present work (though of such,—at least in the latter predicament,— I trust the number will be few), that its utmost pretension is to place them on the threshold of this particular wing of the temple of Science, or rather on an eminence exterior to it, whence they may obtain something like a general notion of its structure; or, at most, to give those who may wish to enter a ground-plan of its accesses, and put them in possession of the pass-word. Admission to its sanctuary, and to the privileges and feelings of a votary, is only to be gained by one means,-sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range. It is not without an effort that those who possess this knowledge can communicate on such subjects with those who do not, and adapt their language and their illustrations to the necessities of such an intercourse. Propositions which to the one are almost identical, are theorems of import and difficulty to the other; nor is their evidence presented in the same way to the mind of each. In teaching such propositions, under such circumstances, the appeal has to be made, not to the pure and abstract reason, but to the sense of analogy-to practice and experience: principles and modes of action have to be established not by direct argument from acknowledged axioms, but by continually recurring to the sources from which the axioms themselves have been drawn; viz. examples; that is to say, by bringing forward and dwelling on simple and familiar instances in which the same principles and the same or similar modes of action take place: thus erecting, as it were, in each particular case, a separate induction, and constructing at each step a little body of science to meet its exigencies. The difference is that of pioneering a road through an untraversed country and advancing at ease along a broad and beaten highway; that is to say, if we are determined to make ourselves distinctly understood, and will appeal to reason at all. As for the method of assertion, or a direct demand on the faith of the student (though in some complex cases indispensable, where illustrative explanation would defeat its own end by becoming tedious and burdensome to both parties), it is one

which I shall neither willingly adopt nor would recommend to others.

(8.) On the other hand, although it is something new to aban don the road of mathematical demonstration in the treatment of subjects susceptible of it, and to teach any considerable branch of science entirely or chiefly by the way of illustration and familiar parallels, it is yet not impossible that those who are already well acquainted with our subject, and whose knowledge has been acquired by that confessedly higher practice which is incompatible with the avowed objects of the present work, may yet find their account in its perusal,-for this reason, that it is always of advantage to present any given body of knowledge to the mind in ast great a variety of different lights as possible. It is a property of illustrations of this kind to strike no two minds in the same manner, or with the same force, because no two minds are stored with the same images, or have acquired their notions of them by similar habits. Accordingly, it may very well happen, that a proposition, even to one best acquainted with it, may be placed not merely in a new and uncommon, but in a more impressive and satisfactory light by such a course-some obscurity may be dissipated, some inward misgivings cleared up, or even some links supplied which may lead to the perception of connections and deductions altogether unknown before. And the probability of this is increased when, as in the present instance, the illustrations chosen have not been studiously selected from books, but are such as have presented themselves freely to the author's mind as being most in harmony with his own views; by which, of course, he means to lay no claim to originality in all or any of them beyond what they may really possess.

(9.) Besides, there are cases in the application of mechanical principles with which the mathematical student is but too familiar, where, when the data are before him, and the numerical and geometrical relations of his problems all clear to his conception,— when his forces are estimated and his lines measured,-nay, when even he has followed up the application of his technical processes, and fairly arrived at his conclusion, there is still something wanting in his mind-not in the evidence, for he has examined each link, and finds the chain complete-not in the

principles, for those he well knows are too firmly established to be shaken-but precisely in the mode of action. He has followed out a train of reasoning by logical and technical rules, but the signs he has employed are not pictures of nature, or have lost their original meaning as such to his mind: he has not seen, as it were, the process of nature passing under his eye in an instant of time, and presented as a consecutive whole to his imagination. A familiar parallel, or an illustration drawn from some artificial or natural process, of which he has that direct and individual impression which gives it a reality and associates it with a name, will, in almost every such case, supply in a moment this deficient feature, will convert all his symbols into real pictures, and infuse an animated meaning into what was before a lifeless succession of words and signs. I cannot, indeed, always promise myself to attain this degree of vividness of illustration, nor are the points to be elucidated themselves always capable of being so paraphrased (if I may use the expression) by any single instance adducible in the ordinary course of experience; but the object will at least be kept in view; and, as I am very conscious of having, in making such attempts, gained for myself much clearer views of several of the more concealed effects of planetary perturbation than I had acquired by their mathematical investigation in detail, it may reasonably be hoped that the endeavour will not always be unattended with a similar success in others.

(10.) From what has been said, it will be evident that our aim is not to offer to the public a technical treatise, in which the student of practical or theoretical astronomy shall find consigned the minute description of methods of observation, or the formulæ he requires prepared to his hand, or their demonstrations drawn. out in detail. In all these the present work will be found meagre, and quite inadequate to his wants. Its aim is entirely different; being to present in each case the mere ultimate rationale of facts, arguments, and processes; and, in all cases of mathematical application, avoiding whatever would tend to incumber its pages with algebraic or geometrical symbols, to place under his inspection. that central thread of common sense on which the pearls of analytical research are invariably strung, but which, by the attention the latter claim for themselves, is often concealed from the eye of the gazer, and not always disposed in the straightest and

most convenient form to follow by those who string them. This is no fault of those who have conducted the inquiries to which we allude. The contention of mind for which they call is enormous; and it may, perhaps, be owing to their experience of how little can be accomplished in carrying such processes on to their conclusion, by mere ordinary clearness of head; and how necessary it often is to pay more attention to the purely mathematical conditions which ensure success,-the hooks-and-eyes of their equations and series,-than to those which enchain causes with their effects, and both with the human reason,-that we must attribute something of that indistinctness of view which is often complained of as a grievance by the earnest student, and still more commonly ascribed ironically to the native cloudiness of an atmosphere too sublime for vulgar comprehension. We think we shall render good service to both classes of readers, by dissipating, so far as lies in our power, that accidental obscurity, and by showing ordinary untutored comprehension clearly what it can, and what it cannot, hope to attain.

CHAPTER I.

GENERAL NOTIONS.-APPARENT AND REAL MOTIONS.-SHAPE AND SIZE OF THE EARTH.-THE HORIZON AND ITS DIP.-THE ATMO

FORMING

SPHERE.-REFRACTION.-TWILIGHT.-APPEARANCES RESULTING FROM DIURNAL MOTION-FROM CHANGE OF STATION IN GENERAL. -PARALLACTIC MOTIONS.-TERRESTRIAL PARALLAX.-THAT OF THE STARS INSENSIBLE.-FIRST STEP TOWARDS AN IDEA OF THE DISTANCE OF THE STARS.-COPERNICAN VIEW OF THE EARTH'S MOTION.-RELATIVE MOTION.-MOTIONS PARTLY REAL, PARTLY APPARENT.-GEOCENTRIC ASTRONOMY, OR IDEAL REFERENCE OF PHÆNOMENA TO THE EARTH'S CENTRE AS A COMMON CONVENTIONAL STATION.

(11.) THE magnitudes, distances, arrangement, and motions of the great bodies which make up the visible universe, their constitution and physical condition, so far as they can be known to us, with their mutual influences and actions on each other, so far as they can be traced by the effects produced, and established by legitimate reasoning, form the assemblage of objects to which the attention of the astronomer is directed. The term astronomy* itself, which denotes the law or rule of the astra (by which the ancients understood not only the stars properly so called, but the sun, the moon, and all the visible constituents of the heavens), sufficiently indicates this; and, although the term astrology, which denotes the reason, theory, or interpretation of the stars, has become degraded in its application, and confined to superstitious and delusive attempts to divine future events by their dependence on pretended planetary influences, the same meaning originally attached itself to that epithet.

Astro, a star; voμos, a law; or veμev, to tend, as a shepherd his flock; so that aor povouos means "shepherd of the stars." The two etymologies are, however, coincident.

† Aoyos, reason, or a word, the vehicle of reason; the interpreter of thought.