principles of many of the most wonderful operations of nature, is by a diligent study of some of the most refined branches of pure analytical science.

And thus to form the accomplished man of science, it is highly useful as soon as possible to make the boy acquire a great facility in arithmetical and algebraical operations, and to accustom his mind to the rigid logic of Geometry. And in speaking of the preparation for an extended course of mathematical reading at the Universitic, I wish to lay great stress on a thorough acquaintance with Arithmetic, Algebra, and Euclid. The mode of teaching these is, in a great majority of schools, extremely imperfect, and this proceeds in general from the incompetency of the masters. To learn Euclid by committing the demonstrations to memory, is worse than useless, and unless the master can throw aside the book, and accustom his pupils to use their reasoning faculties in going through demonstrations and working deductions, he had better give up the idea of teaching them Geometry, and exercise their memories in a way that would prove more useful.

Facility in working Equations, early obtained and constantly kept up, will be most valuable to the future student of Mathematics.

Great ingenuity is often required in the solution of Equations, and if well chosen examples are put into the hands of the pupil he may be made to work many that will afterwards occur in the course of his reading.

The Cambridge course is now of so extended a

nature, that it is almost impossible without intense and sometimes injurious application for a man but slightly prepared when he begins his academical course, to obtain very high honours. It is better, however, to have no preparation, but the common one of Euclid and Algebra, than a bad one. I mean, one that is old fashioned, or not obtained by the study of Cambridge books, because bad habits will be formed, and attention will have been given to things which are considered of little importance in the University. I am not contending that the Cambridge system is perfect, but it certainly does embrace all the most important branches of pure Mathematics and Natural Philosophy; and if a man wishes to prepare for Cambridge, it would be absurd not to use the best means in his power to get as soon as possible into the system pursued. It not unfrequently happens that a man, who might have done very well, is discouraged from reading for honours by finding at the end of his first year that he has only just learnt how to read the subjects. If a youth, before going to Cambridge, were well prepared with Euclid, Algebra, Trigonometry, Conic Sections, the Elementary Parts of Mechanics, and Differential and Integral Calculus, he might look forward with good hopes to a high place in the Mathematical Tripos. It is not at all an uncommon thing now for Freshmen to come up possessed of all the facility of men who have been two years at College, who came up with no more than their first-year subjects.

The competition for Scholarships and Fellowships is now so great, that it becomes well worth while to ensure success by much previous discipline; and the consequence is, that the University course becomes more extended, new subjects are introduced to provide employment for the men who before they come up are well versed in the subjects which fifteen or twenty years ago formed the largest part of the University reading.

ON GREEK AND LATIN COMPOSITION.

A very distinguished scholar who excelled all his contemporaries at Oxford, particularly in Latin and Greek Prose Composition, told me that in reading for the Ireland scholarship (which he won) he spent less time in practising composition than in committing fine passages to memory. This practice of learning by heart is particularly encouraged at all the public schools; and for this reason, even the most idle must learn a little; for, a repetition cannot, like an exercise, be done by proxy. One of my friends won a prize at Winchester by preparing in the half-year ten thousand lines, and repeating them in eight lessons. In the Charter House, pupils were not entitled to a high remove till they could carry on any quotation in the Odes of Horace. At Dr. Valpy's, one of my friends used to repeat every Saturday morning one hundred and seventy lines, after which he was allowed to leave school for the day. The proficiency of Dr. Butler's pupils in composition was

K

ascribed to a similar system. In short, I need not multiply examples, because I do not remember an instance of one good scholar who had not committed much of the finest authors to memory. This practice, however, if adopted at all, should be carried to a considerable extent; for the words and phrases so learned will insensibly obtain a preference in composition, therefore a small number of lines got by heart will probably cramp the style more than if the student were compelled with less readiness to select his words from a larger store which has only been impressed by construing.

To give my own opinion, the practice is very good, but admits of improvement. For it has two advantages, each of which may be better attained in a way rather different, though, I must allow, less readily available to the masters of many pupils. The flow, the rhythm, the fine touches by which particles aid the effect, the idiomatic niceties which alone separate the sublime from the ridiculous, and give force and bold relief, are all too subtle for rule, and can only be learned by models, formulæ, by that practice of the ear, and moulding of the taste, that repetition is found to afford. Repetition supplies also some of the advantages of the spoken language: it gives copiousness and freedom of expression. But, though it makes both the full man and the ready man, as Bacon says of Reading and Conversation, it does not make the exact man. Some modification of this exercise is required for accuracy, for evading the use of vague and rhetorical phrases instead of being “ verbis

tenuis cautusque serendis;" I allude to the practice common to boys who read Virgil, and older persons who read Pope, who seem as if their words stuck together, and they could not use them singly. This literary patch-work, whether in prose or verse, must at any cost be discouraged. Our pupils must be made masters of their words, and not the slaves. They must learn to form clear and well-defined ideas, or mental pictures of what they would express, and consider that in copying these pictures from "the tablets of the brain," like skilful painters, they must not be satisfied with any rough, stencilling process, but study all the effect of the minutest and most delicate touches. They must be taught that they had better have a stiff style which expresses with difficulty than a loose style which scarcely expresses at all. Freedom and facility in writing, as in painting well, is attained only, as Sir Robert Peel elegantly expressed in a quotation from Sir J. Reynolds, by great industry and study at first, though "the pictures thus wrought with such pains, now appear like the effect of enchantment, and as if some mighty genius had struck them off at a blow." As this is my opinion of the danger of our style becoming more that of a servile parody, than of refined imitation improving upon the original, and as I am at the same time desirous of securing the great aid to good taste which I consider to result from perfect familiarity with the finest models of Classic thought, I would recommend

Sir Robert Peel's Speech to the Students at Glasgow.