the difficulties of any one connected course of study, his thoughts are occupied in pursuing these detached novelties, and in considering which of them is most worthy of admiration, or in conjecturing which is most likely to receive honour. The result of such an occupation will probably be that he will know nothing well. He will ascribe an exaggerated value to those parts of his studies in which the new methods differ from the old. The conceit of a supposed knowledge of something which his predecessors did not know, will take the place of the satisfaction which he might feel from understanding what generations of thoughtful men before him have understood, or from following the intellectual processes by which real difficulties are overcome.

80 A too facile admission of new elementary works and new forms of old truths into our educational scheme, is likely to occasion a multiplication of such works, to the detriment rather than the advantage of our mathematical literature. For such works, produced on the first suggestion of some slight advance, fancied or real, in simplicity or generality or ingenuity, would not be likely to obtain any wide or permanent notice among the general mathematical public. Works so produced at a place of Education, might form a perpetual stream of transient local literature; and the students, in bestowing their attention upon such works, might be toiling on in paths held in no value in the rest of the mathematical world; and might be bestowing much labour on mathematical subjects, without approaching to any community of thought with the good mathematicians of their own and preceding times. In order to avoid such evils, I conceive that no book should be adopted into a course of education except by proper authority, and after mature deliberation. I shall afterwards venture to suggest the grounds on which such a choice should turn, and the nature of the authority by which the decision might be carried into effect.

81 It will of course be understood, from what has been said, that even when Elementary Analytical Treatises upon the various branches of mathematics have been selected and adopted in our educational course, they are not to supersede the Permanent Studies of which we have already spoken (17). Conic Sections, Mechanics, Hydrostatics, Optics, and Explanatory Astronomy, in their hitherto common form, should be mastered by every mathematical student; however he may afterwards study these subjects in the shape in which they have been presented by modern analysts. He will travel all the more securely in his analytical course in each subject, from having already gone over a part of the same ground, with the clear intuition which belongs to geometrical reasoning.

82 It may be remarked that the works which I have mentioned in Article 72 as "Capital Works," except Newton's Principia, are all by foreigners, and with the exception of Euler, by French writers of modern times. No English mathematician will be surprised at this; for the French mathematicians have undoubtedly of late been our masters and teachers. The pertinacity with which the English mathematicians clung to Newton's methods, and the mathematical controversies which soon after his time arose between Englishmen and foreigners, for a long time prevented his countrymen from adopting and following out the analytical generalizations introduced by his continental contemporaries. Yet it is not because we have no English works worthy of the mathematician's study, that I have mentioned none in my list, but because it appeared to me necessary to limit the list to a few works of which the eminent place in mathematical literature is clear and undeniable. I might have recommended the beautiful geometrical investigations of Maclaurin; many ingenious solutions of problems by Emerson and Simpson; many labours of Ivory, not

inferior in analytical elegance to any works of continental analysts. But this would have made the mass of subjects too large for a course of Education. The English mathematician will hardly fail to acquaint himself with these works, when he is out of the hands of his teachers. For the same reason I have not spoken of the mathematical labours of the Bernouillis, which form such remarkable points in mathematical history, or of those of many other great mathematicians. I speak only of Mathematical Education: and I am convinced that I have provided sufficiently for the mathematical progress of our best students, by placing before them the works already enumerated, as the highest subjects of their educational study.

83 If it be objected, that since I have allowed that the tenacious adherence to Newton's methods checked the progress of Mathematics in England, I shall discourage such progress by obstinately retaining his works as our Permanent Studies; I reply, that I do not require our mathematicians to stop with those works, but to begin with them, or at least to make them a part of their studies. Let our mathematical students, by all means, go on with their analytical teachers as far as they will and can; but they will not do this the better, for being ignorant of Newton; and as I have said, the works of their analytical teachers cannot discharge the educational office which our Permanent Studies, and Newton among them, are required to discharge. We have around us many instances that those who are most fully acquainted with Newton's works are most likely to go on as successful rivals of the foreign Analysts in the solution of difficult problems. Indeed, no persons in our own time appear to have studied Newton's works more carefully than Lagrange and Laplace themselves.

84 If it be said, that by beginning with Geometry we shall lose all chance of having a school of English

mathematicians able to compete with the mathematicians of other countries; I reply, that I do not believe this to be the case, because I believe such a mathematical education as I have described to be the one best fitted to give the student a complete understanding of mathematical processes; and therefore, the most likely to lead to a solid and extensive progress. I do not believe that men will make better analysts, because they are ignorant of geometrical mathematics, but the contrary. And I do not think it has been found that those who have exclusively studied analysis have been the persons to make the greatest advances in mathematical science in our own times.

85 But I reply further, that the use of mathematical study, with which we have to do, is not to produce a school of eminent mathematicians, but to contribute to a Liberal Education of the highest kind. I am, indeed, fully persuaded that the Mathematical Education which I have described is that most adapted to evoke the mathematical talent of the nation; and that among students so taught, we shall have a better chance of giving to great mathematical genius its full scope, than by involving them in discussions about elementary symbolical novelties. But even if I thought otherwise; if I thought that a course beginning with analytical generalities was the most likely to give us a celebrated School of English Analysts, I should still think that while such Permanent Mathematical Studies as I have recommended are most likely to impart the intellectual culture which belongs to a Liberal Education, they should be steadily retained in the seats of English Education.

Having thus considered the nature of the Permanent and of the Progressive Mathematical Studies which belong to a Liberal Education, I proceed to make some remarks on Classical Studies, as belonging to such an Education; and therefore under the same aspects of Permanent and Progressive Studies.

SECT. 7. Of Classical Educational Studies, Permanent and Progressive.

86 Classical Studies necessarily occupy an important place in Education, both as Permanent Studies which connect men with the culture of past generations, and as Progressive Studies which engage them in the speculations, discussions, and mental movements still going on among men. The former office more especially belongs to the literature of Greece and Rome. An acquaintance with that literature has been a leading character of all literary educated men in all ages. This study has educed men's apprehension of the powers of Language in their highest form, as we have already said; and has connected man with man, giving them a common acquaintance with standard books of history, poetry, philosophy and morality. There has also, as we have said, been diffused among classical students a knowledge of philology, by means of the grammatical and critical comments to which the study of standard authors has led. These effects have been more generally produced by the Latin literature, for Latin has been more generally read than Greek. The study of the Latin authors has never been interrupted among cultivated men. The language has always been known to such persons. For many centuries it was the language of a great part of the civilized globe; first, as the language of the Roman Empire, and then, as the language of the Western Church; and, till within a short time, of the whole literary world. Through this long prevalence, this language contains in its literature the works which have most influenced every age, up to modern times. The languages of many nations in modern Europe are mainly derived from the Latin, and those which are not so derived, are still much tinged by the mixture of Latin words and modes of speech. In English, in particular, this mixture is very large;