Sidebilder
PDF
ePub

238 I seem to be justified in speaking of my own book on Mechanics, as the successful rival of Dr Wood's, by the number of editions which it has gone through*; and by the so-entitled "New Edition" of Dr Wood's having adopted all the peculiarities in which it differed from Dr Wood's. The main features of difference, the distinction of Statics from Dynamics, and the statical proof of the Composition of Forces; features which give a new form to the subject of Elementary Mechanics, may, I think, be considered as having been fully accepted by the University. In the last edition of the work (the sixth) I endeavoured to make it approach more nearly than before to what a standard work ought to be; namely, as I there stated, "that it should consist of the principal, or classical propositions of the science, and of the other propositions which the proof of these renders indispensable." In one respect I fear that I have carried this principle too far; namely, by excluding "the Mechanical Powers" from the book, as being not an indispensable part of the subject, but mere examples;

itself a New Edition of Dr Wood's Mechanics; but this publication does not at all diminish the force of what I have said. There is, in this "New Edition" scarcely a vestige, either of Dr Wood's general arrangement, or of his treatment of particular questions; for the modes of teaching every subject appear to me to be taken from the rival works which had been published in the seventeen years elapsed since the last edition (the seventh) of Dr Wood's Mechanics. For instance, every one of the peculiarities of the work which I have above noticed in the text is obliterated: the Division of Statics and Dynamics, the statical proof of the Composition of Forces, the analytical investigation of the Resultant of Forces, and, I think, every noticeable feature in which Dr Wood's rivals differ from Dr Wood, are adopted. It is still to be hoped that some member of Dr Wood's College will give the Cambridge world a new Edition of his Mechanics.

* The work has also been extensively used in Educational Institutions in other parts of the British Empire and in America.

and further, as being examples not scientifically classified, but received by blind tradition from the later Greek mathematicians. On these grounds, I excluded the Mechanical Powers from the Elementary Treatise on Mechanics, giving them in a more complete form in the "Mechanics of Engineering." But I might more properly have said that these "Mechanical Powers" have so constantly had a place in Treatises of Mechanics that they are to be deemed Classical Propositions in the subject; and though they are not a complete classification of the simplest Mechanics, they serve very well to point out the mode of dealing with most statical problems. With the exception of the Toothed Wheel, the Wedge and the Screw, indeed, the Mechanical Powers are included in the University list of Propositions for the Polloi; but I should propose still to make them part of the standard Elementary Treatise of Mechanics, as they stood in the fifth edition of my own work.

239 There is one part of Dr Wood's Mechanics which it would be desirable to retain, namely, the doctrine of the Oscillations of Pendulums. This subject is so important, both historically, and in its application, that it should be made a portion of our standard Elementary Mechanics. The student of that science ought not to remain in ignorance of the laws of such Oscillations, till he falls in with them, if it so happens, as examples of the Differential Calculus. In all the Editions of my Mechanics, I proceeded upon this conviction, and proved the properties of Cycloidal Oscillations by the Method of Limits; modifying, however, Cotes's demonstration. But in the last edition I have, I think, rendered the proof more simple by restoring it nearly to the form in which Dr Wood gave it.

In the scheme of Mathematical Studies which I shall afterwards offer, I shall guide myself by the considerations now stated.

240 With regard to Newton's Principia, the text itself of the work is, of course, our standard; and our students ought to be able, not only to give Newton's proofs, but to show, by their explanation of the various steps, that they have fully entered into the train of reasoning of the great author. Several members of the University (myself among the rest*) have published books containing the Propositions of several Sections of the Principia, and especially the First Three Sections. But those books ought only to be considered as comments on the original. In the standard course of the University, Newton's Text should be the work adopted. Such books as I have mentioned would enable the student to understand, explain, and, when it is necessary, fill up the steps of Newton's proofs.

241 I have said that a portion of the Principia may be included in our Permanent Mathematical Studies; although the greater part of the book can be read only by our higher Mathematical Students. I think that both the general practice of the University, and the character of the subject itself, would direct us to take the First Three Sections as this Permanent Portion, to be studied by all candidates for our mathematical honours. The remainder of the work may employ, along with other capital mathematical works which I have mentioned, the labours of our more advanced students.

242 In the subject of Hydrostatics, Mr Vince's Hydrostatics might formerly be considered as the standard work in the University, though never very well suited to such a place. Mr Webster's Principles of Hydrostatics, from its form and mode of treating the subject, appears to me very fit to be adopted as our Standard Treatise on this subject.

* First separately in 1832, and afterwards in The Doctrine of Limits in 1838.

243 Dr Wood's Elements of Optics is a work, excellent, for the most part, in the selection and demonstrations of its propositions, and deserves to be retained as our standard work on this subject. More recently, this subject has been treated analytically. So far as the analytical method has superseded the geometrical, I am obliged to say (though I believe that I myself, by College Lectures, may have formerly contributed to bring about such a change), the result has been very unfortunate; for in this subject especially, the geometrical method of tracing the course of reflected and refracted rays is highly instructive to the student in the earlier stages of his progress. I do not think the University ought to hesitate to made Dr Wood's Optics the standard work to be studied by candidates for honours, as an introduction to all other modes of treating the subject.

244 On the subject of Astronomy, the Treatise of Dr Hymers may, I presume, be looked upon as the one at present established in the University; and the work appears to me to be well fitted for this purpose. Perhaps the subject is too extensive to allow us to require a knowledge of the whole of it from every candidate for our honours; and both on this and on other accounts, it may be best to include only a portion of it in our Permanent Studies; and the same may be said on the subject of Optics.

245 The above works do not require a knowledge of the Differential and Integral Calculus; or if that Calculus be referred to in some places (as in some astronomical Problems), those are not essential parts of the subject. It may therefore be a question whether we are to admit the Differential Calculus into the list of Permanent Subjects to be required from all Candidates for Honours. But the fundamental principles of this Calculus are so instructive, and its elementary portions have now become so familiar to all mathema

ticians, that they should, I think, be a part of our permanent course. I would however confine this distinction to the parts which are strictly elementary ; and these I shall afterwards attempt to point out.

246 I may now recur to the objection which we have mentioned already (54), as sometimes alleged against the appointment of a standard course of study; namely, that the demonstrations of which it consists may be learned by rote; and to the answer which we made to this objection (55), that the student who had the demonstration in his memory only, and not in his understanding, might be detected by a few questions. This, however, cannot be done in any way so decisively as by a viva voce examination; and here we are brought again to the question, respecting a vivá voce examination; the balance of its great advantages, and its great difficulties, especially as regards the length of time which it occupies.

247 I believe the advantages of a standard course of study accompanied by a viva voce examination to be so great, that it would be well worthy of the expenditure of time which it would require. The time, indeed, which the Moderator would need to expend in this employment, would not be so great as they always did expend, till within a few years, upon the disputations in the schools; and would have the same advantages which that practice had, of bringing both Moderators and the Questionists before an academical public. It would suffice if each Questionist were examined vivá voce for an hour: two, three, or more, might be examined separately each day, or classes of three or four might be examined together for several hours; and the examinations, continued through the Michaelmas Term, might be extended to the usual number of Mathematical Honours which have been given of late years. But in order that these examinations might retain their interest and efficacy, they must have an influence in their

« ForrigeFortsett »