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nature of the negative sign, we may take the expression ab-", where the positive exponent points out a factor which increases the result, while the negative exponent points out a factor which diminishes the result. 3d. It is asked, there be a zero power, what is the zero root ?
1 / Let us see.
It is manifest that Vā=a?. So, Vā=a?, and, whatever be the value of x, this must still be true. Hence when x becomes
greater than any assignable quantity, we have varam, or Va=a®. The principle is the same as is applied to any other exponent, viz: Any root of a quantity is equal to a power of that same quantity whose exponent is the index of the root inverted.
4th. It is held, that if (1000)=1, and 1°=1, therefore (1000) = 1°, and 1000 = 1. And so it does, so long as we consider the quanti
1 ties with reference to their infinitessimal exponents, but no longer. Some of our correspondents object to the reasoning. But we admit the conclusion, and yet see no reductio ad absurdum. The difficulty, we think, is in forgetting that all finite quantities are equal when measured by an infinitessimal scale, as is done above, or by a scale of infinites, as is sometimes done. This may seem paradoxical, but not more so than the necessary doctrine, that there is no distance in infinite space and no succession of dates in eternity. Our earth at every point of her orbit is the same distance from the confines of space, and the nineteenth century is as early a date, estimated from the Beginning, as the first cooling of the primitive rocks. So, measured by a similar scale, 1000 = 1; but, detached from their zero exponents, it does not follow.
- In education, as in everything else, causes will produce effects; if, therefore, we want good effects, let us combine the causes that will produce them.
- The province of Education opens a wide field for the knavery of quacks and charlatans, who make a practice of plundering the unwary and the ignorant. The wretch who, by his bold and interested presumption, puts to hazard the health of the body, is a subject of mental detestation and reproach ; but he is still more detestable, who tampers with the health of the youthful mind.
- There is a large amount of valuable geographical information derivable daily from newspapers, that may be presented to pupils by Teachers.
C. Kingsbury.... I. W. Andrews, J. Chester.
Mann, M. C. Whiteley.
Hancock, John Ogden, J. Young.
Royce, J. H. Rolfe.
Smyth, J. Hancock, C. S. Royce.
For the above table we are indebted to School Commissioner Smyth, who is busily preparing his Annual Report, to be laid before the Legislature.
SCRAPS - ORIGINAL AND SELECTED.
Summer too soon has gone,
Winter too soon has come on, The leaf has fallen, but the fine ear of informed faith can hear the grass growing, although the eye sees the ice-bound rivulets; and can hear the melody of winds blowing over the blossoms of future summers, and in the dim distance, too far for distinct interpretation, can yet discern the voice of happier generations.
THE REWARD OF DILIGENCE. — Franklin illustrated a text of Scripture, “Seest thou a man diligent in his business ? he shall stand before kings.” And having quoted it himself, added : “ This is true. I have stood in the presence of five kings, and once had the honor of dining with one.” Franklin was diligent from his youth up.
- At a recent meeting of the Morgan Co. Teachers’ Institute, the daily reading from the Bible in Common Schools, and the introduction of History as a recognized branch of education, were recommended. Teachers and parents were earnestly recommended to be paying sub. scribers for the Ohio Journal of Education, and patrons of school periodicals. An out and out indorsement was given to the Library feature. Directors were invited to visit the schools more frequently, and Teachers who decline to take part in the active duties of Institutes were kindly reminded of their duty. Let there be similar sentiments manifested all over the State, and the cause of education will be alive in the hearts of the people.
- Mr. G. W. Gooley, member of the Board of Union Schools, at New Holland, Pickaway Co., Ohio, in a letter dated Nov. 21st, expresses a wish that the public be notified of the facts in the case of a Teacher calling bimself H. B. Smith, “that others may not suffer like imposition." “Who came among us, obtained a situation as Principal Teacher in our “Union School,' at a salary of $40 per month ; served one month to the acceptance of the School Board and the patrons generally ; obtained a check on the 'Exchange Bank' for his wages, and went to Circleville to draw his money, since which time no tidings of his whereabouts have reached our ears, although three weeks have now elapsed. During the time spent in this place, this honorable gentleman managed to obtain credit at different places, amounting to fifty dollars or more. He also took with him a watch given him by the gentleman with whom he was boarding, to be left with a silversmith to be repaired, also a dollar, cost of repairing, neither of which he has returned.” We know no more of the case than is in the above letter, which is published at the urgent request of the writer, to protect others.
" OUR JOURNAL.”—The teachers of this State, if they will commence forthwith, can cheer the hearts of the Executive Committee of the Teachers' Association, by furnishing two or three thousand names of subscribers, with the dollars paid down, to commence a new year of the Journal. Let every subscriber renew. Those who can get five others should do so. Many can get one hundred and more. The will only is wanting. The credit and character of the teachers of Ohio, the great educational State of the West, is involved in the earnest discharge of this duty. Reader send on your money, and proceed at once to enlist others in the work.
A new set of mail books now awaits a list of new subscribers. Let names be plainly written and the Post-offices and counties be given with accuracy.
On the evening of Monday, Dec. 28th, night before the day of assembly in Columbus of the Teachers of the State, the Beethoven Musical Society give a concert, and Mr. W. T. Coggeshall delivers an address to the members thereof.
The Atlantic Monthly for December is a choice magazine for holiday leisure hours. GENERAL DUTIES PROPER TO BE OBSERVED BY TEA( HERS.
To be at their respective rooms at least fifteen minutes before the time appointed for commencing the exercises of the school, and to open them for the reception of pupils five minutes before said time of beginning school.
See to the ventilation of the rooms, securing fresh air without irregular conditions of the temperature of the apartments.
Advert to the importance of forming habits conducive to health in such language as may impress the pupils.
Teachers to be neat and orderly in the appearance and appointments of the rooms in their charge.
To keep an accurate daily register of the names of their scholars, reporting faithfully attendance or absence, punctuality or tardiness, good or bad behavior, and the manner in which their le sons are recited.
Punishments should and will be few, if moderation, kindness and appropriate appeals to the honor, good sense and self-respect of the pupils, be made in good time, and the approaches to faults and offenses should, in this regard, be made the special subject of watchfulness.
DUTIES OF TEACHERS IN CONDUCTING RECITATIONS. — Prepare specially for the lesson, by thoroughly understanding it yourself.
Teach the subject and its practical bearing, not the words only, that it may be thoroughly understood.
Give out no new lesson until that in hand is mastered perfectly.
In assigning a new lesson, aid in its acquisition by explanatory suggestions of what is to be done and how it can best be appreciated.
Rules and definitions to be wrought into the understanding, not memory only.
Depart from the letter of the book, and allow pupils to make applications by some instance of practical business, of the subject under consideration.
Daily application by study and observation, to increase your own fund of knowledge, that by illustration and example, anecdote and similes, more subjects may be known by you than you are required to teach.
Do not, by hurry or petulance, supersede the efforts of pupils in responding, when, by patience and diversity of modes of presenting your inquiries, you may draw out correct answers.
Fix the attention of the class, exciting their interest, and spurring the listless to watchful. ness by irregular calls on different pupils.
Exhibit animation yourself, and avoid regular and formal routine.
Strive to secure from the pupils correct and fluent language in their replies, making it a special point to build up symmetrically their mental growth, and cultivate harmoniously therewith their dispositions and manners.
Make it a ne plus ultra, each lesson must be mastered.
Let the pupils exhibit by analysis, by submitting in their language, the merits and meaning in detail of their lessons.
Keep a daily record of the merit of each pupil's recitation, his deficiency or thoroughness. It must be an understood consideration, that a fair and positive observation is uninterruptedly made and recorded of the history of each one's performances.
Monthly abstracts of these observations should be made out on a small printed note, submitted to parent and guardian, and returned with his or her signature thereto as proof of it having been seen and read.
Simultaneous recitations generally to be avoided, at times permitted for variety, and to awaken the class from dullness.
That the vocal organs may be developed and the voice rendered full-toned, firm and harmonious, by simultaneous exertions of the muscles of articulation in exercises requiring utter. ance in a loud voice.
Order in taking and quitting places, requisite.
Better attention may result from passing by temporarily those who give unsatisfactory replies, and avoid encouragement to the indolent by prompting and the “ drawing out process," where evidently the pupil is presuming upon and awaiting such helps.
As the knowledge of the mental processes of others and appreciation of the faculties and powers of pupils, as well as the art of happily applying in detail, this knowledge fits a Teacher to communicate and educate properly, and touch the right spring of action, at the right time, it is the duty of Teachers to prosecute the study of Mental Philosophy.
- We have received a valuable report of the Dayton Public Schools, James Campbell, Sup't.
PREPARE FOR WINTER.–School rooms and premises should be early supplied with all the comforts for winter—the clothing and exercise of youth should be such as to preserve the requisite warmth and keep open and active the perspiratory orifices.