The two triangles to be proved equal being set before the pupil, he examines them and finds out for himself the two sides of the one that are equal to the two sides of the other, observing that the equal angles in each triangle must be those that are contained by the respectively equal sides; then he writes formally out the exercise in five lines or paragraphs :

1. He names one side in each triangle that is equal, giving the reason why.

2. He names a second side in each that is equal, giving the reason why. 3. He recapitulates,-wherefore the two sides named of the one triangle are respectively equal to the two sides named of the other?

4. He names the included angles, and gives the reason why they are equal.

5. He concludes, therefore, by the fourth proposition, the triangles are equal, in every respect, naming the respects if necessary.

It is hitting a nail on the head that drives it home, and that is just what these exercises do. After doing two or three of them, they get quite clear and brisk. They enjoy the exercise. They examine the triangles; pick out the sides; write out the five formal paragraphs; come up with it. It is examined. Right. Off they are to do another. One hears occasionally, in a tone of triumph, "Therefore, by the fourth proposi tion," &c.

The last exercise is always that crucial test, the second part of the third proposition of the third book.

Now, among these exercises, we introduce the following in an off-hand way, without letting the class into the secret of what we are about.

Draw, says the Master, a couple of circles, with the same centre one inside the other; and draw now a couple of radii (two spokes of the wheel) to the rim of the outer circle; call them AD, AE; put B and C where these lines cut the inner circles, join BE and CD. Now take as an exercise to prove that the triangles AEB and ADC are in every respect equal, and name the respects. They set to work; in two or three minutes they bring up the exercise, the five paragraphs written correctly out.

Then the Master says, Now join BC, and, remembering what you have proved already, try and prove that the triangles DBC and BCE are also equal in every respect, observing to them that the bases of both triangles are the same line.

Down they go to work, and this exercise is brought up in a few minutes.

Then the Master again quite casually says, Let me see, we proved these big angles ACD and ABE to be equal?—Yes, say they, in the first of the two exercises. And we have just now proved that BCD is equal to CBE? Yes. Suppose we take these little poky angles from the big ones. Then

ABC and ACB remain ; And if equals are taken from equals, what do we know about the remainders ?-They are equal. Exactly, then what angles are equal? ABC is equal to ACB.

The tutor's face, which has been solemn and somewhat constrained all this time, now relaxes into a serene smile of triumph and congratulation. Gentlemen," says he, "I have the pleasure to announce to you that you have done the fifth proposition. The Bridge' is passed." They are taken Quite true. It's all over! The tooth is out! It's all right!" So, then, we are all very happy together.

aback. 66

After this we turn to our Euclids: they read over the fifth and sixth propositions, paragraph by paragraph, and then write them out carefully. These exercises are not intended to supersede the careful writing out of Euclid. The appreciating and falling in with Euclid's guarded choice diction I hold to be a great intellectual benefit. It is a help to those who wish their knowledge to be clear and precise, and I cannot think it is lengthy. Very often, when with a little oratory and emphasis, suiting the action to the word and the word to the action, I have gone over a proposition for a class at the black board, they have said to me, "Is that all? we can understand that, but there is such a lot of it in Euclid." Then I take the Euclid in my hand, and say, "You fix your eyes on the figure on the black board, while I read the proposition in Euclid verbatim et literatim, and you will see if there is anything in it that I have not said; also, you will tell me if it can be shortened, and where." At the end of the reading they are always satisfied that the wording of the proof is only what is needed for completeness and precision.

To complete my sketch, I will give a rapid outline of our teaching the seventh and eighth. We always teach them together" without solution of continuity."

The seventh, I frankly tell them, is a teaser. I like to do so, it puts their courage up. I add, it is a proposition introduced only to prove the eighth, which is a most important proposition, as valuable as the fourth, but the seventh is never used again.

I tell them that some schools are afraid of the seventh, and, explaining to them what is wanted to be proved in the eighth, I guide them to show me the proof that is given of the eighth (as a simple deduction from the fifth), in schools where they are afraid of the seventh. "But you are not afraid of the seventh ?" No!-Let us go at it then.

I find it simplest to put the enunciation in this form. If the two sides terminating in one extremity of the base are equal, those terminating in the other extremity must be unequal. Then we proceed step by step, in the way of questions, from the equal angles at the base of the isosceles triangle to the "Much more then..." Some boys have a great difficulty about the

à fortiori argument. We have a familiar illustration which has often proved a great help to boys.-You agree that a father is older than his son ? Yes And that a grandfather is older than the father? Yes. Much more must a grandfather be older than his grandson. Now, then, in the seventh proposition pick me out the father, the grandfather, and the grandson. They do it after a little, and the difficulty is got over, and they go on at once to the eighth, see its connection and take it in. In fact, the coinciding of the angles is no difficulty to them after the drilling they have had in the fourth proposition.

The work is done now. Those who have succeeded in mastering the eight propositions, and have answered our questions upon them, and have written them out correctly, get their pass.

These are formed into a class of honour-men; they go on by themselves, learning their four propositions, and writing them out each time they come, while the master goes over the same ground a second time with those who have not conquered.

Notices of Books.

The Child's Latin Primer. By B. H. Kennedy, D.D. Longmans, London.This is a new edition, adapted (of course) to the 'Public School Latin Primer,' with reference also to the 'Subsidia Primaria,' Course I., which we have lately noticed. The Editor retains the time-honoured Elementary Forms and Rules as memorial lessons, maintaining that, though much has been said and written against this oldfashioned mode of teaching, no experimental proof has been given that a dead language can be taught by any sounder method. Some questions and passages for translation are contained in an Appendix, which are designed to be supplementary both to the present book and to the 'Subsidia.' Another Appendix exhibits a vocabulary. The end and aim of the book is to make learners thoroughly familiar with the normal forms of Latin words, and the normal constructions of the simple sentence in Latin, before they read any Latin author. The opinion of Dr. Kennedy on the general question, what method is the best to follow with boys for the attainment of this end, is no doubt entitled to the very highest respect. And certainly there is no man better qualified to compile a manual to be the basis of such method. Granting the excellence of the 'Public School Primer,' this little work must needs be accepted as an able expositor of its principles and system.

Compendium of English Literature. By Thomas Armstrong. Thomas Laurie, Edinburgh.-We must avow that we have such a steadfast objection to what is

called the 'Method of Question and Answer,' that we can hardly deal fairly with a book, in which the matter is arranged in the form of a conversation. We should hold, for instance, that to teach a boy exactly what to say about Chaucer or Surrey or Pope, in case he has a question of a particular form addressed to him about them, is teaching him very little; and teaching him that little moreover in such a way as to make him exceedingly likely to be contented with it. If others think differently, we are not disposed to quarrel with them. The information given in this little book seems sound, and judgment has been exercised in selecting the writers whose works best illustrate the progress of our literature. The space given to our Prose Writers is very scanty. Even outline-justice can hardly be shown to them in sixteen pages, however lively the conversation. Our objection however lies chiefly against the form in which the facts are given.

Paul Baume's Practical French Grammar. Part I. Simpkin, Marshall, and Co.-The Author admits that this country is deluged with French Grammars and class-books of all kinds. As his justification for swelling the deluge he points out the special merit of his method, which lies in having so arranged his book that a page of practice faces a page of theory. It certainly looks inviting to the solitary learner, to find that when struggling with the difficulty of translating from or into French, he has merely to look above for his words, and across for the rules by which to use them, nor can we see that he has anything to fear but the danger of forgetting too easily what he finds so readily, a disadvantage for which he must compensate himself by employing in continued repetition the time thus saved, which would otherwise be spent in turning pages. System has been carried still further. Each vocabulary, and consequently each page of exercises is concerned with some special class of words, so that phrases of the breakfast-table, phrases of the toilet, &c., are brought together. There is common-sense in this. The book bears evidence throughout of having been most thoughtfully considered, and carefully edited.

Laurie's Standard Copy Books: Nos. 14, 15, 16.-These belong to Mr. J. S. Laurie's Supplementary Series. They are in French. The first contains letters upon various subjects, familiar, affectionate, playful, gossiping, from which one may glean, what otherwise it might be difficult to pick up, the styles of address and of subscription proper to be used towards persons with whom one stands in different relations of intimacy. No. 15 exhibits Complimentary Letters, showing how to accept or decline an invitation to a Pique-nique, and what sympathetic enquiries are due after a Soireé. Short poems are interspersed as exercises to be transcribed. The last contains a few familiar letters, but consists for the most part of business letters, forms of receipt, notes, bills of exchange, &c., such as are likely to prove of service in the foreign correspondence of a house of business.

Dr. Lankester's School Manual of Health. Groombridge and Sons, London.This little work, whose price is eighteen pence, contains a great deal that Teachers might advantageously work up into short lessons for advanced classes. Much of the information here given is to be found in most Reading books, but we have not before met with a separate manual, which, in so short a compass, gives so complete a view of the facts on which the Laws of Health are founded, or so forcibly applies them. Those who are acquainted with the little treatises on kindred topics which Dr. Lankester published some time ago, 'On Food' and 'On Animal Products,' will know how able an expositor he is of Popular Science. His high scientific training ensures accuracy of statement, and what is, in treating of such a subject as

Health, of equal importance, breadth of view; while his long and wide experience as a lecturer enables him with ease to adapt both his facts and his arguments to common intelligence outside his profession, and also to enforce his points by the aid of varied illustration. The result in the present instance is a little treatise which we may trust for soundness, and may read with pleasure.

A Narrative Essay. By the Rev. S. Hawtrey. Longmans, London.-The author of this pamphlet is a Master of Eton. He has for many years taken the most lively and kindly interest in a school for poorer children, called St. Mark's, at Eton, of which he has already written a few short notices. His object in speaking of it again, and this time more publicly, is to show, while others are fighting over principles, what has been done in practice. He speaks at some length of the habits of the school. He declares the daily short prayers in the church to be the keystone of its moral discipline, and wishes our village churches were, as a rule, so turned to account. He is against any system of supervision during prayer, believing that reverence grows rather from sympathy, and that the Master had better, therefore attend to his own prayers. Sundry other hints he gives, on discipline, and on school-work, worth considering, and delivered in the most genial way. His description of how he has taught Euclid, is so good a lesson in method, that we are sure our readers will thank us for having, in another and more prominent place, transcribed it for them. It is the general tone of the book that pleases so much. An earnest enthusiast, like Mr. Hawtrey, bright in intellect and nature, spending his time and thought and hearty energy upon giving the poor boys about him a liberal education, does a noble service, the good of which is incalculable.

Groombridge's Annual Reader.-This is a repertory of the principal events of the year, written to supply what the editor believes to be a great and universally acknowledged want, the want of good and useful Reading-books for the higher class of schools. In the present state of civilization he contends that young persons should be acquainted with the history of their own time. The reader may judge of the kind of topics treated of, by the following selection at random:-'Great Floods in the North of England,' 'The Atlantic Yacht Race,' 'The Royal Effigies at Fontevrault,' 'The Volunteer Review at Dover,' 'The Lions of the Nelson Monument,' 'The Duke of Edinburgh and the Elephant,' 'Dr. Livingstone.' Such subjects would, no doubt, do much to arrest the interest of boys. The book is well printed, in largish type, and contains seventy-eight pages, of the average length of five pages or so each.

Register of the Month.

Scholastic Registration Association.

The Committee, while fully alive to the absolute importance of duly respecting the interests of all persons engaged in the profession at the time of the passing of the Act, is of opinion that the value of the Register would be greatly lessened by