but as the security holds good until the loan is fully repaid, the loans are not called in until they are no longer required, and sufficient deposits for the working of the bank have been subscribed locally. When a loan is repaid, the amount is issued to another approved bank, so that the loan capital is kept in circulation.

As in England, the progress made in the different counties is far from uniform. In some, agricultural education is becoming well organised; in others there is much room for improvement. It is of interest to note what the experience of the Department has led it to regard as the chief conditions of success: (1) a small County Committee, devoted to the work, who, having settled the details of their schemes at the beginning of the year, promptly set about putting the schemes into operation; (2) an energetic and capable secretary; and (3) the appointment of numerous small influential and active local committees to look after the promotion of the schemes in each district. Where progress is slow, it is said to arise usually from the fact that the County Committee is too large; the members attend irregularly and only when the interests of their own district are likely to be affected; attempts are made to have the schemes reopened and revised at a time when they should be in full operation; local initiative is wanting; and too much reliance is placed upon the central authority to settle local difficulties and to push the work forward.

English Literature in the Secondary School

virtues. There is the infinite "realm of beauty, the kingdom of ideas, inspirations and elevating ideals, and this belongs in our modern school to the teacher of English. Man must be studied-socially through his long and thrilling history; intellectually, spiritually, through the great literatures of the world. And for English boys and girls, the English literature is surely the literature par excellence. The importance of this subject, therefore, must be conceded; some right method must be found of teaching it; it is the focus of all our secondary education, the source of its radiance, the spirit which will transform a merely technical training into a living and pregnant culture.

Now it is freely admitted by earnest teachers of English that the results of their work do not give them the satisfaction for which their energy and enthusiasm entitle them to look; that in the important matter of self-expression in terse and comprehensible English their pupils leave them lamentably deficient; that, in spite of certain attainments in formal grammar and language, they have no respect or love for their native speech; and that, as a result of the usual method of introducing them to our masters in literature, they too often leave them with no power to appreciate the distinction between great writing and inferior scribble-very often with a positive disgust for Shakespeare or Scott, or what other author may have been tortured before them in their so-named English lessons. It is appalling to observe the character of the reading of the English schoolboy in those important years which follow his school-days. His literature has become a mere pastime, and nothing more; he reads the cheap newspaper, the monthly magazine, the latest novel, but he reads them all with equal lack of literary vitality, because he can read them easily and mechanically. He does not go to literature for stimulus or for thought; he uses it for his vacant He can read, but he cannot think; consequently his literature must be "light" and must not appeal to powers which he has not. Do we then train our boys and girls in English so that they may the more easily skim the average modern novel or magazine? Is literature but an anodyne for their vacant hours?

Surely this indifference to the charm of true literature, this attraction for the tinsel and repulsion from the gold, is a fact of most sinister significance to teachers. It is surely the condemnation of our methods -the condemnation, too, of the spirit of much of our teaching of English. We have been, indeed, far too practical in our teaching. Even in our lessons in composition and language this is so; we have aimed at clear, not often at beautiful English. And the result was inevitable; we have instructed, but we have not inspired. The aims of literature are æsthetic and ethical, but these have been largely lost sight of in the undue attention which has been paid to details comparatively unimportant, and often inessential. The important things concerning Shakespeare, for example, are not the dates of his birth and death, not the

peculiarities of his grammar, not the philology of his obsolete words; the interest in these matters should be kept strictly subordinate. The real issues, the vital matters, are those which give life to literature. Has it thrown light upon the meaning and mystery of life? Has it helped us to know mankind better? Has it enriched our minds with beautiful images, and so enlightened us about any of the myriad threads in the tangle of human destiny? If a writer like Shakespeare has not interested us in the workings of his great mind upon such matters as these, we have been to him in vain. Is it impossible that boys and girls from fourteen to eighteen years of age can be given such a glimpse of this as will ripen in later years into that love of the highest in literature which is the joy of life?

The difficulties of the teacher of English are many. One arises from the fact that he is in many cases not a teacher of English at all, but a teacher appointed for some quite different purpose. The disadvantages of this arrangement are obvious enough in the case of any other subject, but we must insist that they apply with equal force to English. In no subject is it more important to have the enthusiast and the specialist. Again, teachers of English have not sufficient freedom; they have been harassed by foolish examinations, and by the demands of a commercial or technical curriculum. Well-our answer is: they must have freedom from all conditions that paralyse their individuality. It is through the literary work that the teacher can bring his most powerful influence upon the character of his pupils. How foolish, then, to prescribe for him a weapon which, however useful to another, he has not "proved" by his own experience.

And still again, the teacher of English literature never knows how much (or rather, how little) he may expect his pupils to know when they reach him. He ought to be able to assume at least four elementary acquirements. Even the boy or girl from the primary or preparatory school might be supposed (1) to have the power to read clearly and without hesitation; (2) to be able to write a simple story in readable and grammatical sentences; (3) to have the rudiments. of English grammar, including easy analysis, firmly and usefully fixed in his mind; and (4) to have their minds stored with simple classic poetry, and familiar with some of the best novels which are within their range. How rarely these acquirements can in any real sense be presumed we are only too painfully aware. Yet the teachers in primary schools surely aim at this very moderate ideal, and we would suggest to them what we urge upon teachers in the higher schools and institutions, that the literature should be the focus of all the English teaching-that they should let their lessons in grammar and language be auxiliary to the lessons in literature, and that the composition themes should always arise from the matter read by the class. Of course the lessons in history, geography, science and so forth provide exercises in composition too, but the English required for such composition calls for very little expression of the pupil's own

individuality, is indeed dead language; good English, with life in it, is what we want; we can only hope for success in such a quest by using the masters of English as our models and our touchstones. We insist, therefore, that all reading-books should be classics, or a least well written. Inferior verse and empty doggerel must not usurp the place of true poetry. Above all, the teacher must have a literary conscience of his or her own. He or she will then send up to the higher schools boys and girls who can examine a simple poem for themselves, and read a novel of Scott with comprehension and delight.

These steps gained-and we must not proceed until they are gained, even at the cost of a year or two of secondary school life-our next endeavour must be to open up the country in which a few healthy settlements have been made. We must widen our conception of literature. Just as the teaching of history begins with isolated tales, and passes on later to an attempt to trace the continuous evolution of events, so the teaching of literature, which begins with the study of individual poems or tales, must lead to the study of literature as a whole. The significance of any one book like Addison's Spectator cannot be fully appreciated until it is correlated with other books and with general history. The full meaning of a book is only perceived by those who see it occupying a definite position in the growth of the human intellect, who know the circumstances of its birth and the environment on which it throve. No book, in short, is an isolated, unexplainable phenomenon. It is, as Sir Leslie Stephen says, a by-product of the social and intellectual conditions of the time. The appeal of certain individual books to our hearts and minds is no doubt largely independent of their historical setting; but the instances are very few indeed when the intellectual enjoyment of a book is not greatly increased by the ancillary knowledge which the history of literature alone can give us.

Now, in teaching history we attempt the very difficult task of unfolding the growth of the English nation to boys and girls. We try to show that King Edward I. is not a mere soldier who conquers Wales and fights the Scots; that he is a link in a long chain of men whose doings have led to our being what we are. Why should we treat literature in a manner wholly different? Why should literature not be studied historically? In history we study the deeds of great men, and those of many little men, and we trace the causes and circumstances of as many as we can. We would have literature also studied in this spirit. It should be studied along with the contemporary history of which it is a part. It has been too long considered as the reading, more or less minutely, of a few disconnected and 'select" books. Why should this subject, upon which so much of the real happiness and worth of our pupils depend, be the only one in our curriculum to be treated haphazard and unsystematically? Great books, like great battles, must be placed in their true historical perspective.

Along with the history of literature, we must attempt to judge books from the highest artistic standard. We must inquire frankly into the strong points and the weak points of every book we read. We must seek-very carefully of course-to develop the faculty of criticism. Teachers have been a little too squeamish in this matter; they have feared to bias the young minds entrusted to them, and the result has been a lack of actuality, of colour, of life, in the teaching of literature. But we must remember that the great thing for us, the one result worth working for, is to send our pupils to the great books to read, to ponder, and to enjoy for themselves. How can a teacher do this except by revealing the grounds of his own enthusiasm? We want more attention for the essential and wider questions, much less for accessory and comparatively trivial matters. Our method must be, on the whole, extensive, and not intensive; the pupils must do a great deal for themselves, and out of love for their book. To spend a year, or even a term, upon a play of Shakespeare is preposterous; it is calculated. to make the name of Shakespeare nauseous in the minds of our pupils as long as they live. Shakespeare should be known, but not dissected; he must be enjoyed or left entirely alone. We recommend, therefore, much reading, with plenty of criticism by the teacher and by the scholar.

And on this point of reading we would urge in a parenthesis that the teacher should himself read a great deal to his class. More meaning is often given to a poem by a good teacher at his first reading of it than can be gained by an hour's minute study. How otherwise can he convey the spirit of the piece?

We do not wish to appear to encourage slipshod and desultory reading. That must be avoided on every account. No book should be left until its main purpose is apparent, until the method by which the author has arrived at his goal is equally clear, until we know the principal characters and the most noteworthy beauties in it. This is not obtained by submitting the text to microscopic examination. The exhaustive process should be applied to a few short pieces only. It may be applied to certain select passages of Shakespeare, to Milton's shorter poems, to Gray's poems, for example. Much power in understanding poetry is gained by a thorough study of such a poem as L'Allegro or The Progress of Poesy. But let us choose a few pieces only for this complete analysis, grammatical, philological, antiquarian, and so forth. For the most part we (and our pupils with us) must read to enjoy, must seek for the heart before we discuss the clothing; and authors should be studied for their own sake, and for the sake of their " criticism of life." It is only when literature is studied in this spirit that it becomes the absorbing interest of school life.

We plead, then, for the recognition of English literature as the nœud vital of secondary school life; we plead for its study on a historical and a living basis; we urge teachers to lay every stress upon the personality of the great writers, to criticise them and their works

in the broadest and fullest sense. How many interests spring from the thoughtful study of a single play of Shakespeare! How instructive it is to be able, when reading Twelfth Night, for example, to recall The Merchant of Venice and The Tempest, to note the different tones of these, to estimate what these differences meant in the experiences of Shakespeare's mind. What is comedy? What is humour? What is romance? What is justice? Is Prospero's view of life the final one? What is the significance of Caliban ? What does Shakespeare mean by his picture of Malvolio? A hundred questions throng the teacher's mind, questions of living (and, consequently, growing) interest, as he reads these plays. And let him beware of seeking to answer any of them in precisely cut definitions! They are never answered, because they are a part of the mystery of life itself. Such questions and such problems are the life of literature. It is they which constitute its perennial interest. It is the presence of some one or more of these mysterious questions that makes enduring literature. And the teacher must somehow or other convey this to his pupils.

Yes, everything depends upon the teacher, upon his knowledge and love of literature, upon his humour and sympathy, upon his personality. Without these, and without the power on his part to read well to his class, the best-thought-out method for the teaching of literature will fail. With these, results will be obtained which no examiners can measure or appraise. Our pupils will love literature as the melody of humanity, will be able to discriminate good books from bad, and become as eager to imitate a good piece of composition as they are to repeat their chemical experiments.

Unconventional Lessons in Mathematics

Graphs

By E. M. Langley, M.A.

FOLLOWING the selection of a writer previously quoted, we take the equations x2+ y2=a2; xy=c2; y2=4ax, y=10* as those with whose graphical treatment a boy should be familiar.

After the form of the corresponding curve has been in each case roughly ascertained from numerical values of co-ordinates, the methods for finding a number of points is to be as geometrical as possible, and the treatment to be such as to allow of easy extension to curves of the same geometrical properties whose equations are more complicated.

=

In the present paper xy c2 and y2 = 4ax have been taken as having their equations of the greatest simplicity

=

=

For ▲ MAQ ▲ KPB, and ▲ NQB Δ ΗΑΡ.* Hence, if P is one point on the graph of xy = c2, Q must be another one. Hence, if one point has been found whose co-ordinates satisfy the equation xy = c2, any number of others-Q1, Q2, Q3... -may be found by_ruling through P a succession of lines A,B,, A,B, AB, &c., and taking on them AQ1, A2Q2, AQ3 equal to PB1, PB2, PB, .

Ms As M2 AM, Aj M2 AM,

FIG.

3.

The bisection of the tangent at its point of contact follows immediately from this construction. Hence the tangent at (h, k) must make intercepts 2h, 2k on the axes. Its equation must therefore be

The use of brown paper triangles to cover triangles HAP, KPB, and then, after shifting, to cover triangles NQB, MAQ, affords a method for enabling the gist of the above proof to be easily remembered, and is not to be despised, though it may savour of the kindergarten. Compare the method of proof with that of Euclid's I. 43. Compare also another construction for obtaining any number of points on a hyperbola depending on the truth of I. 43, described in SCHOOL (November 1905, Fig. 3, p. 173), and quite suitable for elementary graph work.

B

A

FIG. 4.

Let P be a fixed point, AB any straight line passing through it and cutting the axes in A, B. Complete the parallelogram OAqB. Then the locus of q is a curve congruent with that found by the previous construction. For if we take Q on AB such that AQ= PB, and join Qq, the triangles OPB, qQA are congruent, and hence Qq is always equal and parallel to OP, which is fixed. In fact, each point on the new curve is reached from one on the old one by a step equal to OP. The point p corresponding to P is on OP produced. If the terms centre and asymptote have been introduced already, it may be pointed out that P is the centre and the parallels through P to OX, OY are the asymptotes. If the co-ordinates of P are (h, k) the equation to the new curve must therefore be (x h) (y - k) = hk. Reversing the steps here taken, we see that, given the equation xy kx hyo, and re-writing it (x − h) (y. - k) = hk, it may be constructed by marking a point (h, k), drawing any number of lines like AB through it, and completing the parallelogram BOAь. The curve could, of course, be plotted by the construction previously given if the asymptotes x = h, y = k be first drawn and the point (2h, 2k) taken as the fixed point p.

Any equation such as xy- kx hy + q = O may be treated by the first method by reducing to the form (xh) (y — k) = hk q, determining one point numerically, and using x = h, yk in the place of ΟΧ, ΟΥ.

H X

The successive positions of M, and therefore of P, can be taken as close together as desired. If OH = = C= HK, x2 the equation is y = с

Since MP intersects OK at a point E such that DE is parallel to OX, the point M may be omitted and the

K