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 Ï 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 have studied Newton's works more carefully than Lagrange and Laplace themselves.

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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;

and the connexion of our language with the Latin is so intimate, that the reader who has no knowledge of that language will inevitably miss some part of the meaning of our best writers. In general, the study of Latin, as a portion of a Liberal Education, is directed mainly to the principal writers of the best times; for example, Livy, Cæsar, Sallust, Tacitus, Lucretius, Virgil, Horace, Ovid, Cicero. And a sound knowledge of these authors is, in truth, a sufficient educational basis for a knowledge of the Latin literature of all ages, and for a due apprehension of the influence which these great models of composition have exercised upon the vernacular literature of each country, and especially upon its poetry and criticism.

87 But a knowledge of the Greek language and literature is also necessary to complete this classical culture; both on account of the manner in which the greatest Roman writers were stimulated and formed by the example and teaching of their Grecian predecessors; and also, on account of the direct operation of the Greek writers upon modern thinkers and writers, ever since the revival of the study of Greek literature in the fifteenth century. In philosophy, the Roman works do little more than transmit to us the influence of Greek speculations: in history, Herodotus and Thucydides occupy a greater place in the thoughts of cultivated men than any Roman historians; and even in poetry, although the tradition of the Latin forms and style of composition has been more extensive and continual than of the Greek, the Greek classical writers have, in later times, been more diligently studied, and more warmly admired, than the Roman poets. No one can be considered as furnished with the knowledge, tastes, and sympathies which connect the successive generations of liberally educated men, who is not familiar with Homer and the Greek Tragedians, as well as with Virgil, Horace, and Ovid. These two great

families of writers, the Greek and the Roman Classics, form the intellectual ancestors of all the cultivated minds of modern times; and we must be well acquainted with their language, their thoughts, their forms of composition, their beauties, in order that we may have our share in that inheritance by which men belong to the intellectual aristocracy of mankind. The study of these title-deeds and archives of the culture of our race must be a permanent portion of the best education of men, so long as the tradition of such culture is preserved upon the face of the earth.

88 But though the classical writers are to be looked upon mainly as Permanent Studies, in their educational office, they are also the subjects of Progressive Studies in every age, and especially in ages of great intellectual activity. The full understanding of these writers implies views of the structure and relations of language, of the principles and significance of philosophy, of the origin and progress of states, which views, each age, borrowing much from its predecessors, moulds in some degree for itself. Ancient Philology, Philosophy, and History, are the subjects of progressive speculations. Those persons in our own time, for instance, who have most diligently studied these subjects, have been led to views which have in them a considerable share of novelty; and men's minds are still employed in eager endeavours to obtain a more complete and profound insight into the causes on which philological and philosophical and historical progress depend. The origin, growth, revolutions, and decline of languages, systems, and states, are now, as they have almost always been, matters full of interest for the classical student. A Classical Education would not be the highest education, if it did not impart to the student a share in this interest;—if it did not give him some acquaintance with such speculations as they are carried on in his own time, and enable his mind to