istic features and the most striking landmarks. He would aid the memory by dividing the subject into periods, each of which would have its distinctive character of progress, social and political, or of decline. The Histories of Greece and Rome are so intimately connected with classical reading, that they must be learnt a little more in detail; but the memory would be much assisted by these general views and the mind would be much enlarged. A few leading dates should be firmly fixed in the recollection, together with a few of those cardinal events on which the destinies of the world have turned; and thus even an average boy would be supplied with the lines and pegs on which to hang in its proper order such historical information as he may acquire hereafter. Geography might be treated in a somewhat similar manner, and there is no reason why a lucid explanation of the progress of ancient geographical knowledge, from the days of Herodotus down to those of Augustus, might not be made as interesting to intelligent boys as it would be instructive.

Besides the difficulties of introducing any change into the system of a great public school-difficulties which can hardly be overrated-one obvious objection to these proposals is that few schools possess masters capable of undertaking this mode of tuition. If this, indeed, were so, no greater argument for the necessity of the change could be adduced. But, in truth, the objection is not grounded in fact. Of the many accomplished men engaged in education, not all perhaps have a vocation for this method of teaching. But many with a little time for preparation and reflection would find that it developed in them powers of which hitherto they had not been conscious, and that it imparted a life and interest to their task which they had never before experienced. Nor would the effect be less powerful on the class. No 'perdricide' gentleman could in future imagine that the world had lost a Hume or a Gibbon because he had been forced as a school-boy to write bad verses. If such a lecture as we contemplate fails to rouse his curiosity and interest, he may be assured it was study of all kinds, and not merely Latin prosody, that he detested.

On Greek composition, which has attracted so disproportionate a share of public attention lately, and on other matters affecting the studies of the Upper Forms, we do not find it necessary to say anything at present. If the requisite improvements are made in the lower parts of the school, the Upper Forms, like the miser's pounds when the pence are properly cared for, may be left to take care of themselves.

But the portion of the Report which the Commissioners have most carefully elaborated and seem to consider the most im

portant

portant (though we are far from so considering it), remains to be examined. It relates to the studies introduced of late years into the curriculum of public schools in deference to popular opinion, and those further extensions which the Commissioners recommend. We shall treat these subjects much more briefly, not because we do not consider them highly important, but because till some improvement is made in the method of teaching the classics, there is very little room for any fresh studies, and if the fresh studies are pursued with no better method than the old, it matters little whether they are introduced or not. The Report proves to us by undeniable evidence that the foundations of our classical teaching are unsound, and till they are repaired we can take only a feeble interest in the completion of the upper story.

The first object of the Commissioners is to raise the study of mathematics and of modern languages to an equality of dignity with that of classics, and to this, as far as it is practicable, we see no objection. Any arrangements with respect to costume and other points of a like nature which can raise the masters of these studies in the eyes of the boys, appear highly desirable. To stimulate the more advanced and able pupils by prizes may be very proper-to allow the marks gained by a boy in the French and Mathematical classes to affect his promotion, as far as regards his place in his own form, is very easy; but his promotion into another form, where his classical studies and exercises are changed, can only be affected by his proficiency in classics. That the French and Mathematical masters should be allowed in their respective classes to arrange the boys in an order different from that of the classical school seems reasonable; and once or even twice a year to publish lists of the school arranged according to the order of precedence in these two departments respectively (Report, vol. i. p. 54), is a much better method of diffusing a spirit of emulation generally than the distribution of prizes, which attract only a few. But there are strong reasons why we should object to make mathematics a condition of admission to a great school, or to enforce the study afterwards with any very strong pressure. It is a fact which is not noticed by the Commissioners, but which must have been observed by all who have been practically engaged in education, that there is very great difference in the ages at which different boys become capable of fully taking in a chain of mathematical reasoning, and this quite irrespective of their general intelligence and capacity. We have known very clever boys who showed no taste, or rather no capacity, for mathematical study till a comparatively late period. Nor is this all. With the exception of a very few, who, like Pascal, exhibit a preco

cious

cious mathematical genius, boys are generally weaker in the powers of calculating and reasoning than in their other faculties. În no way is there so great a chance of overstraining the mind as by forcing on too rapid a mathematical progress; and even if the end is accomplished without damage, time has only been lost. Knowledge has been acquired prematurely at the cost of much effort, which might have been gained with ease when the mind had attained a greater degree of maturity. In confirmation of this we may quote the Commissioners' remark (vol. i. p. 26), that the public school men generally go up to the Universities much less advanced in mathematical attainments than the pupils of the new schools or of the great grammar schools, but that they often get ahead subsequently in the race.

It is very possible, however, that by an improved method of teaching, the utter inaptitude which some clever boys show for mathematics might be removed or at least greatly diminished. This point is important, but it has been little noticed; and though we are hurrying on to close our remarks, we must pause to make our meaning clear. The amount of relief which has been obtained by the simple expedient of applying to the elements of geometry the algebraic notation can be told only by those who remember to have painfully pored over the old editions of 'Simpson's Euclid.' The practical effect of this is to make a complicated train of reasoning at once intelligible to the eye, though the mind could not take it in without effort. Arithmetic is a shorthand for a similar purpose. It enables the mind by means of signs, which are purely arbitrary, to follow out a calculation which, if carried on in words, would be very laborious. The Roman numerals do this very clumsily; the Arabic numerals, with the Arabic notation, enable us to follow the operations of calculation without the least strain on the reasoning powers. All this an intelligent boy who had mastered the ordinary rules of arithmetic could readily understand. The signs of algebra are equally arbitrary; but while arithmetic deals with the signs of known quantities (figures) to discover the unknown, algebra deals equally with the signs of known quantities, and its own signs of unknown quantities, till it obtains the value of the unknown in the signs of the known. Thus the primary meaning and scope of algebra are made intelligible to the learner by introducing him to the science by the very steps which probably led to its invention. For instance, a question is proposed, which perhaps a clear-headed man could work out for himself in his mind, but which to an ordinary capacity is a riddle; by substituting some symbol for the quantity it is desired to find out, and then by performing upon that symbol the arithmetical operations

operations prescribed by the problem, the whole chain of reasoning is made intelligible. Hence is shown the necessity of learning to apply to these symbols the rules of arithmetic.* Without this explanation a lively boy thinks it as absurd to divide a by b, or to multiply x by y, as to divide chair by table, or multiply candlestick by extinguisher. Having hitherto surmounted all elementary difficulties in classics, he is perhaps more fretted by a lesson beyond his comprehension than a dull boy to whom all lessons are puzzles, and he concludes forthwith he has no 'taste for mathematics.' It is a question whether in many cases it might not be well to pass at once from the four first rules of arithmetic (when thoroughly mastered) to algebra. Some might object, at first sight, that this was proceeding to the superstructure before completing the foundation; but this is not so. Algebra exhibits the proof of the rule of which arithmetic gives only the unexplained statement. We remember to have heard an intelligent boy, at the end of a lesson in algebraic fractions, express his regret that the Rule of Three' had so needlessly embittered his early school-life.

To make modern languages a sine quâ non condition of admission to a public school would, we think, be unfair, because there is so great a difference in boys' opportunities of learning them. Some have been educated abroad; the children of the wealthy have had foreign 'bonnes' or governesses: and it would be hard indeed to exclude the son of a painstaking clergyman because his father has been unable in a remote parish to procure an instructor in French or German. At Marlborough, we learn by the Report, the study of French is combined with that of history. We should not augur well of the combination. Mr. Max Müller's suggestion that it should be enlivened with lessons on comparative philology (though we deprecate the use of fine names in proposing innovations) is more judicious. There is great difference in the machinery organised at different schools for French teaching, and the difficulties are many. A foreigner cannot keep order; an Englishman rarely possesses the accent. In some schools an English instructor acts in concert with a French one. There are obvious objections to such an arrangement; but we are glad to hear it works well. There is great difference also in the results obtained. In some schools, we find from the Report, there is a steady opposition to the French lesson; and as is very common

* Vide Elémens raisonnés d'Algèbre,' par Simon L'Huilier, Genève, 1804. This method, the author remarks, is especially useful for those to whom the study of mathematics is valuable rather as a mental discipline than as a special object of pursuit.

on

on such occasions, the omission of one duty is made the excuse for the non-performance of another. French is not cultivated because English is neglected, and the classics are too ill taught to allow the teaching of anything else (Report, p. 85). There is no attempt made to enforce attendance on the French master, and the French school has become a farce.' This should not be. It is scarcely honest. Let the French lesson be made a reality, or let it be abolished. Let it not be set up to satisfy public opinion, and then left as a sham. Let it not be disparaged and discouraged, and then the failure be quoted as a proof that the study of modern languages is incompatible with that of the classics.

The Commissioners plead very hard for the introduction of physical science as an integral part of public school education, with lessons that require previous preparation-marks for success and punishments for failure; but this is at least premature. The teachers and the class books have to be provided, and if so great an experiment is to be made, it should be made tentatively and cautiously. To awaken the taste for physical research in those minds capable of receiving the impression should be our first endeavour, and if this is accomplished, it is much-as much as in boyhood, we believe, can be accomplished. The comparative weakness of the dawning intellect and the unequal development of the several powers of the mind are generally left out of consideration in all discussions of this subject. At Eton, and some other schools, scientific lectures have been established-on popular and easy subjects, we presume, of course. The plan we think good, but the attendance should be made compulsory. As a principle, we would always avoid making any studious effort voluntary. It is not fair to add unnecessarily to a schoolboy's trials, and to force upon him the alternative of giving up a study that interests him, or of making himself ridiculous by works of supererogation. In the more advanced forms, scientific lectures might be given on a more systematic principle, and by degrees questions on the last lecture might be asked, and the form of a lesson more distinctly given. But whatever the success of the experiment, we do not contemplate the possibility of introducing science as a competing branch of education with literature into our public schools. To bring out the full powers of the intellect, it is necessary to give it full scope in one great field. There must be one principal subject of study, to which all others are subsidiary or subordinate. To strain at too much dwarfs the faculties, and dwindles, if it multiplies, the acquirements. The result is mere mediocrity.

Public opinion seems indisposed to make the cultivation of