secondary education of the present scholarship system.

The schoolmaster may be pardoned if, with Professor Lamb, he smiles at the mathematician in trouble with his soul; but, nevertheless, there are certain other aspects of mathematical education which concern him greatly. It is not of the essence of mathematics to provide a knowledge of geometry and arithmetic; nor would the complete satisfaction of the just claims of the calculus to a place in the school curriculum necessarily conclude the real purpose of its teaching. Indications are not wanting that power in the hands of an uneducated and prejudiced democracy is fraught with danger to national institutions, of which Greenwich Observatory is the last signal instance. Signs are only too frequent that many, whom a strange fortune places at the helmsman's wheel, are wanting in those subtle powers of mind which real education alone can give. It is sometimes said with bitterness that the modern man neither thinks nor cares to think. But it is not impossible to provide the youth, that will be man, with that aid from symbols which makes thought attractive and conclusions safe. The essence of mathematics is found where laws of thought appear in the discovery of truth about things; the certainty of its method lies in the self-corrective power of an automatic notation. The ideal teaching will aim at that harmony of the abstract and concrete, of the general character and particular case, which, on the one hand, allows human imagination all liberty of suggestion, but, on the other hand, trains human reason for service in a hard material world of fact.

III.

HISTORY.

BY ARTHUR HASSALL.

THERE is no escaping from the fact that the study of history can be of real use in practical life. It is equally certain that an unintelligent and a superficial use of history will prove of little value. The study of the history of institutions, of the dominant ideas of any one period, of the great Revolutions which have transformed the fortunes of nations is interesting and valuable. The study of history, too, teaches boys to learn "to weigh conflicting probabilities," it widens their experience, it emphasises the necessity of realising various types of character very different from the British type. History therefore appeals to schoolboys; it may be from the military, political, constitutional, or economic side.

The teaching of medieval and modern history has now become pretty general in our public and secondary schools. Formerly, Greek and Roman history were alone taught; but of late years, owing to the exigencies of Civil Service Examinations, of the Oxford and Cambridge Higher Certificate Examination, and of the fact that History Scholarships are annually offered by many of the colleges at Oxford and Cambridge, the necessity of widening the sphere of historical teaching has been recognised. In many schools, no doubt, the advantage of giving boys the opportunity of increasing their natural bent for the study of modern history had been

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seen at a much earlier date. For instance, at Uppingham in the seventies prizes were annually awarded to every class after a special examination in some set books, the character of the books, of course, varying with the position of the class. In the higher classes one or more volumes of Mommsen's "History of Rome," together with a work on modern history, would be set. Motley's "Dutch Republic,' Macaulay's "Essays on Clive and Warren Hastings,' Miss Yonge's "Cameos of English History," were the sort of works selected. The result was that a boy to whom the ordinary Greek and Latin curriculum was distasteful found, as it were, a safety valve for his intellectual energies in the more congenial study of history. Such a boy would often develop into a keen student of history, would take a first-class in the Honour School of modern history at Oxford or Cambridge, and would secure a teaching fellowship in history at some college. It is doubtful if any better system has yet been devised for inspiring boys with a love of history. Since the days, however, when Edward Thring adopted the above excellent system the teaching of modern history in all schools has to some extent been instituted, and, owing to the demands made by the Civil Service Commission and the Universities for a knowledge of certain periods or subjects, has become more organised.

In many schools a modern side has grown up in which boys who propose to adopt a military career are prepared for the Army Entrance Examinations. It is doubtful if the history taught on the modern side of any school for Army examinations is at present of much value. It is, however, in the preparation of boys for History Scholarship Examinations that the success or failure of the system of teaching history at any given school has to be tested. Many boys who are obviously incapable of securing a classical scholarship are interested in history or

literature, and prompted no doubt by the numerous history scholarships that are offered at the Universities, the authorities at various schools are prepared to give special teaching in history to any promising pupil. It is doubtful, however, if many schoolmasters have yet discovered the best methods of training boys in history. In far too many instances Greek and Latin history is displaced for medieval and modern history, and the Greek and Latin languages for French and German. Too often a boy is crammed with facts in English and modern history and is not taught to think. It is not sufficiently recognised that in History Scholarship Examinations a boy who shows in an essay or in a general paper that he can think and express his thoughts lucidly has a far better chance of election than one who may be a veritable storehouse of undigested facts.

No doubt this truth is recognised by many of the most successful teachers, who select a few boys who show a real historical taste and set them each week a number of essays. These essays are discussed out of the regular school hours, and are apart from the ordinary history teaching which is done in school. The extent to which this is successful depends entirely on the skill of the master. If he can adduce telling illustrations, if he has a fund of anecdote ready at hand, if he selects and reads aloud striking passages from the best authors, the lesson will be a great success. This system, which is pursued in certain of our best public schools, is in many ways admirable, but it is by no means generally adopted. In most cases the teaching is given in a half-hearted manner, the teachers themselves not always either caring for the subject or being specially competent. In far too many cases the text books employed are out of date, and no effort is made to replace them by more accurate histories. What can be more deadening than to impress upon a boy facts which have long

since been discarded? And yet this is constantly being done in the majority of our schools.

And

The teaching of history to schoolboys is undoubtedly a difficult task. If the ultimate object of that teaching be success in an Army Entrance Examination or in the Oxford and Cambridge Higher Certificate Examination, the teacher ought to be alive to the necessity of only using the best handbooks, and of employing the methods most suitable in each case for inculcating an intelligent knowledge of the required amount of history. If, however, the object be to train the mind and to enable a boy to secure a History Scholarship at one of the Universities, the teachers at most of our public schools ought to reconsider their methods. Το begin with, it is an egregious blunder to throw aside all the boy's knowledge of Greek or Roman history. No boy can be really interested in history who readily consigns to oblivion the age of Pericles, the second Punic War, and the career of Cæsar. yet most of the scholarship hunters who fail again and again in their quest have simply been crammed in an unintelligent manner with a modicum of modern history. Usually they know something of the European history of the seventeenth and eighteenth centuries. They have a cursory acquaintance with Gustavus Adolphus, a nodding acquaintance with Wallenstein and Marlborough, and an inaccurate acquaintance with the Great Elector, Louis XIV., Frederick the Great, and Joseph II. Had they been grounded in Gibbon their ignorance of ancient history might have been forgiven. But as it is they are like trees planted among rocks—they have no roots, and their knowledge is worthless. In order still further to make their failure more complete many of these scholarship hunters imagine that a very slight acquaintance with French will atone for ignorance of Greek, and for a very scanty know