The Teacher's Reputation.

How is a Teacher to maintain for a great number of years, the reputation of a good Instructor? "How is it," inquired a gentleman of a gray-headed Teacher, "that you, who have nothing beyond a Common School education, have so long continued to rank among the best Instructors of the county; whilst nearly all who were your fellow laborers twenty years ago, are now considered unfit for the occupation."

"A few principles by which I have endeavored to regulate my professional deportment," replied the old man, "have probably done much towards producing this result."

1. "I have not considered or treated others of my occupation, as being my rivals."

2. "I have never knowingly suffered parents or pupils to suppose my attainments greater than they really were.'

3. "When I have found that I have erred in my instructions, I have been prompt in correcting the error."

4. "I have practised visiting schools, for the purpose of making additions to my stock of professional knowledge."

Prejudices unfavorable to subsequent success are often engendered by rivalship. Unkindness of feeling towards the successful, on the part of the friends of the unsuccessful party is often produced, and is apt to operate injuriously to the school and the Teacher.

It is generally unwise for any one to take charge of a school, if so doing, should give another reason to feel that he or she had been supplanted.

If teachers from a distance find employment in our vicinity, by forming an acquaintance we may obtain new ideas, valuable to us in our vocation; and from our previous knowledge of the community, we may be able to make suggestions by which their services may be more effective.

Some of our acquaintances, who, otherwise might have succeeded well in teaching, have failed because their scientific attainments were below what they had induced the community to expect. Whatever may be our abilities, we must fail in the confidence of the public, if found unequal to our pretensions.

Every teacher sometimes errs; and having erred in his instructions, duty to his pupils imperatively demands a correction. He who when he has discovered his error will not retract, is unfit for an Instructor.

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'I will not give it up till I have it from higher authority,” said a Teacher to a boy who pointed him to an error in his instructions to a Grammar Class. The child felt that the error was perceived, but, pride prevented its admission. To that child his instructions were thence

forth of little value.

There are few Teachers who have not in their manner of conducting schools, something which may profitably be imitated by others. Those who visit schools for the sake of improvement, will hardly fail to notice what that something is. In their visits they may find a diffident Teacher of much merit, where the community is unprepared to expect any thing above mediocrity. Visitors, if possessed of a favorable reputation, may confer a benefit on a worthy co-laborer, and advance the educational interests of the public, by helping him to enlarge the bounds of his acquaintance. In this way those who are advanced in life may do much towards helping themselves to an assurance, that their stations will be honorably filled when they shall have passed from the stage of action.

D. C. EASTMAN.

Importance of Thoroughness.

thoroughness

Thoroughness and again I say THOROUGHNESS is the secret of success. You heard some admirable remarks this morning from a gentleman from Massachusetts, (Mr. Sears,) in which he told us that a child, in learning a single lesson, might get not only an idea of the subject matter of that lesson, but an idea how all lessons should be learned,—a general idea, not only how that subject should be studied, but how all subjects should be studied. A child, in compassing the simplest subject, may get an idea of perfectness which is the type, or archetype, of all excellence, and this idea may modify the action of his mind through his whole course of life.

Be thorough, therefore, be complete in every thing you do; leave no enemy in ambush behind you as you march on, to rise up in the rear and assail you. Leave no broken link in the chain you are daily forging. Perfect your work so that when it is subjected to the trials and experiences of life, it will not be found wanting.

It was within the past year that I saw an account in the public papers of a terrible gale in one of the harbors of the Chinese seas. It

was one of those typhoons, as they are called, which lay prostrate not only the productions of nature, but the structures of man. In this harbor were lying at anchor the vessels of all nations, and among them the United States sloop of war Plymouth. Every vessel broke its cable but one. The tornado tossed them about, and dashed them against each other, and broke them like egg shells. But amidst this terrific scene of destruction, our government vessel held fast to its moorings, and escaped unharmed. Who made the links of that cable, that the strength of the tempest could not rend? Yes!

Who made the links of that cable, that the tempest could not rend! Who was the workman, that worked under oath, and whose work saved property and human life from ruin, other-wise inevitable? Could that workman have beheld that spectacle, and heard the raging of the elements, and seen the other vessels as they were dashed to pieces, and scattered abroad, while the violence of the tempest wreaked itself upon his own work, in vain, would he not have had the amplest and purest reward for the fidelity of his labor?

So, in the after periods of your existence, whether it be in this world, or from another world, from which you may be permitted to look back, you may see the consequences of your instruction upon the children whom you have trained. In the crises of business life, where intellectual accuracy leads to immense good, and intellectual mistakes to immense loss, you may see your pupils distinguishing between error and truth, between false reasoning and sound reasoning, leading all who may rely upon them to correct results, establishing the highest reputation for themselves, and for you as well as for themselves, and conferring incalculable good upon the community.

So, if you have been wise and successful in your moral training, you will have prepared them to stand unshaken and unseduced amidst temptation, firm where others are swept away, uncorrupt where others are depraved, unconsumed where others are blasted and perish. You may be able to say that, by the blessing of God, you have helped to do this thing. And will not such a day be a day of more exalted and sublime joy than if you could have looked upon the storm in the eastern seas, and known that it was your handiwork that saved the vessel unharmed amid the wrecks that floated around it? Would not such a sight be a reward great and grand enough to satisfy and fill up any heart, mortal or immortal?

HORACE MANN.

MATHEMATICAL DEPARTMENT.

SOLUTIONS OF QUESTIONS PUBLISHED IN THE MAY NUMBER OF THIS JOURNAL.

Substitute (2) in (1), and the values of the lines we have 3 16.0594x2+129.6576x-818.1916 = 0. By HORNER'S method. x = 11.029+,

If the bearing had been 45°, this problem could have been reduced to a quadratic. The figure can be constructed by the intersection of two parabolas.

D

QUESTION 19. Solution by R. W. MCFAR LAND.—Statement-Let ABC be equilateral. Since it is on the same base as ADB, it is only necessary to prove AC + CB <AD + DB.

DEMONSTRATION.-Erect a perpendicular on AB, and produce BC to meet it in E. EHC = HCA in all their parts, as HC is commnn, and all their angles are equal; hence, H is the

=

middle point of AE. Then EC = CA = B CB.. DE - DA.

=

But BE DE+DB, whence BC + CA <BD +DA.

2

QUESTION 20. Solution by GAMMA. x + = √x + 6 √, or

√x

xx4. Multiply by x. x2 = x2 + 4x

x

11x

zx 1

Multiply both numerator and denomination of the

3

fraction by (x
√x2 + x

3

11x

(3x — 1) (x — √ x2 + x

x)

х

Multiply by 9, and add 3x2 + 9x + 24 to both sides, and extract the square root.

ACKNOWLEDGMENT.-All the questions were solved by Adspectum, Bowlder, S. Loure, Geo. Huldey, R. W. McFarland, J. N. Soders and M. C. Stevens. Wm. Fillmore solved No. 20.

QUESTIONS FOR SOLUTION.

No. 25. By J. MCCARTY.-Two stakes, respectively 6 and 10 feet long, are placed at such a distance apart that their tops range with that of a certain tree. A line drawn from the middle point of the shorter stake to the top of the tree, cuts off, on the longer stake, 35 inches from its top, what is the height of the tree?

Several correspondents have requested a solution for the following problem from Robinson's Plane Trigonometry:

=

=

No. 26. Given AB 428, the angle C 40° 17', and (AC+ BC) = 918 to find the other parts; the angle B being obtuse.