Oration- -"Athens during the Age of Pericles," Awarding Diplomas. VALEDICTORY HYMN. The literary exercises evinced study and originality, while their composition and delivery showed that the rhetorical training of the scholars had not been in vain. Though abounding with chaste ornament, and elegant expression, none of the productions ex hibited a tendency to sacrifice solidity and depth for mere brilliancy and effect. We do not wish to rank one performance above another, but can hardly refrain from alluding to the commendable independence of thought and a becoming degree of humor exhibited in a criticism on Mrs. Browning, and an essay on Young Ladies. The discussion, "La Sainte Alliance De Peuples," was well received. In the selection of themes, their treatment and delivery, the orations of the young gentlemen were highly creditable to the performers, and their instructors. The valedictory poem will appear in our SCHOOL EXERCISES. Solutions to Geometrical Problem in the March Number. WE received, too late for insertion in May No., a solution from "Farmer's Boy," Poplar Ridge, Cayuga Co., New York, which reflects great credit upon the sons of Agricolae in the Empire State. The solution gives, in the main, the same line of proof as that given in the May number. We have also received a solution, which we present below, called forth by that given in our last, furnishing a different style of proof. Considering the indirect method as not so satisfactory, our correspondent has given us a direct proof, which is clear, rigid and logical. While the indirect method, taken by our correspondent last month, is perhaps as conclusive and positive, this is undoubtedly more ingenious and scientific. Still we must, in justice, bear in mind that great credit is due to our correspondent of last month for furnishing the problem as original-he having never seen it-and for giving a satisfactory solution. The proof was so evident that circle D was tangent to and included within circle A, that our correspondent did not deem it essential to give it. It will be necessary for our readers to draw lines connecting the following points, in order to make our figure apply to the following solution. It can be done with a simple lead pencil: Connect OG; OC; OH; B'C; B'A; AT; and produce AC to G. MR. SCHOOLMASTER: Dear Sir-In compliance with your request in No. II. of the SCHOOLMASTER, I send you the following solution of the "Geometrical Problem" of No. I. Having investigated this same problem, several years ago, though from a different statement, it is not difficult to conceive what class of circles is necessary to answer the conditions, since that, "The unoccupied space is exactly equivalent to one-sixth of the original circle," is one of the corollaries deduced from the solution of the problem according to that statement. Construct circles B, B' on the semi-diameters of A. That they will be tangent to circle A, and to each other needs no explanation, Draw AG tangent to B' and B. At G, draw tangent GO AG. From O draw tangent OHOG, which may be proved by drawing another tangent from O to E; for then will OH=OE=OG, all being tangents from the same point, O. Bisect the angle GOÏ, cutting AG in C. Draw CH, B'H; then, since OHOG, OC is a common side, and the angles at O are equal, the two triangles HOC, OOC are equal, and CH=CG. But angle G is a right angle, therefore OHC is a right angle, and CHB' is an unbroken line, and the hypothe nuse of the right angled triangle CAB'. With C as a center and radius CG describe circle C. It will be tangent to circle A, B, B'. To ascer tain the ratio of radius of C to those of B and A, proceed thus: CI1-3 rad. A, therefore, ID 1-6 rad. A ; BD= AC 2-3 rad. A, BV≈1-2 rad. A, therefore VD= 1-6 rad. A; hence, ID=VD; therefore, if with D as a center, and radius DI, we describe a circle, it will be tangent to the circles B and C, in the points I, V, radii DI, DV being in the radii CI, BV produced. It remains, to prove circle D tangent to circle A. Draw a diagonal AD, and produce to Ta point in circum. D. ADB'C= 1-2 rad. A+1-3 rad. A=5-6 rad. A; but DT=1-6 rad. A, therefore AT 6-6 rad. A rad. A; therefore point T is also in the circum. A; and, radhi AT, DT being on the same line, the circles D, A are tangent at T. The construction of circles D', D", D"", C', is accomplished by producing the sides of rectangle BC, and constructing three other rectangles equal to BC; the corners of the rectangles determine the centers required. Putting rad. A 6, we have radii D, C, B, A respectively 1, 2, 3, 6; their areas, as the squares 1, 4, 9, 36; the sums of all the circles of each order, respectively as 4, 8, 18, 36. Small circles: large circle :: 30: 36:: 5: 6; hence, small circles 5-6 large circle, or unoccupied area =1-6 large circle. Rectangle joining centers A, B, C, D, has sides as 3:4. Rectangle joining centers D, D', D", D", has sides as 3:4. Parallelogram joining centers B', A, C, D, has sides as 3:5. The tri angles joining centers ADD', AD”D”, CBB', C'BB' are equal and isosceles, with sides as 6:5, 5. CBCB' is a thombus with diagonals as 3:4. Respectfully, Lonsdale High School, May 1858. J. M. R. CORRECTION.-In our last, we announced the appointment of Mr. Wm. S. Kent at River Point, stating that he had been for several years at AC=AG-CG-2B'A-CH; CB' CH+HB' Phenix. He has been for five years teacher at CH+B'A; (CH+B'A)2=(2B'A-CH)2+B'A2; North Scituate, and not at Phenix. His brother, Expanding, CH2+2CH× B'A+B'A2=4B'A2-4 Mr. John R. Kent, still continues, as for the last B'AXCH+CH2+B'A2; whence, 6CH×B'A=4 two years, at the latter place. B'A2; or, CH-2-3B'A; but B'A=1-2 rad. A ; hence also, CH-2-3x1-2 rad. A=1-3 rad. A. Finally, draw perpendiculars from centers C, B, intersecting in D; then, CD=1-2 rad. A; ANSWERS and solutions to questions in our last lie over till next month. OUR BOOK TABLE. COMPENDIUM OF AMERICAN LITERATURE; Chronologically arranged, with Biographical Sketches of the Authors. By Charles D. Cleveland. E. C. & J. Biddle, Philadelphia. This volume, of 740 pages, is on the same plan as the author's " Compendium of English Literature," and "English Literature of the Nineteenth Century. It embraces a succinct account of the lives and writings of over one hundred American authors of the past century, commencing with Jonathan Edwards, and ending with George William Curtis, together with choice and characteristic extracts from their works. To those who know Prof. Cleveland, or have read his previous volumes, it is unnecessary to say that he is entirely independent in his views, and writes freely and fearlessly of the mental and moral caliber of the authors whose works he notices He has succeeded admirably in the difficult task, so boldly undertaken, of giving us, in a single volume, the very cream of American literature and of biography of American authors. It is a valuable book, and should be in every man's library. We hope it will be called for at our bookstores. MUSIC. OLIVER DITSON.-CLAPP & COREY. -We have received from Messrs. Clapp & Corey, music dealers, the following piano music, published by Oliver Ditson & Co: Ma Negli Estremi Istanti. Will Ye no Come Back Again? Always Cheerful Gallup. You Need na Come Courting Me. We had the pleasure a few days since of visiting the splendid music house of the above-named publishers-the largest music store in the world. They are known as the most eminent publishers of sheet music in the country. It is well worth any one's time to make a visit to this great emporium of the musical world. Messrs. Clapp & Corey have constantly on hand at their store, Westminster street, all the latest and best in their line. THE RISE, PROGRESS AND PRESENT STRUC This work is divided into three parts, viz: Part I., Historical; Part II., Philological; Part In each department it is of inestimable value to every student. The department on the Grammatical study of the language is very full and complete, giving a rigid analysis of every part of Etymological and Syntactical study, with copious examples for illustration. THE NATIONAL FIFTH READER. By Richard We would not undervalue the study of the classics, but we do think the study of the English language has been and is sadly neglected. We wish this work, which we consider one of the best treatises on the English language, was in the hands of every teacher in America, to be read and appreciated. San ADLER'S PRACTICAL LATIN GRAMMAR.- A TREATISE ON ARITHMETIC, combining Analysis and Synthesis, adapted to the best modes of instruction in Common Schools and Academies. By James S. Eaton, M. A., Principal of the English Department, Phillips Academy, Andover. Brown, Taggard & Chase, Boston. 1858. Mr. Eaton has been long known as one of the most accurate, thorough and successful teachers The book before us is a novelty, and will evi- of Mathematics in Massachusetts. For many dently claim and receive-as it surely deserves-years past at the head of the Mathematical and the careful attention of instructors of this beau- English Department of one of the most renowntiful language. ed Academies in the United States, he has had It attempts to make the study of Latin easy unusual facilities for that training which is necesand pleasant, and, besides, more rapid, by inter-sary to precede the making of a valuable textmingling the forms, idioms, constructions, and book on Arithmetic. rules, with practical and interesting lessons in translation, which apply these forms, idioms, &c. The plan seems to us a good one, and we hope it will be introduced by some of our schools, where a trial of its merits may be made, which shall settle the question of its superiority over the old system. If, by a trial in the school-room, it proves itself as valuable as it seems to us on a somewhat cursory examination, all teachers and learners of Latin will thank Prof. Adler for so great a contribution to classical science, and the enterprising publishers will find themselves amply remunerated for the expensive outlay necessary in the publication of so beautiful a book. - ESSAYS IN BIOGRAPHY AND CRITICISM. By Peter Bayne, M. A. Gould & Lincoln, Boston. We confess ourselves unable to criticise this book. Its beauties and its worth can only be known by a reading, and as for its faults, we have not seen them. Those who have read Bayne's “Christian Life" will be ready to appreciate the book. It contains eight essays, as follows: (1), Thomas DeQuincey and his works; (2), Tennyson and his teachers; (3), Mrs. Barret Browning; (4), Glimpses of recent British Art; (5), Ruskin and his critics; (6), Hugh Miller; (7), The Modern Novel,-Dickens-Bulwer-Thackery; (8), Currer Bell,-Ellis-Acton-Currer. The author says, in his preface: "They partake largely of the character of an introduction, in successive chapters, to the works of great au thors living and deceased." Nor has he disappointed the expectations of his friends in the preparation of this work. In methodical arrangement, accuracy of statement, concise and lucid rules, and the practical character of the book, it ranks high among its competitors for the public favor. The subject of fractions is taught with simplicity and thoroughness. Interest, Percentage and Analysis are well developed. The application to Square Root contains many difficult, but appropriate examples. Circulating Decimals and continued Fractions ably discussed articles, and the Application to Geometry is quite varied and practical. We commend the work to teachers as a book of unusual merit. PETERSON'S FAMILIAR SCIENCE, or the Scientific Explanation of Common Things. By R. E. Feterson. Childs & Peterson, Philadelphia. One of the most valuable of all our text-books for common schools. It treats of the science, and gives the scientific explanations of common phenomena in Natural Philosophy, Chemistry and Physiology. This study is receiving more attention than formerly, and deserves more still. ANNUAL REPORT of the Superintendent of Com mon Schools of Connecticut. 1858. Hon. David N. Camp has kindly sent us a copy of this, his annual report. It is an able document. Its remarks on Moral, Physical, and Home Education are admirable. SHEPPARD'S CONSTITUTIONAL TEXTBOOK. CHILDS & PETERSON, Philadelphia. 1858. In the preface the author justly remarks: "It is almost impossible to exaggerate the importance of a thorough study of the Constitution of the United States by the pupils of our schools. It is, nevertheless, a study which has hitherto been sadly neglected, chiefly, as teachers are aware, for want of a plain, practical, and thorough work upon the subject." This want exists no longer. Sheppard's Constitutional Text-Book is all that any teacher could wish, and ought to be used in every Gram mar and High School in the land. We are happy to learn that it is now rapidly coming into use in all parts of the country, especially in the best schools of New England. May we not soon find it in many of our Rhode Island schools? Childs & beautiful theme for the present volume, and admirably has he handled it. The book is a bril This is a work of 500 pages, illustrated by liant gem. We hope it will be called for at our celestial maps and more than 200 fine engrav-bookstores, and we are sure it will be read, and ings. It is executed in the admirable style in read with interest. which this enterprising house usually issue their publications. The work has received more enceniums from more learned men than probably any other textbook on this subject extant. It is certainly an admirable treatise on a highly interesting science. It contains a treatise on the globes and a comprehensive Astronomical Dictionary, both of which are of much value to the learner. We should like the work better were the "question and answer system" dispensed with, and the usual method of treating the subject substituted, with questions appended at the bottom of the page for those who might not choose to supply their own questions. CORNELL'S FIRST STEPS IN GEOGRAPHY. D. Appleton & Co., New York. A beautiful little book, full of pictures and neat little maps for the little folks. It is a very attractive book. LEAVES FROM AN INVALID'S JOURNAL, AND POEMS.-By Mrs. E. N. Gladding. George H. Whitney, Providence. 1858. This little unassuming book of 235 pages, en closes may a gem, cut out, polished and encased, during hours, which the authoress, while racked with pain, employed in this labor to relieve long, wearisome days and nights of their tediousness and monotony. She has consented to give them to the world, not for cold criticism, but for love's sake to her friends. May she find those friends numerous and ever true. REPORT of the Superintendent of Public Schools of the City of Chicago, Illinois. 1858. We have been favored by Hon. Wm. H. Wells, with his last annual report. It contains some very good doctrines with regard to regular at tendance at school, and upon the subject of heat ing and ventilation. |