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DEMONSTRATION BY JOEL E. I ENDRICKS.
[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°— 600 = 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. 0. 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.
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 ?
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?
C. R. S.
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 influ. ence 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 grea test 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 Examirers, 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 guilt of immoral practices, it is their imperative duty to revoke his certificate, inasmuch 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 submitting 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 sec. tion 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 ap. on 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 cir. 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-dis. trict for building purposes, except when the people of the township shall, by vote, order otherwise.
If the effect of this opinion shall be a practical repeal of section 23, it will be, in the opinion of the undersigned, no cause for regret; as said section has been a constant source of difficulty between various school authorities, and of injury to the cause of education throughout the State.
I LOVE THE WEST.
BY C. W. SANDERS.
1. I love the west, the gal-lant west, With its bright and sun - ny streams; 2. I love the west, the migh-ty west, With its wild and sha - dy glens;
land of my childhood's dreams.
With its rivers old and grand;
The freight of many a land.
With its green hills, and its flowers;
Where the wild vine weaves its bowers.
4. I love the west, the beauteous west,
With its prairies broad and free; The heart with purest rapture swells,
As we gaze on the flowery lea.
For my home and heart are there;
Is my humble, ardent prayer.
– The official proceedings of the Semi-annnal meeting of the Ohio State Teachers' Association, recently held in the good old Borough of Steubenville, appear in our pages herewith. On our hearts are recorded those indelible memorials of persons and things which hopeful men and women treasure up at an association where the finer and nobler qualities of our nature are awakened by concerted action for the welfare of our race, and the elevation of the noble profession of mental and moral instructor of our youth.
– Vacation has come, and relaxation and recuperation await the Teacher. Let each one be re-baptised for the great missionary work to be resumed in a few weeks! It has been said that the undevout astronomer is mad. With all the gifted powers of the star gazer, his work is but to see and admire-of course to reverence. But the humble Teacher has in keeping an immortal soul — has in charge the training of those who may owe directly to him or her, their temporal and immortal interests. It is true, then, as Gov. Chase has said, in that chaste and elegant letter read to the Association, and which should be printed in letters of gold, and read by every Teacher and school officer in the whole United States, that “it is impossible to over-estimate the importance of universal education, where every boy is to be a voter, and any boy may be a President.”
Good men and women of the Teachers profession in Ohio, the Journal wishes you a pleasant re-union among your friends during your vacation visits, and invokes you to renewed and more determined effort in the field of labor, which requires eminent fitness of scholarship as well as faith and patience.
– Friends of Normal Schools should scan thoroughly the letter of Gov. Chase above alluded to, and consider the proposition broached by the Chief Executive officer of the State, looking towards making the Ohio and Miami Universities of Athens and Oxford, under legislative control, parts of a general plan in our State for Educating Teachers.
- A correspondent sends us the following. Members of the Ohio State Teachers' Association please take notice:
“Much has been said and done about rendering the Ohio Journal of Educa. tion self-supporting, and members of the Association are called upon to come forward and make pledges to procure subscribers for its support. To this they have responded with the accustomed liberality of Ohio Teachers-of brave labor. ers who can raise $3000 at a sitting, and $1000 in a few seconds.
“But this will no more make the Journal self-supporting than the possession of the mines of South America made Spain wealthy—or of the mines of California tends to enrich us. Our true wealth consists in our powers of action, our industry and enterprise. If the tone of our Journal be not in advance of the age, and therefore calculated to educate it - if the articles be not replete with profound scholarship, sound sense, superior practical information, and valuable statistical tables - if it be not a Journal which exchanges delight to recognize and carefully read for items and extracts, it will never be widely read, frequently quoted and self-supporting.
“The great question is, how shall this be done? Let Teachers resolve to write something for the Journal – let them resolve to write something valuable and something that shall be quoted, noticed and criticised. They will then write