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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 B D 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.
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 Atwoods 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 gť, 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 mechanics.
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. ticles 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* 3.14 square centims. area, should fill at the following instant, the ring of (22 –1) *3.14=3x3:14, at the next instant the ring of (3-2) 3.14=5x3-14 centims. area, and so on;—that is, the
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it be strength will the disk fall back again."
Tags ja rare-propagation, both when the vibradinos patirles e ibe Dedium are transversal and also when 14 Vrste cearls enlainedand a careful scount grade stortion of strings rods, and pares. the laws obered Iriber. tveibers of OTESTODAS. &c. Derasiona's, however, the einsnes are too means adequate: for instance, on page 3:2
- cibe og relative to the action of a fine organ-pipe : namento soris Erected through a narrow slit and strikes the opocie ze cibe aperture or · mouth of the instrument." Tag: bere the description comes to a sudden conclusion, se he reader is left to erp ain for himself as best he can what beroes of the air thus striking against the sharp edge, and how it
s in bestion the air-column in the pipe. A little fur:her on, ibe pitch of an organ-pipe is spoken of as depending on its length on.. the lengths of two open pipes which yield notes whose vibration-frequencies are as 2 to i being as 1 to 2. It might at least bare been mentioned that the pitch is a function also of the cross section of the pipe.
On page 317 pitch and tone are used synonymously.
These, however, are small matters. On the whole the chapter on Acousties is good, the portions relating to the organ of voice and the difference of vowel sounds of the same pitch as depending on the presence of various overtones, differing in intensity, combined with the fundamental, being especially well worked out.
In the Optics, after some well-considered directions have been given for the construction and silvering of mirrors, several simple cases of reflection are described and geometrically solved. There is here the same absence of general formulæ which we noticed in the case of the mechanics. The student is instructed to work out each example separately, and to determine geometrically the relative sizes of an object and its image and their distances from the mirror, No mention is made of spherical aberration (which the
experimenter cannot fail to notice and be perplexed by), nor, in the case of lenses, of chromatic aberration.
The student is taught how to make a spectroscope for himself which, though rough, is all that is absolutely necessary to show the distinctive spectrum-lines of such elements as sodium, lithium, calcium, &c. The description of this little apparatus, and of the method of using it, occupies many pages and is too long to quote
it may, however, be stated that it consists of a single disulphide-of-carbon prism, which is made from the wider part of a lamp-cylinder cut obliquely at both ends and closed by glass plates, with an aperture on the upper side for pouring in the liquid. This is placed at one end of a long wooden box with square section, the further end of which is closed by a thin plate of wood with a narrow vertical slit in it. Following the directions given, the student will have no difficulty in arranging apparatus for exhibiting the reversion of the bright lines in the spectrum of an element, and in apprehending the cause of such reversion.
We find nothing about the phenomena of Interference or Diffraction. This is scarcely to be wondered at, since experiments on these subjects demand the use of more elaborate instruments than the author contemplates his students to be in possession of. His plan is throughout to confine himself to the exposition of such phenomena and principles as can be reproduced and exemplified by the student with such apparatus as he can construct for himself. The student is not expected to make measurements of any kind; he is not supposed to have arrived at such a state of proficiency in his subject. Indeed no measuring-instruments are described or even mentioned in any part of the book. We think, however, it would not have been inconsistent with the plan of the work had some of the elementary experiments on the polarization of light been given,
In the treatment of Electricity the same order is adopted as in the ordinary books on Physics. This portion of the work, not less than the rest, is characterized by copious illustration of principles and by many-sided hints and suggestions for insuring the success of the experiments described. In the main we agree with the writer of the Preface, that though the instructions may sometimes appear to readers unaccustomed to experimental work needlessly minute, yet it will appear in actual trial that the apparently small matters to which attention is sometimes called are just such as make the difference between success and failure. At the same time the thought forces itself upon us as we read through these many pages of instructions, that the author would have done wisely had he sometimes curtailed them, and so left space
for and important matters which he has been obliged to omit. We should like to have seen explained and illustrated the law of inverse squares as applied to electrical and magnetic attractions and repulsions, something about the torsion-balance, Faraday's theory of induction, specific inductive capacity, thermo-electricity, the tangent-galvanometer, electrical resistance, &c. Of none of these is any mention made.