enter the school in the lowest Form. The great majority come in from the elementary schools at the age of 12-14. Hence what I have termed the "third year " is really the first year so far as they are concerned. This is the case in most schools of this type, and is a standing difficulty to teachers of every subject. I omitted to mention it, as I considered it to be a fact familiar to all who are engaged in secondary education.

Prof. Armstrong, by a curious interpretation of what I actually wrote, accuses me of a belief that children cannot reason. His belief is "that we simply do not know what young people are capable of, and that we must not allow ourselves to be hampered by preconceived notions." After expressing his agreement with Prof. Perry "that a boy of 13 ought to be far advanced in the calculus," he proceeds to advise an audience of teachers as to a method of obtaining a knowledge of what children can do: "Consult the works of Captain Marryat as to what children can do, for his stories are not entirely the work of his imagination, but based on solid fact." Is this the "heuristic method" of child study?

(2) "The value of Nature Study as a preliminary subject is much exaggerated. It is important that there should be no misunderstanding on this point." Evidently Prof. Armstrong speaks here from experience; otherwise he would not be so positive, but one cannot help comparing his experience with that of Prof. Miall in England, and that of Prof. Jackman in America. If he would again refer to my preliminary remarks, he would see that I mention that the time spent on Science in a secondary school is short, and that therefore the subject must be related to other branches, especially drawing, mathematics and geography. Nature Study lends itself admirably to painting and designing. It serves as an introduc

tion to geography, and affords concrete examples in arithmetic. Would Prof. Armstrong prefer to see the balance rather than a plant form used as the basis of a design? And will he, as a member of the Consultative Committee, urge the Board of Education to withdraw their circular encouraging Nature Study in primary schools?

(3) Prof. Armstrong advocates the use of the balance "from the infant in arms and kindergarten stages upwards.' He would like Kipling to write "a song with a refrain of ' Weigh, weigh, weigh!' which could be hummed to and sung by girls during their science lesson." I am willing to admit with Prof. Armstrong that weighing is of great importance, and that it ought to be introduced as soon as it conveniently can. For the purpose of connecting measurements with arithmetic and geometry, as my colleagues and I have been attempting to do, we find that the measurement of lines and angles is of greater importance. For the purpose of teaching approximation methods in arithmetic we have found that measurements of length, area and volume are at least as well adapted as measurements of weight.

With Prof. Armstrong's remark that," if people learn to weigh things, they will perhaps in time learn to weigh opinions," I totally disagree. When he speaks on the subject of Chemistry, I am prepared to listen with due respect, but when he wanders into psychology I feel at liberty to have a different opinion.

Intermediate School, Cardiff, March 11th, 1901.

there should be no difficulty in eliciting the definition that a measure or factor of a number is any number that will go into that number exactly. Now write on the blackboard the number 36, placing underneath all the factors of 36 arranged in order. The factors should, of course, be elicited by questions. Inci. dentally it should be pointed out that the numbers go in pairs, viz., 1 × 36=36, 2× 18=36, &c. Do the same with the number 48. The blackboard then appears thus:36

:

48

A question will then at once elicit the G.C.M. or H.C.F. The lesson must now be "rubbed in" by such questions as:— Why is 6 a factor of 48? Why is 6 a common factor of 48 and 36? Why is 12 the H.C.F. or G.C.M. of 48 and 36? Why is 8 not a common factor of 48 and 36? Why is 12 the greatest common factor of 48 and 36? What is the II.C.F. of 27 and 45? &c., &c.

The boys should then work out, exactly in the same way as on the blackboard, the G.C. M. of 108 and 72, and of 81 and 108. The measures, common measures, and G. C. M. of 48, 72, 108, may then be worked on the blackboard, which would then present the appearance:

A. ABBOTT.

A Method of Teaching Greatest Common Measure. IT is difficult to get boys to grasp what is really meant by Greatest Common Measure, or Highest Commor. Factor, and they fail to see when it is necessary to make use of them in working problems. Perhaps the following method of teaching G.C.M. may be found useful. After a few preliminary remarks and questions as to what a factor or measure of a number is,

88

What is the duty of an Assistant-Master? YOUR Correspondence columns have already assisted me on more than one occasion. I should like, with your permission, to raise a question of the highest importance to assistant-masters and mistresses, with a view to elucidating principles which may enable men in my position to act, should the necessity arise, in consonance with the canons of conduct which meet with the approval of all high-minded men and women.

I am painfully conscious of the fact that when a difference of opinion actually arises between a headmaster or a headmistress and an assistant, that what the man of science calls the personal equation introduces into the discussion a disturbing factor of a very grave kind. If, by means of this letter, I could raise a discussion in your paper, I am sure that it would be of the greatest benefit to many assistant-teachers who, actuated though they are by the best motives, feel, when the actual time for discussion comes, that it is mere presumption for them to oppose their views to those of the "head." The assistant is, I also know, apt to be weighted in the conflict with the personal consideration that he may jeopardise his future prospects by any appearance of independence, and, even at the cost of principle, he may, in order to keep his post, act in opposition to his real convictions.

The difficulties I have in mind are most likely to arise in connection with discipline, moral tone, the relative importance of work and games, and kindred problems. Is it necessary for an honest assistant, as soon as he finds himself in disagreement with the headmaster on questions of these kinds, to resign, or may he take refuge in the thought that the responsibility is the headmaster's, and that, despite his own opinions on the subject, he ought to carry out orders he believes to be wrong and support measures he believes to be inadequate? It is almost unnecessary to add that I recognise fully that the headmaster, as a rule, is even more sensitive of the honour of his school than any one of his assistants. But while human nature is what it is, the capitation fee is likely to cause a bias in the mind of the "head" which is absent from that of the assistant. I refrain from recording recent experiences of my own which, though they prompt this letter, have nothing to do with the important principle involved. I enclose my card, but prefer, if I may, to sign myself

I HAVE been asked by the Secretary to the Kiel Holiday Course to undertake the distribution of their prospectus to the leading educational papers in England.

I attended last year's course and found it most helpful. It is arranged for German teachers-I was the only English-speaking student there-hence it has the advantage of taking the more advanced student straight to the centre of German thought and interests. Such lectures as those of Prof. Titius on 66 "Ethics," Prof. Baumgarten on "Pestalozzi," Prof. Matthaei on the "Art of Engraving in Germany," as well as many others, were invaluable as a stimulus to intellect and sympathy.

Kiel is a most pleasant spot in the hot July weather, its harbour being a constant source of refreshment as well as of interest.

Royal Holloway College, Egham, March 18th.

E. M. CUNNINGHAM.

tances.

The Social Position of Assistant-Masters.

I SHOULD be very much obliged if you would give space in your columns to a grumble concerning the same matter as that alluded to by your correspondent, "A Cambridge Man," in the last issue of THE SCHOOL WORLD, namely, the undeserved social inferiority attributed to assistant-masters. Surely, as your correspondent well remarks, we might be given an opportunity of proving ourselves to be desirable and worthy acquainIt would seem our ideas are never to be influenced by feminine society, our lives (dreary enough, some of them!) are rarely cheered and brightened by any of the thousand-and-one "little attentions" which cost nothing, yet are worth so much. For my own part, as a young member of the profession, I must confess to a feeling of utter disgust at the way in which the mere assistant-master "is set aside, slighted, and sometimes even actually insulted, by those under whose roof he lives, and for whose good he spends his best energies. I fear my own case is but one of very many; but a few lines from me seemed a necessity, if only to cordially thank "A Cambridge Man" for his stout championship of the rights of all those who, like myself, are proud to sign themselves

No. 13.-English Essays written to Skeleton Provided.

It was announced in the March number (p. 120) that the result of this competition would, if possible, be given in the present issue. The large number of essays received has, however, made it impossible for the Examiner, in whose hands the award was placed, to examine thoroughly the essays in the few days which intervened between the last date for receiving entries, and that of going to press. The names of the prize winners will be published in the May number, when we shall also print the four prize essays.

No. 14.-Answers to Test Papers in Geography.

For the best set of answers to any eight questions from one of the geography papers given on p. 152 and p. 155, but not from both, a prize of books to the published value of half-a-guinea, to be selected from the catalogues of Messrs. Macmillan & Co., Ltd., is offered. A second prize of books, to the value of five shillings, will be awarded for the next best set of answers to eight questions from either paper. There will thus be two prizes for each paper.

The competition is open to pupils of any age, irrespective of whether they are boys or girls, or in English, Welsh, Scottish or Irish schools. A coupon (p. v.) must be sent in with every separate paper or packet of papers. The competitor's name should be written upon each paper, which must also be endorsed

by the teacher or other responsible person, certifying it to be the unaided work of the competitor.

Papers should be sent to The Editors, THE SCHOOL WORLD, St. Martin's Street, London, W.C., on or before Saturday, April 13th. No papers posted after that date will be examined. The result of the competition will be announced in the June number.

Knight together can, but it is necessary to drive the King to a corner of the board commanded by the Bishop. Staunton, in his "Handbook," gives the following position:-Black K on KRI; White KB on K6, B on KB5, Kt on KKt5. (Remember that the B and K alone can drive the opponent to the side of the board.) BLACK. K-Kti.

OUR CHESS COLUMN.

No. 27.

THE interest taken in our monthly competitions is very small, judging by the number of papers sent in. It was an easy matter to annotate the game given in the February number, yet the competition was very unpopular. This month I offer a prize-a five-shilling book to be selected from Messrs. Macmillan's catalogues-to the sender of the best game, original or otherwise, of not more than 30 moves. Anyone can enter for this competition. Answers should be received on or before April 13th.

One of the games in our Inter-School Correspondence Tournament has been finished - Nonconformist Grammar School, Bishop's Stortford, having beaten Friends' School, Saffron Walden. Appended is the score :

This month I am giving a few hints which I find are useful to boys in end-games. It is by no means an uncommon occurrence for a player with a winning superiority to throw away his chances by stalemating his opponent. One very frequent case is that in which one of the players is left with King and Rook's Pawn against King. If the latter can succeed in getting in front of the Pawn on the Rook's file, the game is drawn ; again, if he can command the Bishop's file and confine the opposing King to the Rook's file, in front of the Pawn, he can only be stalemated. He must play from B1 to B2, and

I.

2.

WHITE. Kt-B7 (ch.). B-K4.

I.

2. K-BI.

Mating with two Bishops is comparatively easy, as it is only nccessary to prevent the King's crossing diagonals, and these can of course be commanded. Where you have King and Queen against King be careful lest you give stalemate. Force the King to a side of the board, and keep him there, bring up your own King opposite with one square between them, and then mate by moving the Q on to the R file. A similar process holds good in the case of a Rook. It sometimes happens that if a Pawn queens stalemate is given; look out for this trap and choose a Rook instead. If you have a Rook against a Knight the game is drawn unless the King and Knight are in a corner of the board.

Mason, in "The Principles of Chess," gives some useful hints: Two united Pawns, one on the sixth, and the other on the seventh rank, and not being compelled to move, defend themselves against the Queen.

Two united Pawns on the sixth rank, having the move, queen against (1) the Rook, (2) the Bishop, (3) the Knight.

A Rook Pawn and a Bishop will not win against the lone King, if the King can front the Pawn, and the latter does not queen on a square commanded by the Bishop.

EDITORIAL AND PUBLISHINg Offices, ST. MARTIN'S STREET, LONDON, W.C. Contributions and General Correspondence should be sent to the Editors.

Business Letters and Advertisements should be addressed to the Publishers.

THE SCHOOL WORLD is published a few days before the beginning of each month. The price of a single copy is sixpence. Annual subscription, including postage, eight shillings.

The Editors will be glad to consider suitable articles, which, if not accepted, will be returned when the postage is prepaid. All contributions must be accompanied by the name and address of the author, though not necessarily for publication.

xi.

ENGLISH.

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Siepmann's Elementary French Series.-New Volumes. UNE ANNEÉ DE COLLÈGE À PARIS. Par ANDRÉ LAURIE. Adapted and Edited by FABIAN WARE, B.-ès-Sc. Notes and Vocabulary by C. S. H. BRERETON, M.A.(Cantab.), Lic-ès-L. Globe 8vo, 2s. Word and Phrase Book. Sewed 6d. KEY, 2s. 6d. net.

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AU POLE EN BALLON.

Par VICTOR PATRICE. Adapted and Edited by P. SHAW JEFFREY, M.A. Globe 8vo, 2s. Word and Phrase Book. Sewed, 6d. KEY, 2s. 6d. net. Educational News.-"A more exciting and interesting narrative of adventure the heart of youth could not desire. The notes are numerous and extremely good. The volume is one of the best of an excellent series."

OF INSTRUCTION.

With special reference to Elementary Schools.

By GEORGE COLLAR, B.A., B.Sc., Principal of the Stockwell Pupil-Teachers' School, and CHAS. W. CROOK, B.A., B.Sc., Head-Master of the Higher Grade School, Wood Green, N. Globe 8vo, 3s. 6d.

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OUTLINES OF EDUCATIONAL DOCTRINE. By JOHN FREDERICK HERBART. Translated by Professor ALEXIS F. LANGE, Ph.D. Annotated by Professor CHARLES DE GARMO, Ph.D. Svo, gilt top. 58. net.

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*The above is intended to form the concluding volume of the Shorter
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Also published.

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A MANUAL OF ELEMENTARY SCIENCE. Course of Work in Physics, Chemistry, and Astronomy. For Queen's Scholarship Candidates (Sections I. and II.). By Prof. R. A. GREGORY, F.R.A.S., and A. T. SIMMONS, B.Sc. (Lond.). Globe 8vo, 3s. 6d. INTRODUCTION TO PHYSICAL CHEMISTRY. By JAMES WALKER, D.Sc., Ph.D, Professor of Chemistry in University College, Dundee. Second Edition 8vo. 10s. net. Journal of Education.-"The author has succeeded admirably in his task, and the work should be gratefully received by those for whom it is intended."

PRACTICAL ORGANIC CHEMISTRY FOR ADVANCED STUDENTS. By JULIUS B. COHEN, Ph.D. Globe Svo. 3s. 6d.

BOTANY. An Elementary Text-Book for Schools. By L. H. BAILEY, Illustrated. Extra crown 8vo. 68.

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EXAMINATION.

By the Tutors of the University Examination Postal Institution.

Containing particulars as to books recommended for 1901 and 1902, and general suggestions for a method of study, and statistical tables (not obtainable elsewhere).

New Edition, 76 pages, ready in the course of February, obtainable, post free, by any Candidate by writing to the Manager of the Institution, Mr. E. S. WEYMOUTH, M.A., 27, Southampton Street, Strand, London, W.C.

343 U.E.P.I. Candidates prepared successfully for this Examination during 1895-1900, of whom 62 gained distinction. At the latest Examination, December, 1900, which is confined to Mathematics and Languages, of the three candidates who took distinction in German two were prepared by this Institution; so also was one of the two who took distinction in French. Also in Mathematics, one of the two who took a first class was prepared by one of the Mathematical Tutors of the Institution.