, and we predict a hearty welcome to his little volume, as a lucid and delightful compendium of valuable knowledge. The author states in the Preface, that “he has endeavored to award equal and exact justice to all American astronomers; and if any individual should feel that his labors in this department have not been fairly represented, he is requested to furnish in writing a minute account of the same,” and he shall receive amends in a second edition of the work. Professor LOOMIS’S _Mathematical Course_ has met with signal favor at the hands of the best instructors in our higher institutions of learning. New editions of his _Algebra_ and the _Geometry_ have recently been issued; and a new volume on _Analytical Geometry_, and the _Calculus_, completing the course, will soon appear.