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acquisition of these we may refer him to those other parts of this Cyclopædia which profess to treat of the several subjects in question. Of course, the more of such knowledge he brings to the perusal, the easier will be his progress, and the more complete the inform. ation gained; but we shall endeavour in every case, as far as it can be done without a sacrifice of clearness, and of that useful brevity which consists in the absence of prolixity and episode, to render what we have to say as independent of other books as possible.

(7.) After all, we must distinctly caution such of our readers as may commence and terminate their astronomical studies with the present work (though of such, at least in the latter predicament, we 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, — a sound and sufficient knowledge of mathematics, the great instru, ment of all exact enquiry, 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 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 we shall neither adopt ourselves nor would recommend to others.

(8.) On the other hand, although it is something new to abandon the road of mathematical demonstration in the treatment of subjects susceptible of it, and 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 and better practice which is in. compatible 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 as 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 dissi. INTRODUCTION.

pated, some inward misgiving cleared up, or even some link 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 completenot 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 reason.. ing 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 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. We cannot, indeed, always promise ourselves to attain this degree of vividness in our illustrations, nor are the points to be elucidated themselves always capable of being so para

phrased (if we 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 we are very conscious of having, in making such attempts gained for ourselves much clearer views of several of the more concealed effects of planetary perturbation than we had acquired by their mathematical investigation in detail, we may reasonably hope that the endeavour will not always be unattended with a similar success in


(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 encumber 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 enquiries 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

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reason,- that we must attribute something of that in. distinctness of view which is often complained of as a grievance by the earnest student, and still more com. monly 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 our power lies, that acci. dental obscurity, and by showing ordinary untutored comprehension clearly what it can, and what it cannot, hope to attain.




(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 de. notes the reason, theory, or interpretation of the stars +, has become degraded in its application, and confined to

* Armne, a star ; youos, a law; or very, to tend, as a shepherd his flock; so that ar tovouos means “ shepherd of the stars." The two etymologies are, however, coincident.

+ Loyos, reason, or a word, the vehicle of reason ; the interpreter of thought.

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