needs of theoretical and practical science, and have thus given enough for the educational purpose. In other words, all geometry is and must be logical, and the practical uselessness of a proposition is no proof of its educational value. The ideal text-book should contain matter which is selected for its scientific and practical importance; the selection should be made with great care and intelligence, so as not to omit the most essential and far-reaching parts of the subject; and to accomplish this the author should have a wide acquaintance with mathematics, both theoretical and practical.

The book before me does not exhibit such a wise and careful selection. Many important parts of the subject are lightly treated, or even entirely omitted, while a range of rather difficult propositions of no special practical value is introduced, apparently from foreign text-books. The reviewer has been unable to find a standard and very important proposition relating to the segments of the side of a triangle made by the external and internal bisection of the opposite angle; has noticed the inadequate treatment (p. 246) of the measurement of the circle; and has vainly attempted to make out from the book what is meant by a "pedal triangle" (p. 289). The arrangement of the plane geometry differs from that which is usual, on the plea of a better collocation of the matter which refers to one subject. It seems to an old-fashioned teacher a pity to treat similar triangles in Book 7, now that proportion is so familiar to our pupils from a quite early age. Euclid introduces it in Book 6, but his Books 7 to 10 relate to arithmetic, and his order is out of date at present. Moreover, there is a cross-division which is by no means a help to the scholar, in dividing Books 1 to 4 (straight lines and angles, triangles, quadrilaterals, circles) according to the subject-matter, and Books 5 to 7, proportion, mensuration, plane figures, similar figures, according to methods of treat

ment.

The reviewer has no doubt that a skilled manipulator of boys can use this book to enable his pupils to pass examinations, even at Harvard; but he has very grave doubts whether they will be so well taught geometry by its help as from the books of the best reputation which have preceded it. TRUMAN H. SAFFORD.

WILLIAMS COLLEGE.

IX.

EDUCATION IN FOREIGN PERIODICALS.

Professor Laurie on Present Educational Problems.

[The following extracts are taken from the presidential address of Professor S. S. Laurie of Edinburgh, at the last annual meeting of the Teachers' Guild of Great Britain and Ireland, as reported in the London Journal of Education.-ED. EDUCATIONAL REVIEW.]

Curriculum of Secondary Schools.-"A multitude of subjects pressing for recognition in the school, and a multitude of deadening and oppressive examinations following close upon the teaching—these are the evils (as we all know) under which secondary education groans in these days. It becomes us to consider whether, under modern conditions, we can secure for teachers and scholars some of the concentration which was the chief merit of the schools of former times. No sound educationalist is an encyclopædist. On the other hand, the educationalist who holds that we can prepare the youth of the country for the work of the twentieth century by means of a little of one dead tongue and less of another, must be accounted an anachronism. We cannot allow boys and girls of eighteen years of age to pass out of our hands as educated who are ignorant of the national and world life which they inherit, or of the living nature in the midst of which they are placed, and which they have to bend to their purposes. And yet we cannot teach everything, and must be often perplexed in présence of the numerous subjects-each with a certain completeness in itself-which now claim admission to the school curriculum. Which and how many of the branches into which human knowledge has now ramified shall we select for the secondary school, and how far shall we carry the study of each, are questions which not only Great Britian, but the whole civilized world may be said to be now considering.

"It is a fair question, Has the science, or theory, of education any light to throw on our darkness, or are we to grope on empirically, hastily taking up, and as hastily dropping, first one subject and then another, in obedience to the demands of an uninstructed and exacting public, and fitting those we select into the time-table as if it were a piece of mosaic? I think

that theory may help us at least to a solution of our difficulties, if it cannot wholly solve them. First of all, the theory of education requires us to transfer our attention entirely from subjects of instruction to the minds we are instructing. This alone is a great point gained. When we take up this attitude to education, we at once see, for example, wherein lies the truth and falsity of encyclopædism. Encyclopædism is unquestionably a characteristic of a completely educated mind, but not encyclopædism in respect of the material of acquired knowledge, but encyclopædism of faculty. That is to say, a complete education should bring the mind into intelligent contact with representative studies, and representative methods of investigating truth. Encyclopædism, in the sense of universality of faculty, would seem to be within our reach."

What is our Telos? "Thus far there is guidance; but just at this point, theory again interposes, and asks the question, 'To what, and for what, ultimate end all this labored training of faculty?' The question will be answered by theory thus: In order that each man may do efficiently his special work as a member of society; but even this only in subordination to a supreme end-the fulfillment of the ethical purpose of human life in him. The ethical end governs all (and by ethical I mean the moral and religious). It comes to this, then, that it is general power of faculty we have to give, and with this, the substance and motive forces of ethical living. A leaving-examination, looked at from this point of view, consists of two questions, which have to be addressed to every pupil :

"1. The first is one question, but it has a twofold aspect. I ask a youth, on this or that point, which may be suggested by the occasions of life: What is your own thought, and what is your own utterance? The thought may be confused, and will certainly be inadequate; but we are content to find that he thinks; the utterance may be halting and unformed, but we are content to find that he strives, with fair success, to utter the thought in his own language-to express himself. But a satisfactory pass, even in this twofold examination, is a subordinate matter, though essential; for the final aim has yet to be considered-that for which all knowledge and all faculty exist-life, living, doing. There is still, therefore, a second, and, as I have already indicated, a supreme and governing question.

"2. And that question is, What are the motive forces of all

your activity; what ideas inspire you; what ideal of life do you strive after, so that the best and highest in you may be made manifest in all your manifold relations to your fellowmen?

"The answer which the youth of eighteen, whose secondary course is completed, can give to these two questions, is the measure of his education. From this leaving-examination no one can ultimately escape, and if we teachers dwelt more than we do on this final testing of our work, we might, perhaps, be guided to the solution of many minor difficulties, and regard with careless equanimity much that now assumes unduly large proportions."

Language the Central Subject.-"Now, it is clear to me that if the supreme end' be that which alone gives significance and vitality to all our daily work, we must find, as our central subject of instruction, one which, while giving general discipline to the mental powers, with a view to mental power, will, at every step, help forward the growth of the ethical in our pupils. What is this subject? At this point, it may appear that theory deserts us, and idiosyncracies, prejudices, custom, take its place. I have discussed the question elsewhere, and I shall accordingly be excused for merely dogmatically asserting here that the answer which theory gives is that the central subject we are in search of is Language-language as a discipline, and language as a liberal course of reading in literature, history, and what else you please. By language, too, I mean the vernacular; but, inasmuch as we require to study a foreign. tongue to give meaning to our own, I add Latin, as being at once our own tongue, and in contrast with it. Whatever else we may teach, all, it seems to me, must grow round this central and magistral subject-language, English and Latin."

The Place of Physical Science." Theory, as I understand it, largely confirms the practice of the past as regards subjects of instruction, though extending their significance and range. This may be said without depreciating the claims of physical science. While sensible of the many advantages conferred by school science, I doubt if it can give true mental discipline before the age of sixteen or seventeen. Prior to that age supremely good teaching may give, by means of concrete and experimental studies, a certain discipline as well as knowledge. But the true discipline begins only when science is taught as a re-investigation and verification of the scientific

results already ascertained; and I am disposed to think, from all I have yet observed, that only in the department of botany is this possible before the age which I have mentioned. All before this age is of the nature of object lessons-as such extremely valuable, and indeed necessary, but restricted in their educative effect. In any case, physical science, at best, has to do with inductions and deductions from sense alone, and accordingly it can never, by any possibility, have the educative effect of language, nor can it, even as an exercise in investigation, give that general power over all possible material that may be presented to the mind to deal with in the complexities of human life. The student of science is always exercising his intelligence on a limited part of human experience, while the student of language, in the extended sense, which is the true sense (any other sense being the invention of pedants), may be said to be always in contact with the whole. The humanities alone truly educate a human being. "This, then, is the answer which theory, I think gives to the question, 'What shall I teach? First of all, and always, language (the vernacular, Latin, and what else there may be time for)—but this in a large and liberal sense; secondly, a certain amount of pure mathematics, and, in subordination to both, the elements of physical science, giving prominence, for reasons intellectual and practical which I have not time to enter into now, in this department to physical and industrial geography. Such a course of instruction, well organized, would suffice to foster in our young men both moral and intellectual interests, and to secure a certain encyclopædism of faculty. The introduction of any other subjects is to be determined by predisposition and natural aptitude, or, it may be, by considerations of utility alone-whether the subject be Greek, French, German, advanced mathematics, or physical science. I do not think it matters much which of these are selected, if our curriculum has already assured the education of the minds of our pupils. Nor can there be any objection, if the general education of a boy has been sound, to devoting the last year of his stay at school to preparation for certain public examinations. This should certainly not be left in the hands of the professional coach."

The Place of Greek.-"I have been speaking of secondary education within its own limits, and without reference to the primary instruction on which it rests, or the higher education