MY experience in presenting the elements of practical astronomy to rather large classes of students in the University of Michigan led me to the conclusion that the extensive treatises on the subject could not be used satisfactorily, except in special cases. Brief lecture notes were employed in preference. Arrangements were made with a local publisher that the notes should be written out in full and printed, almost exclusively it was supposed, for use in my own classes. The process of enlargement had just begun when the call to my present position was accepted.

The author feels that critical examination of this monograph may show in many points a want of consistency and continuity. The ground covered is so extensive, the material so diverse as well as voluminous, and the relations to be investigated so numerous, that no conclusion could be reached on one point which was not liable to be modified by subsequent decisions upon other points. The author trusts that the difficulties growing out of these features of the work, as well as those incident to the administration of an office not especially organized for the work, will afford a sufficient apology for any defects that may be noticed.

NAUTICAL ALMANAC OFFICE, U. 8. Naval Observatory, January 7, 1895.

I HAVE endeavoured in this book to give a simple description of the heavenly bodies and their motions in a form which should appeal to those who know little or nothing of the subject. It has been my aim to strike a mean between the larger and more difficult technical books and the extremely simple ones which weary us with accounts of children walking round tables and oranges. The book is the outcome of the notes which I have used in teaching Astronomy to Junior Forms in a Public School, where experience has shown me that many boys will follow up the subject, read for themselves, and enjoy practical work, when once they have been given a start.

THIS book is intended for the use of students who have a fair knowledge of elementary algebra and plane geometry, and is the outcome of several years of experience with classes of this sort. The author hopes that the volume will also be acceptable to more advanced scholars.

HPHE present volume is intended to meet the wants of those Students whose knowledge of Mathematics is limited to an acquaintance with the Elements of Euclid, Algebra, and Plane Trigonometry. In a few cases easy formulae in Dynamics are introduced, but the articles containing these may, if necessary, be omitted without a breach in the continuity of the work.

THE READER of this volume is expected to possess such knowledge of Mathematics as may be gained by studying the Elements of Euclid and Algebra, together with a rudimentary acquaintance with the geometry of Planes and Spheres.

I T must be in compliance with custom, rather than from any distinct view of good likely to result, when an Author begins his Work by defining the Science he means to treat of. A definition is not easily laid down. It is not difficult, indeed, to define a branch of science in general terms ; but such are seldom intelligible to the Student. If we enumerate what is too summarily expressed, and explain a general statement by detailing certain cases comprehended under it, we, probably, forestall what belongs to the body of the Work. We attempt to do immaturely what, it is almost certain, will be done imperfectly ; and this without an adequate advantage ; for, a definition such as we allude to, entailing no consequences, is not required in the beginning of a Work: at the end it is unnecessary.

EVERY one strives to adapt means to ends, and when the author prepared his large work on Astronomy, he had no other end in view than to teach Astronomy to such as may be competent to the task and fully prepared to learn it. His first aim was to produce a book of the right tone and character, without any regard to the number of persons who might be prepared to use it. That effort was entirely successful, but the book is not adapted to the great mass of pupils, because it requires of the learner considerable mathematical knowledge, and a corresponding discipline of mind, therefore but few persons, omparatively speaking, feel qualified to study that book. At the same time a book of like tone, character, and spirit, is demanded by teachers for the use of their more humble pupils, except that it must be on a lower mathematical plane, and this book is designed to supply that demand.