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equal to two thirds of the radii B and B', be drawn to touch externally the circles B and B'. Then will the circumference of circle A be tangent to those of circles C, B, and B'.

Mathematical Questions.

1. Two men, A and B, travelled the same road, and at the same rate, from New York to Boston.

In proving this it is necessary simply to show When A had travelled to within 50 miles of BosA G to be equal to A E and A F.

It is evident that A B C is a right-angled triangle. By construction B C is equal to five thirds of radius B; and as A B is three thirds, then, in accordance with a well known property of right-angled triangles, AC must be four thirds. CG is two thirds, thus making A G equal to six thirds, to which A F, and A E are also equal. From this it follows that circles C and C', answer the conditions named in the prob

lem.

These circles, having each a radius of one third radius A, have together an area of two ninths circle A. This, added to the former one half, gives us thirteen eighteenths, the space occupied by circles B, B', C and C'.

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Next, draw the circles D, D', D", D'", each with a radius one sixth of radius A. That they will not intersect the previously drawn circles is evident from the case of D. Completing the The rectangle A B C D, C D is equal to A B. radius C forms two thirds of this line. Hence radius D is one third, which is equal to one sixth of radius A. In the same manner, B D is equal to AC or four thirds of radius B. Take from this radius B, radius D remains, equal to one third, or one sixth of radius A. The circles, therefore, do not intersect.

ton he overtook C, travelling at the rate of 3
miles in 2 hours, and in two hours met D, trav-
B over-
elling at the rate of 2 miles per hour.
took C 45 miles from Boston, and met D 2 hours
before he came within 31 miles of Boston.
Where was B when A reached Boston ?

2. What two numbers are those whose product is equal to their difference and the quotient from the division of the greater by the less is equal to the square of the greater?

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As each of these four circles has a radius of one sixth radius A, their areas must together MR. WILLIAM S. KENT, who has been for a equal four thirty sixths; which, being added to long time an efficient teacher at Phenix, has rethe former thirteen eighteenths, gives an aggre-cently taken charge of the Grammar School at gate area of five sixths of circle A. The unoc- River Point. We wish him abundant success. cupied space must, therefore, be equal to one sixth.

From the discussion of the above, several inferences may be drawn, to the consideration of which, the reader is, in conclusion, most respectHESIL. fully invited. Providence High School, April 21, 1858.

Please send in your subscriptions.

THE SECOND VOLUME of the New American Cyclopædia is now ready, and offered to subscribers by D. Kimball & Co., Market Square.

WE shall notice Eaton's Arithmetic in our next. See the advertisement of the publishers, Messrs. Brown, Taggard & Chase.

OUR BOOK TABLE.

LIFE THOUGHTS, gathered from the extemporaneous discourses of Henry Ward Beecher,

by one of his congregation. Phillips, Samp

son & Co., Boston. 1858.

practical rules, to govern him in the work. It embraces the principles of Punctuation, Syntax, and Prosody.

Its exercises for Reading, Reproducing and Comparing with the original, are admirable. We

commend the book to the favorable attention of those in want of a work for the school-room on English composition.

A THEORETICAL AND PRACTICAL ARITHMETIC;
Designed for Common Schools and Academies.
Revised Edition. By Daniel Leach and Wil-
liam D. Swan. Hickling, Swan & Brewer,
Boston.

There is no necessity for our saying a word for this book. But we must speak. It is full of Live Thoughts. Here are recorded and preserved the richest and choicest of the thoughts and sayings of this great man, and eloquent preacher. Very few writers or speakers are so felicitous in illustration as Henry Ward Beecher. The writer of this volume remarks, in the preface, that "it is not given to the world as the full-boughed tree; but only as some of the leaves which have fallen from it through two successive seasons." We think that it is rather the full, ripe, golden grain of two successive seasons, plucked from the dry stalks, separated from the chaff, and served up claims to be "eminently both a practical and as nutritive, wholsome, palatable bread.

Price, $1.00. For sale by Gladding & Brother.

A NEW SYSTEM OF ENGLISH GRAMMAR.-Progressively arranged, concisely embodying the Principles of Analysis and Synthesis. By W. S. Barton, A. M. Gould and Lincoln, Boston. Here is another Grammar added to the already infinite number of text-books on this subject. But, unlike many, it has some good things in it; some things worth learning. It is evidently the result of study and practice. In many things, it follows with remarkable closeness Greene's system. For example, see. Pronouns, Conjunctions, and especially Syntax.

Arithmetic is one of those subjects, with regard to which there is a great diversity in teaching, and on which there is such a variety and number of text-books that many find it difficult

to decide which is the best. The work before us

a theoretical treatise on the science of numbers."

The authors say "they have bestowed great labor on the rules and definitions, in order to make them concise, lucid and accurate."

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The book is not cumbered with unnecessary and extraneous matter, and is therefore not so large and high-priced as some other text-books on this science

The contractions in the Appendix are, many of

them, original, ingenious and useful. There is a simplicity and conciseness about many of the rules which we like. It is the text-book in the Public Schools of Providence.

Teachers will do well to procure a copy, as we THE TEACHER AND THE PARENT; A Treatise feel assured they will find it useful.

PRACTICAL EXERCISES IN ENGLISH COMPOSI-
TION or the Young Composer's Guide. By
W. S. Barton, A. M. Gould & Lincoln, Bos-

ton.

This seems to us, on a hasty examination, to be a well-arranged and very useful work. It gives abundant practice in the difficult art of composition, calling attention to the most common and natural mistakes, and placing before the pupil's eye, what appear to us, simple,

upon Common School Education; containing practical suggestions to Teachers and Parents. By Charles Northend, A. M. Eighth Edition, Enlarged. A. S. Barnes & Co., New York. This is a book that EVERY TEACHER and EVERY PARENT should own. It is one of the few standard educational works that are really practical. It ranks side by side with the world-renowned "Page's Theory and Practice of Teaching."

On the receipt of $1.25, the publishers will forward a copy, frce of postage. Teachers, send for it.

THE ATLANTIC MONTHLY for May completes SMITH'S ILLUSTRATED ASTRONOMY, designed for volume 1. It contains the following articles:

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'American Antiquity; Roger Pierce; Amours de Voyage; Intellectual Character; Loo Loo ; Charley's Death; The Catacombs of Rome;. The Pure Pearl of Diver's Bay; Camile; The Hundred Days; Epigram on J. M.; Beethoven, his Childhood and Youth; A Word to the Wise; Henry Ward Beecher; Mercedes; The Autocrat of the Breakfast-Table."

The literary character of this work is undoubtedly of a higher order than that of any other Monthly Magazine in America. Those who wish to improve themselves in English literature should, by all means, read the ATLANTIC MONTHLY monthly.

PETERSON'S MAGAZINE for May comes to us with its usual full supply of stories, poetry, fashions, and an original steel engraving. It is one of the cheapest magazines in the country.

A COMPENDIUM OF THE PRINCIPLES OF ELOCUTION, on the basis of Dr. Rush's Philosophy of the Human Voice. To which is added a copious selection of exercises for Reading and Declamation. By Sam'l R. Gummere. Uriah Hunt & Son. Philadelphia.

the use of the Public Schools in the United
States. Illustrated with numerous original
Diagrams. By Asa Smith. Sanborn, Carter,
Bazin & Co., Boston.

We are personally acquainted with this book in the school-room. It is the best elementary work on Astronomy that we have ever seen. It consists of a quarto book of 79 pages, with numerous illustrations, which seem to us admirably adapted to assist the scholar to understand the movements and relations of the earth and the heavenly bodies, and to apprehend the laws of

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ARTHUR'S HOME MAGAZINE.-We welcome the monthly visits of this excellent magazine. Its contributions are of a superior order, and its visits cannot fail to be pleasing wherever it goes. The May number has some choice articles.

AUTOBIOGRAPHICAL SKETCHES AND RECOLLEC
TIONS, during a thirty-five years' residence
in New Orleans. By Rev. Theodore Clapp.
Phillips, Sampson & Co., Boston.

The author of this book is an aged Universal

The work of Dr. Rush, which forms the basis of this book, is known as one of the best extant on Elocution. Mr. Gummere is an experienced teacher of celebrity in New Jersey and Pennsylvania, and has devoted himself with great zeal and labor to the preparation of a work on Elocution, which should at least receive his own ap-ist clergyman, who in his old age has given to the probation. He is independent in his views, many of which will strike the common scholar as, at least, quaint, especially his system of pronunciation, with regard to which, he frankly says many will "find him a skeptic, beyond all hope of redemption."

GODEY'S LADIES Book for May is excellent. We regard this magazine as standing at the head of this department of family reading. The May number is embellished with a very fine steel engraving. It is an exquisite picture, alone worth the price of the book.

world the story of his life. He portrays with vigor and pleasing earnestness the scenes of his early life in New England, his college course at Yale, and Theological study, at Andover, his call and settlement at New Orleans, his change of doctrinal views, and subsequent ministerial and philanthropic labors. The book is written with talent and scholarly ability, but appears to us false and sometimes unfair in its reasonings.

WE are indebted to Hon. James F. Simmons, U. S. S., for the fifth volume of the Report of the Pacific R. R. Exploring Expedition.

The R. J. Schoolmaster.

VOL. IV.

JUNE, 1858.

NO. 4.

For the Schoolmaster.

erted, and to adduce a few illustrations for

The Reciprocal Influence of Language and proof and amplification.

Character.

BY THE EDITOR.

AMONG the noble powers given to man by his Creator, and which we must suppose he shares in common with angelic beings, is that faculty by which he communicates his thoughts, feelings, desires, to another.

But before we proceed to our subject, it will be well for us, that we may have a correct perception of the ground upon which we tread, to define our terms. "Language," says Webster, "consists in the oral utterance of sounds, which usage has made the representatives of ideas. This is the primary sense of language. Articulate sounds are repreAmong the renowned and valuable inven- sented by letters, marks, or characters, which tiens of man, is especially prominent that of form words. Hence, language consists also clearly and understandingly representing to in words duly arranged in sentences, written, the eye, the burning thought as it is conceiv-printed, or engraved, and exhibited to the ed in the soul, or the priceless result of calm eye." Custom is defined to be an habitual and laborious study and reflection. practice, an established manner, a repetition

of the same act."

That speech has an untold power upon the mind, is so much an axiom that it need not Now the act pre-supposes the idea which be questioned here. That the orator and the called it into existence; and as words are the writer exert a powerful influence upon the representatives of ideas, it is evident that the character of such as come within their magic idea must have had existence previous to the circle, is equally clear, and need not be dis-word; and since we may naturally conclude cussed or disputed. It will be our aim in the that the first forms of language were names present article to render it evident to all, that of things and actions, it follows that lancharacter, on the other hand, has an equally guage must have been preceded by things and powerful influence upon language; so that actions, for a name would never be given to one would hazard little in saying that the lat- a thing without existence. ter may be an accurate index to the former. We shall endeavor to point out some of the ways in which this reciprocal influence is ex-language.

Therefore, since custom is the "repetition of an act," we conclude that custom precedes Shadows," says one, "follow

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substances, so words result from things. There will, therefore, be a correspondence between the customs of a people and their language, and as the one changes, so changes the other.

It would be easy to show from history that those nations which are sunk the lowest in ignorance and degradation, have a greater number of words to designate the various species of vice, and a less number relating to the development of the higher faculties of our

nature.

It is said that a Brazilian tribe has no word to express the idea of "thanks;" and we do not wonder at all, when we are also told that although "inveterate askers," upon receiving a gift, it is their custom merely to remark, “I am glad of this," or "this will be

useful to me."

tion this word entirely disappeared, except as it was applied by sorcerers in their superstitious incantations, as the cognomen of a fab ulous ghost.

The Chinese have maintained but a limited commerce and a restricted intercourse with other nations, while they have preserved a rigid adherence to the customs of their fathers, and a strong aversion to every species of innovation upon established usage. Confining themselves within their huge walls, and permitting no foreigner to intrude upon their do mains, they have presented the anomoly of a people retaining the same unchanged customs and language for thousands of years. While in other parts of the world nations have fallen, and others risen to the first rank of power, this people-remaining in statu quo, and plodding on in the same path in which their fathers were accustomed to tread-has stood apart, as if forming no portion of the human family. If, then, there exists this correspondence between a people's character and language, and if the one be an index to the other, then

The language of Van Dieman's Land has four words to designate the taking of life, not one of which conveys any reprehension, or points out the difference between "to kill" and "to murder," and although abounding in words denoting "hate," even of the deep-national peculiarities and distinctions must be est dye, yet they have not one word to convey the idea of "love!"

History shows, also, that as a nation has improved in the arts and sciences, in general civillization and happiness, so has its language been refined and purified. As one vice after another becomes extinct, the very name by which it was known eventually is lost. As the practice of a virtue becomes established, the name of that virtue, its attributes, and numerous words more or less nearly related to it, become established and received into general use. So also is the contrary true, that as a nation degenerates in character, the language deteriorates in like proportion.

A missionary tells us of a Caffre tribe in Africa, having at one time a word designating the Supreme Being, and in a single genera

found to correspond to certain characteristics in their language, and we should be able to prove from history our position that as the character of the people changes, so changes the language. Let us now examine a single peculiarity of several nations, and the corresponding indices of their languages.

The three prominent modern lauguages arc the French, the German, and the English. These three languages contain nearly all the modern literature of the world, and the nations speaking them are the leading and the most powerful nations. We also find, in proof of the position we have assumed, that the prominent characteristics of these three languages point to the distinctive peculiarities of the several nations.

The leading features of the German mind

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