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Oration — " Athens during the Age of Pericles," SCHOOL EXERCISES.

J. M. Addeman, Boys' Sen. Class—Classical

Department.
Valedictory - Henry S. Latham, Jr., Boys' Sen. | Solutions to Geometrical Problem in the
Class Classical Department.

March Number.
Awarding Diplomas.

We received, tou late for insertion in May No.,
VALEDICTORY HYMN.

a solution from “Farmer's Boy,” Poplar Ridge, The literary exercises evinced study and orig

Cayuga Co., New York, which reflects great inality, while their composition and delivery

credit upon the sons of Agricolae in the Empire showed that the rhetorical training of the schol

State. The solution gives, in the main, the same ars had not been in vain.

line of proof as that given in the May number. Though abounding with chaste ornament, and

We have also received a solution, which we elegant expression, none of the productions ex

present below, called forth by that given in our hibited a tendency to sacrifice solidity and depth

last, furnishing a different style of proof. Confor mere brilliancy and effect.

sidering the indirect method as not so satisfactoWe do not wish to rank one performance above

ry, our correspondent has given us a direct proof, another, but can hardly refrain from alluding to the commendable independence of thought and

which is clear, rigid and logical. While the in

direct method, taken by our correspondent last a becoming degree of humor exhibited in a criticism on Mrs. Browning, and an essay on Young

month, is perhaps as conclusive and positive,

this is undoubtedly more ingenious and scientific. Ladies. The discussion, “La Sainte Alliance

Still we must, in justice, bear in mind that great De Peuples,” was well received. In the selec

credit is due to our correspondent of last month tion of themes, their treatment and delivery, the orations of the young gentlemen were highly

for furnishing the problem as original-he hav

ing never seen it—and for giving a satisfactory creditable to the performers, and their instruc

solution. The proof was so evident that circle tors. The valedictory poem will appear in our

D was tangent to and included within circle A, next.

that our correspondent did not deem it essential The singing was excellent and well illustrated

to give it. the success of Mr. Sumner in awakening an in

It will be necessary for our readers to draw terest and promoting improvement among the

lines connecting the following points, in order to scholars in this much neglected but important

make our figure apply to the following solution. art.

It can be done with a simple lead pencil : Ten young ladies graduated from the school.

Connect OG; OC; OH; B'C; B'A; AT; and Of the young gentlemen eleven were graduates,

produce AC to G. and eleven candidates for the University.

MR. SCHOOLMASTER : MODEL LETTER FROM NEW JERSEY. - Wel Dear Sir-In compliance with your request in commend the following to the notice of our read No. II. of the SCHOOLMASTER, I send you the ers as a model. “We confess to a liking for " following solution of the "Geometrical Problem” such letters.

of No. I. Having investigated this same prob“Mr. Mowry:

lem, several years ago, though from a different Sir – I received the May number of The statement, it is not difficult to conceive what SCHOOLMASTER to-day, and opening to the 87th class of circles is necessary to answer the page, my eyes caught these words, •If you don't conditions, since that, “ The unoccupied space want The SCHOOLMASTER do please notify us.' is exactly equivalent to one-sixth of the original I thought as I did want it I would send my dol-circle,” is one of the corollaries deduced from lar immediately, for I would not do without it if the solution of the problem according to that it cost three times as much as it does.”

statement.

H

I have constructed my diagram with as few CI«-1-3 rad. A, therefore, ID=1-6 rad. A; BD= lines as possible, and have adopted the same ar- | AC=42-3 rad. A, BV=1-2 rad. A, therefore VD= rangement, &c., (as far as consistent with my 1-6 rad. A; hence, ID=VD; therefore, if with method) as that published, in order to compare D as a center, and radius DI, we describe a cirwith your engraving.

cle, it will be tangent to the circles B and C, in
the points I, V, tadii DI, DV being in the radii
CI, EV produced. It remains, to prove circle D
tangent to circle A. Draw a diagonal AD, and
produce to T a point in circum. D. AD=B'C=
1-2 rad. A +1-3 rad. A=5-6 rad. A ; but DT=1-6
rad. A, therefore AT=6-6 ræd. A rad. A;
therefore point T is also in the circum. A ; and,
radti AT, DT being on the same line, the circles
D, A are tangent at T. The construction of cir-
cles D', D", D}””, C", is accomplished by produc-
ing the sides of rectangle BC, and constructing

three other rectangles equal to BC; the corners YT

of the rectangles determine the centers required. O

Putting rad. As6, we have radi D, C, B, A SOLUTION

respectively 1, 2, 3, 6; their areas, as the squares

1, 4, 9, 36 ; the sums of all the circles of each Construct circles B, B' on the semi-diameters

order, respectively as 4, 8, 18, 36. Small circles : of A. That they will be tangent to circle A, and

large circle :: 30 : 38 :: 5;6; hence, small cirto each other needs no explanation, Draw AG

cles *5-6 large circle, or unoccupied area =1-6 tangent to B' and B. At G, draw tangent G0=

large circle. AG. From O draw tangent OH-OG, which

Rectangle joining centers A, B, C, D, has sides may be proved by drawing another tangent from

as 3;4. Rectangle joining centers D, D'', D", O to E; for then will oH=0E=OG, all being

D”, has sides as 3:4. Parallelogram joining tangents from the same point, 0. Bisect the

centers B’, A, C, D, has sides as 3:5. The triangle GOW, cutting AG in C. Draw CH, B'H;

Jangles joining centers ADD', AD'D””, CBB', then, since OH=0G, OC is a common side, and

C'BB' are equal and isosceles, with sides as 6;6, the angles at 0 are equal, the two triangles HOC, |,

'15. CBCB' is a thombus with diagonals as 3:4. COC are equal, and CH=CG. But angle G is

Respectfully, a right angle, therefore OHC is a right angle,

J. M. R. and CHB' is an unbroken line, and the hypothes

Lonsdale High School, May 1868. 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 CORRECTION.-In our last, we announced the tain the ratio of radius of C to those of B and A, appointment of Mr. Wm. S. Kent at River Point, proceed thus :

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+2CHXB'A+B'Al=4B'A24 Mr. John R. Kent, still continues, as for the last B'AXCH+CH2+B'A2; whence, 6CH XB'A=4 two years, at the latter place. D'A%; or, CH=2-3B'A; but B'A=1-2 rad. A ; hence also, CH=2-3x 1-2 rad. A=1-3 rad. A.

Finally, draw perpendiculars from centers C, ANSWERS and solutions to questions in our B, Intersecting in D; then, CD=1-2 rad. A; 'last lie over till next month.

OUR BOOK TABLE.

Mrsic.--Oliver Ditson.-CLAPP & COREY.

-We have received from Messrs. Clapp & Corey, COMPENDIUM OF AMERICAN LITERATURE;

Chronologically arranged, with Biographical music dealers, the following piano music, pub-
Sketches of the Authors. By Charles D. lished by Oliver Ditson & Co:
Cleveland. E. C. & J. Biddle, Philadelphia.

Ma Negli Estremi Istanti.
This volume, of 740 pages, is on the same plan

The Ballad Singer. as the author's “Compendium of English Lit

Will Ye no Come Back Again? erature,” and “English Literature of the Nine

Love Spell Gallup. teenth Century. It embraces a succinct account

Always Cheerful Gallup. of the lives and writings of over one hundred

Vaillance Polka. American authors of the past century, commenc

You Need na Come Courting Me. ing with Jonathan Edwards, and ending with

Oh! Dear; What Can the Matter Be. George William Curtis, together with choice and

The Happy Hour of Meeting. characteristic extracts from their works.

The Rock River Waltz. To those who know Prof. Cleveland, or have

The Reason Why.-Ballad. read his previous volumes, it is unnecessary to

Happy Family Waltz. say that he is entirely independent in his views, and writes freely and fearlessly of the mental

We had the pleasure a few days since of visite and moral caliber of the authors whose works he ing the splendid music house of the above-namnotices

ed publishers—the largest music store in the He has succeeded admirably in the difficult world. They are known as the most eminent task, so boldly undertaken, of giving us, in a

publishers of sheet music in the country. It is single volume, the very cream of American lit

American lit. well worth any one's time to make a visit to this erature and of biography of American authors. great emporium of the musical world. It is a valuable book, and should be in every |

Messrs. Clapp & Corey have constantly on hand man's library. We hope it will be called for at at their store, Westminster street, all the latest our bookstores.

and best in their line.

THE NATIONAL FIFTH READER. - By Richard Tue Rise. PROGRESS AND PRESENT STRUC G. Parker, A. M., and J. Madison Watson.

TURE OF THE ENGLISH LANGUAGE. -- By the A. S. Barnes & Co., New York. 1858.

Rev. Matthew Harrison, A. M. E. C. & J. The publishers have sent us this new reading Biddle, Philadelphia. book, which completes their series. It is a book This work is divided into three parts, viz: of 629 pages, and is designed to be "a complete Part I., Historical; Part II., Philological ; Part and sufficient work for advanced classes in Read- III., Grammatical. ing, Elocution, and English and American Lit. In each department it is of inestimable value erature. Its selections are from more than one to every student. The department on the Gramhundred authors, English and American, and matical study of the language is very full and comprise extracts on almost every conceivable complete, giving a rigid analysis of every part subject, thus furnishing practice in every style of of Etymological and Syntactical study, with copreading. We were surprised at the varicty and ious examples for illustration. excellence of these extracts. They comprise the We would not undervalue the study of the choicest gems in the English language. The in- classics, but we do think the study of the Engtroductory part we are much pleased with. It lish language has been and is sadly neglected. gives 50 pages of excellent, practical instruc- We wish this work, which we consider one of the tion on Articulation, Syllabication, Accent, Em- best treatises on the English language, was in phasis, Slur, Inflection, Modulation, and other the hands of every teacher in America, to be topics of elocutionary instruction.

read and appreciated.

1858.

ADLER'S PRACTICAL LATIN GRAMMAI. – San- A TREATISE ON ARITHMETIC, combining Anal

born, Carter, Bazin & Co., Boston. 1858. L ysis and Synthesis, adapted to the best modes This new Grammar of the Latin Language is

of instruction in Common Schools and Acad

emies. By James S. Eaton, M. A., Principal on the principle of the Ollandorff method of

of the English Department, Phillips Academy, teaching German. Dr. Adler is well known as

Andover. Brown, Taggard & Chase, Boston. the editor of the popular edition of Ollendorff's German Grammar, and a successful teacher of Mr. Eaton has been long known as one of the languages, ancient and modern.

| 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 deservesam 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 Nor has he disappointed the expectations of translation, which apply these forms, idioms, &c. his friends in the preparation of this work. In The plan seems to us a good one, and we hope methodical arrangement, accuracy of statement, it will be introduced by some of our schools, concise and lucid rules, and the practical characwhere a trial of its merits may be made, which ter of the book, it ranks high among its comshall settle the question of its superiority over petitors for the public favor. the old system. If, by a trial in the school-room, The subject of fractions is taught with simplicit proves itself as valuable as it seems to us on a ity and thoroughness. Interest, Percentage and somewhat cursory examination, all teachers and Analysis are well developed. The application to learners of Latin will thank Prof. Adler for so Square Root contains many difficult, but approgreat a contribution to classical science, and the priate examples. Circulating Decimals and conenterprising publishers will find themselves amp-tinued Fractions ably discussed articles, and the ly remunerated for the expensive outlay necessa- Application to Geometry is quite varied and ry in the publication of so beautiful a book. practical. We commend the work to teachers

| as a book of unusual merit. Essays IX BIOGRAFIIY AND Criticism. - By

Peter Bayne, M. A. Gould & Lincoln, Boston.

We confess ourselves unable to criticise this PETERSON'S FAMILIAR SCIENCE, or the Scienbook. Its beauties and its worth can only be

tific Explanation of Common Things. By R.

E. Peterson. Childs & Peterson, Philadelphia. known by a reading, and as for its faults, we

One of the most valuable of all our text-books have not seen them. Those who have read

for common schools. It treats of the science, Bayne's "Christian Life" will be ready to ap

and gives the scientific explanations of common preciate the book. It contains eight essays, as

phenomena in Natural Philosophy, Chemistry follows: (1), Thomas DeQuincey and his works;

and Physiology. This study is receiving more (2), Tennyson and his teachers; (3), Mrs. Bar

attention than formerly, and deserves more still, ret Browning; (4), Glimpses of recent British Art; (6), Ruskin and his critics; (6), Hugh Miller; (7), The Modern Novel,-Dickens-Bulwer-Thack- ANNUAL REPORT of the Superintendent of Com ery ; (8), Currer Bell, --Ellis-Acton-Currer. I mon Schools of Connecticut. 1858.

The author says, in his preface: “They par- | Hon. David N. Camp has kindly sent us a copy take largely of the character of an introduction, of this, his annual report. It is an able docin successive chapters, to the works of great au ument. Its remarks on dioral, Physical, and thors living and deceased."

| Home Education are admirable.

SHEPPARD'S CONSTITUTIONAL TEXT - Book. – THE OLD RED SANDSTONE.-By Hugh Miller,

CHILDS & PETERSON, Philadelphia. 1858. A new, improved and enlarged edition. Gould

In the preface the author justly remarks: “ It & Lincoln. Boston. 1858. is almost impossible to exaggerate the import- Sir Roderick Impey Murchison, in his addrese ance of a thorough study of the Constitution of before the British Geological Society, said : – the United States by the pupils of our schools. “Hugh Miller's 'Old Red Sandstone,' to a beIt is, nevertheless, a study which has hitherto ginner, is worth a thousand didactic treatises." been sadly neglected, chiefly, as teachers are This is the seventh edition of the world-noted aware, for want of a plain, practical, and thor- | book, and contains large and interesting addiough work upon the subject.”

tions. These additions include more than 160 This want exists no longer. Sheppard's Con.

pages, embracing five papers read before the stitutional Text-Book is all that any teacher

Royal Physical Society of Edinburgh. They

* add much to the interest and value of the book. could wish, and ought to be used in every Grammar and High School in the land.

We are happy to learn that it is now rapidly THE TRUE GLORY OF WOMAN, as portrayed in coming into use in all parts of the country, es- |

the Beautiful Life of the Virgin Mary. By pecially in the best schools of New England.

Rev. H. Harbaugh, A. M. Lindsay & Blak

iston, Philadelphia. 1858. May we not soon find it in many of our Rhode

The writer of this book is well known to the Island schools?

Christian public as the author of three beautiful

volumes on The Future Life. He has chosen a BOUVIER'S FAMILIAR ASTRONOMY. — Childs & beautiful theme for the present volume, and adPeterson, Philadelphia.

mirably 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 toith interest. which this enterprising house usually issue their publications.

LEAVES FROM AN INVALID'S JOURNAL, AND The work has received more enconiums from

POEMS.-By Mrs. E. N. Gladding. George more learned men than probably any other text

H. Whitney, Providence. 1858. book on this subject extant. It is certainly an This little unassuming book of 235 pages, enadmirable treatise on a highly interesting science closes may a gem, cut out, polished and encased, It contains a treatise on the globes and a com- during hours, which the authoress, while racked prehensive Astronomical Dictionary, both of with pain, employed in this labor to relieve long, which are of much value to the learner.

wearisome days and nights of their tediousness We should like the work better were the and monotony. She has consented to give them "question and answer system " dispensed with, to the world, not for cold criticism, but for love's and the usual method of treating the subject sub- sake to her friends. May she find those friends stituted, with questions appended at the bottom numerous and ever true. of the page for those who might not choose to supply their own questions.

REPORT of the Superintendent of Public Schools

of the City of Chicago, Illinois. 1858. CORNELL'S FIRST STEPS IN GEOGRAPHY. D. We have been favored by Hon. Wm. H. Wells, Appleton & Co., New York.

with his last annual report. It contains some A beautiful little book, full of pictures and neat very good doctrines with regard to regular ata little maps for the little folks. It is a very at-tendance at school, and upon the subject of heat. tractive book

ing and ventilation

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