lish intellect. In our nation of kings we should create and foster many such mature monarchs of mind and heart, and with all the grand masters for exemplars, we may truly hope that lofty spirits will be begotten.

Glancing forward through the coming eventful years, we perceive schools of a high grade in each country town, furnished at public expense, where children must attend; the youthful city vagrants and rural idlers all sharing in the salvation of the cheerful primary school. We shall find the Teachers something more than mere school-room automatons; something beyond the mere negative existence which discloses no evil; they are positive, living men and women, whose look is an inspiration, whose words are echoes from the "bards sublime," and the spirit and letter of whose teachings are, "Live a holy spirit-life for God and eternity." Overgrown children, self-abused adults, and moral delinquents no longer presume to tamper with the tender youthful mind, and parents have discarded that idea of expediency which desires just as little education as will do, and in just as superficial a manner as will answer the demands of successful business. Men will then cease to juggle and cheat for sacred things, and will have learned to bask in the warm sunshine of noble impulses and purer thoughts. A stricter morality, a more rigid Christianity will then be taught, with the Bible for a text and class book.

Teaching will be held a profession, with its legitimate moral and spiritual preparation; and our nation shall find a bulwark and strong out-post in the public schools.

Each freeman who is to have a voice in the government will be educated therefor, even as princes are trained in view of the responsibilities and dignities of a crown. Searching the annals of the world, we find a republic even yet an experiment, and we can have no reasonable hope that it can ever be a successful one except founded upon the rock of an enlightened Christianity; and wo may yet betide us, for shifting from such a foundation, and permitting the bane and light of that des. potism which renders our vaunted liberty a defiant falsehood. But yet, ever onward shall we be impelled, through the long summer afternoon of our prosperity, and perchance through the darkness and storm of the succeeding night, until at the dawn of the millennial ages, freed souls may shout a majestic Te Deum for life and victory.

NORTH FAIRField, Ohio.

L. A. T.

Mathematical Department.

PROF. W. H. YOUNG, ATHENS, EDITOR.

SOLUTIONS OF QUESTIONS PUBLISHED IN JOURNAL.

No. 7. I pay thirty-five dollars for two notes-one for $15, due in 4 mo., at 6 per cent. ; the other for $30, due in 6 mo., at 8 Required the discount on each.

SOLUTION BY A. A. K.

per cent.

The debt on the first note will be, at the end of 4 mo., $15,3; on the second, at the end of 6 mo., $313. What is really required is the rate of discount; for, with this obtained, all difficulties vanish. the rate per ct., per annum, of discount. Then and z will be the rates, respectively, for 4 and 6 mo., and

Let x=

200

311 1+ 200

Substituting this value for x in the first term of the equation, for the present worth of the first note, and in the second term for the present worth of the second note, and we find, respectively,

$12.2596 and $22.7405. Therefore,

$15.30 12.2596 = $3.0404.

$31.20 22.7405 = $8.4595.

Discount on first ;

66

66

second.

No. 8. What is the time of vibration of a rod of uniform thickness, 78 in. long, suspended by one end as a pendulum — 39 in., being the recognized length of a pendulum, beating seconds?

SOLUTION BY THE EDITOR.

By the length of a pendulum, we are to understand the distance from the center of motion to that of oscillation. The center of oscillation in a rod, bar, cylinder or any prism (demonstration too extended for the Journal), is two-thirds of its length from the extremity by which it is suspended. Hence the pendulum length of the rod in question is of 78 52. And by mechanics,

=

√39: 52:: 1 : 1.154 sec. Ans.

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No. 9. On each side of any triangle construct an equilateral triangle, and connect the centers of the equilateral triangles. Prove that the connecting lines form an equilateral triangle.

OHIO JOURNAL OF EDUCATION.

DEMONSTRATION BY JOEL E. HENDRICKS.

[The diagram may be readily constructed by the directions.] Let ABC represent any triangle; let ADB, BEC and AFC represent equilateral triangles, described upon its three sides; and let G, H and I represent, respectively, the centers of these three equilateral triangles. Join H, I and G, AG, BG and DC. Then the angle GAB= GBA = HBC = IAC = 30°; and, therefore, the angle CBD = HBG (each being equal to HBD-30°). In like manner we prove that CAD=IAG. Then, because BD: BC :: BG: BH; therefore, (Eucl. 6. 6.), BGH = BDC. And in like manner we prove that AGI = ADC. Hence AGI + BGH = ADB = 60°. But AGB = 120°. Hence IGH = 120°— 60° 60°. In precisely the same manner we may prove that GHI and GIH, each, equals 60°. Therefore the triangle GIH is equiangular, and consequently equilateral.

=

ACKNOWLEDGMENTS-Joel E. Hendricks and A. Schuyler solved all ; A. A. K. and J. B. Dunn solved No. 7; James Goldrick solved No. 9. Some correspondents found the Bank Discount for No. 7, and some erred in regarding the entire length of the rod in No. 8, as its pendulum length. A. A. K. solved all in the May No.

REMARKS.-Owing to the necessity of curtailing as much as possible the expenses of the Journal, we shall hereafter dispense with diagrams when practicable. Correspondents will prepare their demonstrations accordingly. Of course, when a diagram is essential to the clearness of a demonstration, one will be furnished. S. S. O. will find an answer by mail.

EXPLANATION.-A number of errors will be found in the mathematical department of the last Journal. Partly from the fashion and partly fact, we will attribute the blame to the mails, as the Journal had to go to press before the proof was received. The like will not happen again, for henceforth we will not wait for solutions after the first of the month previous to that in which they are expected to appear. Solutions may be acknowledged when received as late as the 10th, but cannot be published unless received by the 1st.

The copy of "Bond" was sent to the printer without alteration. The rules given in the article and the demonstrations are sufficiently clear, but the example, we confess, was made unintelligible.

2

E

QUESTIONS FOR SOLUTION.

No. 13. A bridge when measured on the floor is 80 feet in length, and by looking across from one end to the other, it is found that the middle is two feet higher than the ends. If the floor of the bridge be the arc of a circle, what is the diameter of that circle?

C. R. S.

No. 14. If a solid globe of glass one foot in diameter, be blown into a hollow sphere one eighth of an inch in thickness, what will be the diameter of that sphere?

OMEGA.

ANSWERS TO QUESTIONS ON THE SCHOOL LAW.

BY THE STATE COMMISSIONER OF COMMON SCHOOLS.

QUESTION 1. In

Township, the local directors employed a young man to teach their school. After a few weeks, it was discovered that his moral influence over his pupils was of a most pernicious character. He had, in a clandestine manner, circulated among them a vile and licentious book, which was calculated to excite the grossest passions, and lead to shameful and ruinous practices. Many of his pupils were withdrawn by their parents from the school, and the directors were requested to dismiss him from their employment. A majority of them, however, decided to continue him in charge of the school. Have the Township Board of Education authority under our School Law, to interfere in the matter, and discharge the Teacher? If not, what course can be pursued, lawfully, to secure the dismission of the Teacher ?

ANSWER. It is deeply to be regretted that instances like this should arise under the operation of our school system. The object of our schools is the improvement of those who attend them. Such improvement will not be secured under the instructions of ignorant or immoral Teachers. The greatest possible defect in the qualifications of those to whom the instruction of our children is committed, is the want of high-toned morality. No where else are evil principles and vicious habits more destructive in their operations than in the Teacher. A noble, honorable and pure spirit, is an indispensable requisite in all whose work it is to mould the characters and shape the destinies of the young. That such a Teacher as he in regard to whom complaint is made, should be removed from his office without unnecessary delay, all considerate persons must admit. The question is, how shall this removal be effected? It is thought by some that the Board of Education have authority, when, in their estimation, the interests of schools require it, to interfere in such matters, and overrule the decisions of the local directors. If they have this right it is wholly inferential; for it is not explicitly conferred by the School Law. In sec. 6 of this law, it is declared that "It shall be the duty of the school directors, in each sub-district, to take the management and control of its local interests and affairs, to employ Teachers, *** and to dismiss any Teacher, at any time, for such reasons as they may deem sufficient." The right of appeal from their decision in such cases, is no.

where expressly given. In the opinion of the undersigned, the action of the local directors in such cases, should be considered decisive and final. Otherwise numerous and unfortunate collisions will arise between the local directors and the Board of Education.

Section 45 of the general School Law, provides an appropriate and sufficient remedy for all such cases. Its language is, "If, at any time, the recipient of the certificate shall be found incompetent or negligent, the Examiners, or any two of them, may revoke the same, and require such Teacher to be dismissed."

If, upon due examination, the Examiners find that the Teacher has been guilty of immoral practices, it is their imperative duty to revoke his certificate, inas much as the law makes a "good moral character" a requisite to obtaining such certificate.

QUESTION 2. Can a Board of Education, under the restriction of the last Legislature, levy a tax, general or special, for building purposes, etc., which will amount in the aggregate to more than two mills on the dollar, without submit. ting the subject to a vote of the people? The effect of the law seems to make this restriction, whether designed or not. And such restriction is certainly needed, on account of the abuses practiced under the authority of the 23d section. The special assessments are becoming the rule, and the Township levy the exception. This practice not only imposes heavy and perplexing duties upon the Auditors, but is also the source of constant jealousy and strife among town. ship officers. A sub-district levy for building purposes, usually runs from eight to fifteen mills on the dollar; and the above restriction would virtually do away with such levies, as the amount produced would be insufficient to accomplish the objects desired.

ANSWER. Numerous inquiries have been addressed to this department, relative to the effect upon the 23d section of the recent amendments of the 22d section of the general School Law. Many entertain the opinion expressed in the above inquiry, which comes from the Auditor of Meigs county. Others claim that section 23 is in no manner modified by the amendments above named. They contend that inasmuch as this section was neither amended nor repealed, it still gives Boards of Education authority to levy, without restriction, taxes upon sub-districts, for building purposes.

In order to arrive at just conclusions upon this subject, a correct idea of the original purpose and design of section 23 is necessary. It formed no part of the law as first drafted and presented to the Legislature. The purpose and spirit of the law were to impose township taxes for all school purposes, whatever. To this plan some members objected; and as a compromise of conflicting opinions, section 23 was added. This section was never designed to originate power with the Boards of Education to assess taxes additional to those named in section 22. It is in its character supplemental to that section, defining how, under given cír. cumstances, the taxes named in said section 22, shall be levied. Whatever amendments, therefore, go to restrict or limit the power of taxation conferred by section 22, pass, by necessity, to the following section.

Among the amendments to the School Law, passed April 17th, 1857, is a modification of section 22, which limits taxation for all school purposes, other than the payment of Teachers, to two mills on the dollar, of the taxable property of the township; excepting in cases where a vote of the township shall decide that a greater tax is necessary. As section 23 is, virtually, part and parcel of section 22. no greater tax than two mills on the dollar can be levied upon any sub-district for building purposes, except when the people of the township shall, by vote, order otherwise.