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pose, it might be desirable to remove it out of the fifth into the fourth year, that it might come about the same period as the Classical Tripos; but on such details of this scheme I shall not now enter.

280 If it were thought advisable, attendance at the Lectures of some or other of the above Professors might very reasonably be required of those who were not Candidates either for Classical or Mathematical Honours; and in this manner the general education of the University would be materially improved. I believe that in Oxford, in some at least of the colleges, a rule of this kind is acted upon.

281 In order further to assimilate the General Tripos to the Mathematical and the Classical Tripos, two Medals for General Science might be established, to be given to the first and second prizemen. I will venture to say that if such a General Tripos as I have described were established, funds for providing one or two such medals would be found, without burthening the University chest. And I think it very likely that, in such case, the merits of candidates shown in this General Tripos would be taken into account, as well as their places in the Mathematical and Classical Tripos, in electing Fellows, and in other appointments both within and without the University.

282 It may perhaps be suggested that the encouragement afforded, by such a scheme, to the cultivation of the progressive sciences in the University would be more complete, if we were to establish a General Scientific Tripos without making it a condition that the Candidates for its Honours should previously be declared Junior Optimes. But in order to estimate the value of this suggestion, we are to recollect what was formerly said, of the necessity of Elementary Mathematics, as a permanent element of a Liberal Education. The sciences which we have mentioned could not for this purpose supply the place of the Mathema

tical part of our University Studies. Moreover, the sciences themselves would be more fully understood, in consequence of the steadiness of thought and clearness of conception which the study of Mathematics promotes. A student who should distinguish himself in the examination in Science, after obtaining a Junior Optime's place, would be unlikely to have acquired his knowledge of science in a superficial manner, or as a matter of memory merely. And in order to see how little discouraging the requirement of the previous step would be, we are to recollect that we are supposing the qualifications of a Junior Optime to be clearly defined and limited, so as no longer to demand an indefinite and doubtful course of reading. The mathematical studies which such a step would require, would leave time, throughout the student's career, for attending the lectures of the Professors of the Sciences, and for cultivating in other ways the knowledge which the General Scientific Tripos would call into play.

283 How the examination should be arranged with regard to the union or separation of the different sciences, would be a matter for deliberation, if the general design of establishing such an examination were once taken into consideration with a view to its adoption. The main purpose of the present volume being directed to other parts of the University system, I touch briefly upon this; being only desirous of showing in what manner some of the evils often complained of as existing in the University may, perhaps, be remedied.

284 Besides the physical sciences, there are other branches of human knowledge which naturally offer themselves to our consideration, as belonging to the Higher Education of men in our time; other languages and other histories, both ancient and modern, besides those of Rome and Greece; and Comparative Philology, which I have already mentioned; and also those which are sometimes described as the Moral and Intellectual

Sciences; or as provinces of Philosophy; for instance, the Philosophy of the Human Mind, Moral and Political Philosophy, the Philosophy of Science, the Philosophy of History, the Philosophy of Language, and the like. These are subjects which ought to be actively cultivated at Universities; and it is to be hoped that there will always be at the English Universities persons who will make these and the like branches of knowledge the subjects of the labours of many studious years. It is desirable that our Students also should have their attention drawn to some parts of these subjects; but in what manner this is to be done, so that their minds may be led to think steadily, clearly, and rightly on such matters, is a 'more difficult question even than the like inquiry with regard to the kinds of knowledge already spoken of. Our Universities should furnish lectures in these branches of philosophy, as well as in those other departments of knowledge; but in them as in those others, lectures, even if delivered by highlygifted men, may find scanty audiences, especially in an atmosphere saturated with examinations. In these subjects too, as in those others, the influence of examinations may be tried; and this may be done with no inconsiderable success, as I can testify from my own experience. But in these subjects, still more than in those others, examinations are a very ineffective machinery for evoking philosophical thought; and the relation which examinations must bear to lectures, so that the effect may be salutary to the mind, is a problem of no ordinary difficulty.

CHAPTER IV.

PLAN OF A STANDARD CAMBRIDGE COURSE OF MATHEMATICS.

SECT. 1. Permanent Mathematical Subjects (for Junior Optimes.)

[Since the first edition of this Work was published, the University has established a standard scheme of the more elementary portions of Mathematics, namely, those portions which are required of Junior Optimes. See Part II. Sect. 5 of this book. Also Mr Harvey Goodwin has published An Elementary Course of Mathematics, the design of which is to include such portions of the science as belong to this scheme. Of this book I have spoken in the Second Part. I have moreover myself published Conic Sections, their principal properties proved geometrically. I have also published a new edition of my Elementary Treatise on Mechanics. I have in Part II. explained the reasons why I consider the course which this Work follows, more suitable to an Elementary Treatise than Mr Goodwin's. I have also published Newton's Principia, Book I. Sections I. II. III. in the original Latin, with explanatory Notes and References. As I published these works in order to embody the plan of a standard Course of Elementary Mathematical Subjects which I proposed in the former edition of this work, it will not be considered strange or presumptuous that I should introduce them here. 2nd Ed. Part I.]

(1) ARITHMETIC.

Mr Hind's Arithmetic, in the later editions, appears to me to be drawn up in such a manner as to be suited

for use in Schools for those who are intended to go to the University. It includes the use of Logarithms, and the Mensuration of various figures (Triangles, Circles, &c.), which I have spoken of as desirable appendages to the parts of Arithmetic usually learnt at school.

(2) ALGEBRA.

Dr Wood's Algebra may still be considered as marking the extent to which this subject should be read by the common student. In reading the First Part of the work the student will probably at first need additional explanations and examples, which he may obtain from many works in common use. In the Second and succeeding Parts the subject admits of developements much more extensive than Dr Wood has given; but still this work may be considered as the Standard of our Algebra, excluding its recent progress*.

(3) PLANE TRIGONOMETRY.

The work most worthy of being made our Standard work on this subject appears to me to be Legendre's Géométrie, which includes Trigonometry, both Plane and Spherical, and contains a few Notes which may be looked upon as classical in mathematical literature. There is an inconvenience, however, in his exclusive reference to the French graduation of the circle. The

* Mr Lund, in his last edition of Dr Wood's Algebra (1845), has very properly kept his additions distinct from the original text by a difference of type. He has omitted the Second Part of the Treatise altogether, which I cannot but regret; for that portion of Dr Wood's book represented very well the General Doctrine of Equations as a long established part of Mathematics; whereas Dr Hymers' Treatise, to which Mr Lund refers as replacing this Part, belongs to the Progressive Mathematical Studies of the University.

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