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and growing State. The small boy, with mild expressive countenance, now carefully conning bis simple lesson, may yet be the humble, but fervent messenger of heaven, whose earnest impassioned eloquence will plead the cause of suffering, sinful man at the throne of grace. And who knows but the meek little girl, now in childish accents reading aloud, may live to tread the missionary path along the Ganges and teach the Hindoo in his native home the sublime truths of that divine religion whose power is more potent, even on the savage idolator, than all the barbarous force a mighty Empire can command. Great is the responsibility of parent and Teacher ; they form this plastic material, and in so doing they mould the future destiny of our happy land and its heavenborn institutions. If false views mar, and vicious habits destroy future usefulness, it will be the result of bad example and a want of proper training. Let no Teacher think himself acquitted when the daily course of study is accomplished : no, his work is scarcely commenced

-forming correct habits, developing natural talents, making ardent, active, healthy, independent thinkers, instead of weakly, servile imitators all this forms but a part of his study. Let no parent think his part of this great work done, when he sends his children to school ; let him aid the Teacher, have a tacit understanding with him on everything relative to the child's interest, assist in choosing the right kind of School Directors, and visit the school to see its working for himself. And the School Director! Legislative enactments point out his duty; and with uplifted hand he swears to perform it - let him beware who trifles with an oath to him are committed the interests of education in his district, and woe to the children of those who sustain him in the negligent, careless performance of his duty; they will reap the bitter fruits when it is too late to remedy the evil. Let the Director aid the Teacher in every judicious effort, support him with his legal authority when necessary, encouraging and gently enforcing regularity of attendance, visiting the schools often, and seeing for himself that all is right; all of this the law and his oath require.

SHARON. Sharonville, O., Oct., 1857.

- Sweat is the destiny of all trades, whether of brows or of the mind. God never allowed any man to do nothing. How miserable is the condition of those men who spend the time as if it were given them, and not lent; as if hours were waste creatures, and such as should never be accounted or.

COUNTY SUPERINTENDENTS.

When Samuel Lewis was Superintendent of Schools in Ohio, he advocated' most earnestly the appointment of County Superintendents. His arguments were repeated by Secretaries of State, who subsequently were the superintendents of the School Department for Ohio. In 1845 a law was passed giving counties the privilege of electing School Superintendents. Only one county (Ashtabula) practically availed itself of the privilege. The appeals and arguments of Mr. Lewis, and his successors in office, were widely circulated in Pennsylvania and other States; and in Pennsylvania, at least, had more permanent influence than in Ohio. Counties in that State now elect school superin. tendents and fix their pay. In some counties the salaries are liberal. Ohio should practice what her best policy dictates.

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Mathematical Department.

PROF.

W. H. YOUNG, ATHENS, EDITOR.

(All communications for this Department should be addressed to the Editor, Onio University, Athens, O.; and to be in time, must be mailed by the first of the month preceding that in which they are expected to appear.]

SOLUTIONS OF QUESTIONS PUBLISHED IN SEPTEMBER.

No. 15. There are three rectangular blocks of marble, all of the same shape, which is such that they may be placed together, so as to make a similar joint block. The largest is eight inches long. How long is the joint block?

SOLUTION BY A. A. K.-As the blocks are similar, we may suppose the two smaller to be equal, and together equal to the largest. Therefore, these two may be joined into one of the same shape and equal to the largest, and with it would constitute a similar joint block. Now, as the joint block will be double the large, 8 in. block, and as the contents of similar solids are as the cubes of their homologous edges, we have the proportion 1 : 2::(8) 3 : x3, whence x = 10.07936, the length of the joint block.

2 n

odd num

a2

No. 16. Find three series of perfect squares, any term of the first of which shall be the sum or difference of the corresponding terms of the other two.

SOLUTION BY A. SCHUYLER.—Let az, 62 and a2 + 62, be the first terms, respectively, of the three series. Since a2 +ba, by the conditions, must be a perfect square,

its
square

root will be some whole pumber greater than b. Therefore, let Vaz + 12 = 6+n, which gives a n2

a? 1 6 To simplify the problem, let n=1; then b=

2

a3 1 But by hypothesis b is entire; hence is entire: therefore,

2 a2 - 1 is even, ond consequently a is odd. Hence if, of

any

.1 ber, a be the square root of the first term of the first series, 6

2 will be the square root of the first term of the seeond series, and Vaz + 62 will be the square root of the first term of the third series.

* It will be found, on trial, that the problem admits of an indefinite number of solutions. For a full discussion of a similar problem, I would refer to page 337 of vol. III, Ohio Journal of Ed.

No. 17. Suppose the diameter of the upper base of the frustrum of a cone to be 20 in., that of the lower base 28 in., and the altitude 40 in., what will be the perpendicular distance between the lower base and a parallel plane, dividing the solid into two equivalent frustra ?

SOLUTION BY Jos. TURNBULL.-Let a = the radius of the circle in the dividing plane. Then since the altitude and the difference of the radii of the bases are as 10:1, we have 10 (14 - x) required alti

n. 10 (14 — 2) tude. Then, from known principles,

X

3 (143 +14x + 2) = (142 +14 X 10+102) + 2, one of the

4 partial frustra, by the conditions, being equivalent to one-half the given frustrum. Hence we find x = 12.32 t, and 10 (14+x) = 16.7 in., which was required.

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ACKNOWLEDGMENTS.-No. 15 was solved by A. Schuyler, James McClung, A. A. K., and E. Adamson ; No. 16, by A. Schuyler, Joseph Turnbull, E. Adamson, James McClung, and J. S. Burnham; No. 17, by Joseph Turnbull, E. Adamson, A. Schuyler, James McClung, and James Rutherford. A solution to No. 14, by J. N. Caldwell, arrived one day too late for acknowledgment last month.

Associate Editorial.

HIGH SCHOOL.

From Annual Report of E. E. WHITE, Sup’t of Portsmouth Schools. The High School is the crowning department of our schools — the capstone of the pyramid. It, however, not only surmounts and adorns the system, but it imparts strength, energy and vitality to it. It has been remarked that a High School is worth more in its influence apon the lower schools than all it costs, independent of the advantages received by its actual pupils. All experience attests the truth of this statement. The influence of a properly conducted High School permeates all the other schools, causing greater thoroughness, more regular attendance, and more exemplary conduct. It stimulates the teachers to greater exertions and vigilance, by exbibiting the results of their methods and labors in close proximity. It also secures greater uniformity of instruction in the lower grades of school. To the scholars in the lower classes it presents a strong and constant stimulus, exciting a desire for promotion and awakening a laudable emulation. Its influence upon the scholars of the Grammar Schools, in promoting diligence in study and correctness of deportment, is immediate and powerful. It offers a strong inducement to parents to continue their children in school, even at a little sacrifice, until they are qualified for an honorable promotion to the highest educational advantages of the children of their neighbors.

The organization of a successful High School is always followed by a large increase in the number of scholars in attendance upon

the lower schools. It becomes a center of influence, imparting dignity and reputation to the entire school system.

The value of this department, however, does not consist wholly, or primarily, in its reflex influence upon the lower schools. It possesses within itself great merits and advantages. The demand for facilities to acquire a higher education is now imperative. The advantages and benefits flowing from such culture are numerous and evident. Colleges, Seminaries and High Schools exist wherever intelligence and refinement are valued. The great merit of the Public High School is, that it presents these high advantages, gratuitously and as a RIGHT, to all classes of the community. Its chief honor is, that many of those who are in it prepared for an enlarged usefulness would, but for its existence, bave entered upon the duties of life with nothing further than the mere rudiments of knowledge. " It takes the children of the people and sends them out into life, endowed with such eminent advantages of education that they will be a blessing to society, adorning their various pursuits with intelligence, enriching them with discoveries, elevating and equalizing the rank and respectability of their widely different occupations, making industry honorable, and securing to labor its proper dignity.” *

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The utility of the High School is further evinced in its permanency. It has oftentimes cost great effort to effect its organization, but when once a part of the public school system, it becomes as fixed as the very system itself. Its success silences all opposition and converts its enemies into advocates.

In order that the High School Department may possess these advantages and exert this influence in a high degree, it must be properly organized and wisely conducted.

1. In the first place, it must be adapted to the system of which it forms a part. In small cities and towns it must either contain a limited number of scholars, or its standard of admission must be low. The number and qualifications of the scholars annually admitted must depend upon the number and efficiency of the lower schools.

2. The course of study should secure a continuance and thorough completion of the work commenced in the departments below. If the standard of admission is low, the course of study should adapt itself accordingly. The attempt to put little boys and girls, that have not yet entered their teens, over a severe College curriculum, is a fatal error. Thoroughness in the common branches of study is the basis upon which alone a higher education can be successfully built. To plaster over an indifferent or superficial elementary scholar with a thin coating of Geology, Geometry, Chemistry and Astronomy-after the manner of those who convert wooden houses into stone-and then call the result a higher education, is a serious sham.

3. The examinations for admission should always be conducted in the most thorough and impartial manner. Scholars should feel that, to pass this ordeal successfully, is the reward of diligence and assiduous exertions in their studies. Let the impression creep into the lower schools that the examination is a "mere form," that a certain number of seats must be filled, or that scholars can slip in upon the general merits of their class, and the reflex influence of the High School is practically

* President Board of Education, New York City.

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