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and able to draw inferences, or, at least, "to represent a mind endowed with powers of thought but wholly devoid of knowledge" (vol. i. p. 127). This, however, would be to give a very inadequate notion of the contents of this first part, though we do not see how to give a better account of it in few words. So, again, the second part might be said to contain an exposition of the doctrines of permutations and combinations, and of probabilities, which is closely connected with them, designed to lead up to the position that "we cannot adequately understand the difficulties which beset us in certain branches of science, unless we gain a clear idea of the vast number of combinations or permutations which may be possible under certain conditions. Thus only can we learn how hopeless it would be to attempt to treat nature in detail, and exhaust the whole number of events that might arise" (vol. i. p. 216). Yet this is not an adequate statement of the aim of Book II.; and the same would be found true of similar statements made in regard to the other books. Of course, in the case of any elaborate treatise the same may to some extent be true; but in the work before us the difficulty assumes unusually large dimensions, and renders the task of the reviewer peculiarly hard.


Probably the merit of the work lies mainly in the acute remarks which are freely scattered through it, and in discussions of particular points, which are often of great interest, and for the sake of which alone the work is well worth perusal. As an instance of this we will give a brief account of a single chapter (the twentysixth), which concludes the fourth book on Inductive Investigation;" it is headed, "Character of the Experimentalist." After insisting on the impossibility that the efforts of many ordinary men should supply the place of the genius of exceptional men, and remarking that "nothing is less amenable than genius to scientific analysis and explanation," our author goes on to specify some of the mental characteristics of the natural philosopher. His mind must be readily affected by the slightest exceptional phenomena; his associating and identifying powers must be great; his imagination active; his powers of deductive reasoning sure and vigorous; and he must have so strong a love of certainty as to lead him to compare with diligence and candour his speculations with fact and experiment. It is sometimes thought that the philosopher will be cautious in following up trains of speculation; and the notion derives some countenance from the fact, that only successful trains of thought are commonly reserved for publication. But Mr. Jevons points out, from the examples of Kepler and Faraday, that, to use the words of the latter, "in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized." He then considers the method pursued by Newton in the 'Principia' and the Optics' as a type of the true scientific method "of deductive reasoning and experimental verification." The chapter ends with a notice of a characteristic of the philosop hic mind, to which we have never before had our attention so pointedly drawn, and which is well illustrated by

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the example of Faraday, viz. the tenacity with which it will cling to a conception as likely to prove true and important in spite of repeated failures to verify it by experiment-which is of course a totally different thing from its being negatived by experiment. Thus Faraday first attempted to demonstrate a relation between magnetism and light in 1822; and though he frequently renewed the attempt, he was unsuccessful until, partly by accident, he obtained a result in 1845. In this case his tenacity was rewarded with success. Another series of attempts to demonstrate a reciprocal relation between gravity and electricity proved unavailing to the end. This instance very appropriately leads up to the remark, that "frequently the exercise of the judgment ought to end in absolute reservation," the power to maintain this state being yet another characteristic of the philosophic mind.

In concluding our notice we will venture to do no more than to mention a single thought which has occurred to us several times while reading the work before us. It is this, that although given trains of reasoning, whether deductive or inductive, command universal assent, yet as soon as we get into a discussion of what constitutes the cogency of the reasoning, we are landed in the region of doubt and debate. This might be thought a paradox were it not so well known to be true. No one doubts the conclusiveness of the deductive reasoning by which Euclid proves his forty-seventh proposition; but let the question be started, What is deductive reasoning? and whence does it derive its conclusiveness? and we shall find the highest authorities giving different answers. remark applies to the far more complicated process by which the universal gravitation of matter is proved. Several of Mr. Jevons's logical doctrines might be taken in illustration of these remarks; we will mention one or two.

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1. Mr. Jevons, supported by high authority, regards the formula "Whatever is, is,' as a fundamental law of thought-though Shakspeare, to all appearance, regarded it as mere matter for a joke, and Locke treated its pretensions with scorn, and Mr. Mill thought the treatment just*.

2. Mr. Jevons tells us (vol. i. p. 48) that "in ordinary language the verbs is and are express mere inclusion more often than not. 'Men are mortals' means that men form part of the class mortal." There is, of course, a fundamentally different view of the case, according to which the word is merely predicates of men the

* It might be supposed that the words "Whatever is, is," mean " Whatever exists, exists;" but this is, apparently, not the case, its meaning being "X is X;" e. g. a circle is a circle, or, as Mr. Jevons put it, "a thing at any moment is perfectly identical with itself." So that the clown in Twelfth Night seems to have understood the maxim when he said, "For as the old hermit of Prague, that never saw pen and ink, very wittily said to a niece of King Gorboduc, That, that is, is;' so I being master parson, am master parson." The reference to Locke is Book IV. c. 7, of the Essay concerning Human Understanding;' that to Mr. Mill is p. 408 of An Examination of Sir William Hamilton's Philosophy.'

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attributes of mortals—the fact of mortals forming a class being purely subsidiary and not necessarily coming into view at all.

3. We are told (vol. i. p. 136), "Neither in deductive nor inductive reasoning can we add a tittle to our implicit knowledge, which is like that contained in an unread book or a sealed letter. Sir W. Hamilton has well said, 'Reasoning is the showing out explicitly that a proposition not granted or supposed is implicitly contained in something different which is granted or supposed.' So far as the words "nor inductive " are concerned our author would, we suppose, stand nearly alone in his opinion. It is generally held that induction, or inductive inference, is a process that puts us in possession of something new; but when limited to deductive reasoning, the opinion expressed in the above sentence is very commonly held, though there are some who regard it as fundamentally erroneous. Suppose we took a full-grown man with perfect powers of reasoning, but wholly ignorant of geometry, there would be no difficulty in giving him a perfect knowledge of the definitions and axioms of the science. But when he came to prove the propositions of the first book (say the 47th) that would be quite another question, his success or failure would depend on his powers of invention. No working of the keys of any logical machine would put him up to the essential steps "through A draw A L parallel to BD or CE, and join AD, CF." It certainly seems to us that considerations of this kind land us on this conclusion:-Either the first book of Euclid is not a specimen of deductive reasoning, or else the account commonly given of deductive reasoning is somehow or other erroneous. If we may venture on a surmise, we should say that the passage above quoted is couched in metaphorical language, and that the words "explicit " and "implicit" are used equivocally. To explicate is to unfold. We unfold a table-cloth when we put it on the table, we explicate the definition of a circle when we draw a learner's attention to all the points involved that it must be a plane figure, bounded by one line, &c. But, except by an improper use of language, we do not speak of an oak tree as being unfolded from an acorn; the oak tree is indeed derived from the acorn, but only by the continual assimilation of new matter. It is only in this latter sense, at least as it seems to us, that the first book of Euclid can be said to be unfolded from the definitions and axioms.

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We have gone rather beyond our intention in the last paragraph, and will not venture further into the region of doubt and debate. We will therefore only add that, whether the student ends by adopting Mr. Jevons's logical views or not, he will not fail to learn a great deal from an attentive perusal of this very able and comprehensive work.

Introduction to Experimental Physics, Theoretical and Practical, including directions for constructing Physical Apparatus and for making experiments. By ADOLPH F. WEINHOLD, Professor in the Royal Technical School at Chemnitz. Translated and edited, with the Author's sanction, by BENJAMIN LOEWY, F.R.A.S. With a Preface by G. C. FOSTER, F.R.S.

This is an elementary treatise on Experimental Physics which differs materially from those ordinarily used in our Schools and Universities. The object of the writer has been to present the general facts of elementary physics as plainly as possible, always in a concrete form, to keep abstractions as much as possible in the background, and to give instructions with such detail and minuteness as will enable the reader who is provided with simple tools and materials and endowed with a proper amount of patience, to make all the apparatus and perform all the experiments described in the book. These instructions are without doubt the most valuable part of the book, and constitute the feature by which it is distinguished from other elementary works on physics.

The subjects treated of are General Properties of Matter, General Mechanics and Mechanics of Solid Bodies, Mechanics of Liquid and Gaseous Bodies, Acoustics, Optics, Electricity, Magnetism, and Heat. To judge by the number of pages assigned to each of these subjects, they are considered of very unequal importance. While Heat is disposed of in 78 pages, as many as 316 are allotted to the Mechanics of solid and fluid bodies. The disproportion, however, is not so great as it seems, since of the latter many pages are occupied with a description of tools and methods of operating, which are as much employed upon apparatus for Heat as for Mechanics.

The study of Mechanics is introduced by an experimental investigation of the laws of falling bodies by Atwood's machine. This plan is one of which we cordially approve. An intelligent comprehension of the meaning of the term force is one of the most difficult to instil into the mind of a student. Usually an abstract definition of force is given in the beginning of the text-books which the student learns by heart; and not until he has worked his way through all manner of propositions involving the relations of forces does he learn the connexion between force and weight, how the weight of a body is a concrete expression of the attractive action of the earth upon it, and how forces are to be measured by the motional effects which they produce in bodies. It is a misfortune, however, that greater stress is not laid on the distinction between weight and mass, and also between force and acceleration. The term mass is introduced suddenly (p. 52) without any indication of the meaning it is intended to bear, and is frequently used as synonymous with weight.

The avoidance of abstractions and formulæ is sometimes carried to an excess. For instance, in the case of falling bodies, the ex

periments are described which prove that the velocity attained when a particular force is acting is directly proportional to the time from the beginning of motion, that for a given mass moved the accelerations are as the forces which produce them, that for a given acceleration the spaces described are as the squares of the times, &c. The student finds that in 2, 3, 4 seconds the spaces are 4, 9, 16 times respectively the space described in the first second. But he is not invited to go beyond these particular cases, nor to find a general expression which shall apply to all his experiments. The formulæ s=1⁄2 gt2, v=gt, &c., find no place in this book. Now, much as these and similar formulæ are abused by candidates for examinations, who learn them by heart and acquire a rule-of-thumb trick of applying them to problems without having any notion of their physical meaning, we do not think they should have been excluded from a work on elementary


The principles of fluid-pressure are discussed and exemplified at great length; atmospheric pressure also and the barometer receive a good deal of attention: perhaps, however, a fuller description of the Aneroid Barometer might have been given with advantage. It is an instrument of such common use, that a brief account of the mechanism by which the motion of the lid of the box is transmitted to the index, and the mode of graduating the dial-face, would have been desirable.

The few pages devoted to the phenomena of air-suction, lateral pressure, Clement's disk and the spray-disperser are very lucid, leaving nothing to be desired in the way of explanation. The author's explanation of the phenomenon of the Clement's disk we will give nearly in his own words :—

"The effect of suction produced by a current of air is rendered especially obvious if the current is allowed to expand between two flat disks. A circular disk of cardboard 10 centims. in diameter has a hole in the middle. A glass tube about 8 millims. wide, bent at right angles, is passed through a cork which is glued upon the disk so that the bore of the tube is exactly over the hole in the disk. A second disk of stout paper or thin cardboard is suspended to the other by three threads; the distance between the disks should be 10 millims. If air is strongly blown through the tube it will expand between the plates in a radiating manner, and the particles of air will tend to move with the same velocity. But if the particles of air are to maintain the same velocity, then the same quantity of air which at any instant fills the space within the circle of 1 centim. radius will in the next instant have to fill the space within the ring of 2 centims. radius, in the next that within the ring of 3 centims. radius, and so on. If the particles of air are to maintain their original velocity, it is necessary that the quantity of air which at a certain time fills the inner circle of 1 x 3.14 square centims. area, should fill at the following instant, the ring of (221) ×3·14=3×3-14, at the next instant the ring of (32-22) ×3·14=5 × 3·14 centims. area, and so on;—that is, the

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