matics. The student may derive from it some real knowledge of mathematics, but little or none of the science which he has professedly been studying.

Few persons can undertake any serious study of astronomy, for want of the necessary appliances. There is, indeed, a purely mathematical branch of astronomy, which may be thoroughly mastered by the study of books alone, aided by actual practice in mathematical reasoning. But this theoretical astronomy, as it is called, is too difficult, except in its mere rudiments, for use in general education; and it is rather a branch of mathematics than of natural science, although its results are applicable to astronomical work.

For most students, then, the study of astronomy merely means the acquisition of such an amount of general information about that science as may serve to add to the rational interests and pleasures of their lives. The present work is accordingly intended rather to be read than to be learned by heart. The useful mental discipline which can be gained from books of general information chiefly consists in the practice of the arts of consulting them as works of reference, of correctly interpreting their meaning, and of properly estimating their authority. Although this practice cannot be extensively carried on at school, it is certainly injudicious to bring up young people to regard knowledge as consisting in the power of passing examinations which test only their memories, not their judgments.

But since these examinations in matters of mere general information are unfortunately in extensive use in our schools and colleges, teachers may find it necessary, if they use this book at all, to require their pupils to prepare parts of it for recitations of the customary

kind. To accommodate the book to this use, heavy type has frequently been employed to call attention to subjects on which questions may conveniently be asked; and in the first, or descriptive, portion of the book, the sections relating to the subjects which are most important, or best suited for recitations, have been numbered in heavy type. The sections of the eighth and following chapters are of necessity somewhat closely connected with each other; no distinction, therefore, has been made between them, and each chapter after the seventh will probably be studied or read without omissions, in any manner which may be preferred. No useful purpose, however, can be served by learning the meaning of azimuth (for example) by heart. If any one measures or calculates a few angles of azimuth in the course of his daily work, he will never forget what the word means; if he never has occasion to measure or calculate an angle of azimuth, why should he remember what it is? It is enough if he knows where to look for its meaning and its connection with other astronomical terms, on any occasion when he may require this knowledge. Accuracy does not mean omniscience, and indeed the attempt to acquire omniscience is certain to result in inaccuracy.

To facilitate the use of this book as a work of reference, its index has been made somewhat extensive, and frequent references have been inserted in the text from subsequent to preceding sections relating to associated topics. At the top of each page will be found the number of the section to which the first line of the page belongs. It may perhaps be found useful, after the book has been read, to spend a moderate time in studying it by subjects, with the aid of the index. Its lan

guage has been made plain and clear to the best of the writer's ability, and perhaps with the result of making parts of it tediously diffuse; but it seemed better to run some risk of this kind than to fall into the opposite error. Mathematical and technical expressions have been avoided, so far as possible, in the first seven chapters; and illustrative geometrical figures have been replaced by verbal illustrations wherever this seemed practicable. For reasons which need not here be discussed, many learners acquire little from their early mathematical studies except an undiscriminating dislike of mathematics in general. Under these circumstances, they are disposed to pass over a mathematical explanation of any subject as hastily as possible, and to attach no strictly definite meanings to the terms used in it, to the manifest detriment of their reasoning faculties. On the other hand, students who have some actual working knowledge of mathematics may exercise themselves profitably in reducing an explanation given in ordinary language to a strict mathematical form, and illustrating it by geometrical figures of their own drawing, or, still better, by solid models of their own construction. Whatever they can do for themselves of this kind will teach them more, both of mathematics and of the subject to which they apply it, than they would gain from ten times as much work laid out in merely following the demonstrations of their text-books. Other reasons for the plan pursued in the present work are that too frequent references from the text to illustrative figures become vexatious to almost all readers, and sometimes result in making the student better acquainted with the figures themselves than with the subjects which they are meant to explain. Moreover, an explanation de

pendent on an illustrative figure cannot conveniently be followed by a listener, if it is read aloud; this, however, is a comparatively slight drawback to the use of a school-book. As this work may be used by students who have never attained any facility in mathematical reasoning, or who have lost what they formerly had, the small amount of geometry required for the explanation of the telescope, and of the rudiments of practical and theoretical astronomy, is included in the eighth chapter, and in those which follow it. Any one who either remembers his geometry, or can work it out for himself, will be able to find neater methods of proof for the propositions employed in the fourteenth chapter than those which are there given because they seemed the most direct.

A good way of testing the learner's comprehension of any work of general information is to ask him questions, the answers to which are not contained in the work itself, but may readily be inferred from it. It is useless to publish many such questions with the work; because, if the learner knows them in advance, they are no longer tests of his knowledge, but only of his industry. The following questions may serve as specimens of the kind just mentioned. They may be useful after the whole work has been read; and the student should have the work before him to assist him in answering.

Why are the apparent paths of solar spots such as they are said to be in section 59?

Why ought each successive magnitude of stars to include more stars than the preceding magnitude? See sections 79, 457.

At what time of night may we expect that shooting stars will be, on the whole, most abundant, on the prin

ciple that the forward side of a moving object is, on the whole, most likely to encounter other objects?

Why does the Earth's rotation prolong an eclipse of the Sun? Does this prolongation happen at all places on the Earth from which eclipses of the Sun are ever seen?

Does the Earth's movement in its orbit shorten or lengthen the time of a transit of Venus? of an eclipse of the Sun?

What are the poles of the prime vertical? of the equinoctial colure?

Why should Paramatta be said in the Almanac to be fifteen hours east, rather than nine hours west, of Washington?

It will also be well to accustom the learner to distinguish accurately between different uses of the same word. The following are examples of words used in various senses: altitude, aurora, corona, diameter, hemisphere, horizon, penumbra, phase, umbra.

Teachers who wish to exercise their pupils in simple astronomical calculations will find materials for this purpose in the sixteenth chapter. The precessions of stars, and hence their approximate proper motions, the periods of the synodical revolutions of the planets, the relative weights of equal masses at the surfaces of different bodies, and other problems of like character, may be studied by the aid of the data contained in this work; but of course some little knowledge of algebra and trigonometry must previously be had.

The only way of enabling a reader to estimate the authority of any statement placed before him is to accustom him to demand references to original authorities, and to test the correctness of every statement