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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 principle 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

whenever he can.

This part of education is too often neglected ; and grown men sometimes take any thing in print for gospel, and at other times are unreasonably sceptical. It would be well if readers required references throughout all popular works on science; but it would probably appear pedantic to fill this book with citations. Accordingly, it is only in the sixteenth chapter, which contains distinct statistical statements, that authorities are referred to. Care has been taken, however, throughout the book, to check, by means of original treatises, the statements derived from popular works; and it is hoped that few errors have escaped attention in the revision of the text. For the historical portion of the book, Delambre has been the chief authority consulted.

The illustrative lithographs have been copied, with Professor Winlock's permission, from the series of “Astronomical Engravings from the Observatory of Harvard College.” On consideration, it has been thought best not to attempt any representation of nebulæ or comets. Good representations would be so expensive as to add too much to the price of the work ; while ordinary ones, such as usually appear in popular works on astronomy, are of little or no service to the reader.

The thanks of the author are due to Professor Winlock for occasional assistance in settling doubtful points, and for many valuable suggestions.

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