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positions of successful methods of discipline or instruction, which are very valuable indeed, and should be multiplied as much as much as possible.

These monthlies, like the other educational literature of the day, very distinctly exhibit realist tendencies. Articles on "object-lessons," or on practices similar in principle, such as modes of teaching geography, arithmetic, etc., by means of visible illustrations and demonstrations, are perhaps the most noticeable feature of their contents. In current information as to the progress of schools and education in their respective states, they are not by any means as full as desirable. But such information is difficult to procure.-Ib.

[The foregoing slips from a widely circulated and influential Journal are evidently from the pen of one who has thoroughly and wisely surveyed the educational field, and are well worth consideration. The remarks in the last extract, in regard to Educational Journals, are we think just, and we have been disposed for sometime past to take the same view.]

MORALS OF THE SCHOOL.

The public school should inculcate upon all its attendants, such moral lessons as will be bright lights through the various paths of life; teaching the dignity and sacredness of humanity-the imperative demands of justice between man and his fellows-the real character of liberty, and unselfish zeal with which it should be maintained and guaranteed to all -the courtesies and kindness which gladden and embellish social intercourse-the trustful reverence for God and habitual, cheerful obedience to His commandments, which enable men to receive with humble gratefulness the joys, and to bear with unmurmuring patience the trials of life, and which fit them for the destiny that awaits them when the joys and trials of life shall have forever passed away.-Teacher & Pupils' Friend.

SELF CONCEIT AND FAITH.

The ancient perpetual truths prove, at each fresh enunciation, not only surprising, but incredible. The reason is, that they overfill the vessels of men's credence. If you pour the Atlantic Ocean into a pint basin, what can the basin do but refuse to contain it, and so spill it over? Universal truths are as spacious and profound as the universe itself; and for the cerebral capacity of most of us the universe is really somewhat

large! But as the major numbers of mankind are too little self-reverent to dispense with the services of self-conceit, they like to think themselves equal, and very easily equal, to any truth, and habitually assume their extempore, off hand notion of its significance as a perfect measure of the fact. As if a man hollowed his hand, and, dipping it full out of Lake Superior, said "Lake Superior just fills my hand!" To how many are the words God, Love, Immortality just such complacent handfuls! -Atlantic Monthly.

SUPERINTENDENT'S DEPARTMENT.

SCHOOL REPORTS.

The matter of Reports has been quite fully discussed in the Journal, but it may not be amiss to state briefly the system. District Clerks will report to Town Clerks instead of to Town Superintendents as heretofore. For Joint Districts smaller blanks have been issued. To each Town Clerk of Towns represented in the Joint District the small blank must be sent. The number of children reported upon each small blank must be the children residing in that part of the Joint District found in the town to whose Clerk the blank is sent. In addition to the small blanks one large blank must be filled and sent to the Clerk of the Town in which the School House is situated, omitting from this Report the items relating to children-the three first items.

The Reports of District Clerks must be in the hands of Town Clerks on or before the 10th of September.

Town Clerks will report to County Superintendents on or before the 25th of September. It is the duty of Town Clerks to see to it that District Clerks' Reports are properly made and in due time.

County Superintendents must make their Reports to the State Superintendent on or before the 10th of October.

The attention of District Clerks is called to Sections 30, 88 and 92 of School Code, 1859.

Town Clerks will be governed by the Law formerly governing Town Superintendents. See Sections 46 and 89, Code of 1859, and Chapter 179, General Laws of 1861.

J. L. PICKARD,

State Supt. Pub. Inst.

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21×8×7×67056 84. From this we find the perpendicular BG=11.2 by dividing the base AC (73) into the area (84). Also GC = √14—11.22= √1.96-125.44 70.56=8.4. = Now the area of

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base GC must be shorter and also its perpendicular. Let x be the

Cx x x0
2

42 or the triangle ABC. I should mention

point such that to draw ox parallel to BG. Now we know that similar triangles are to one another in the duplicate ratio of their homologous sides ... BGC : oxC:: BG: ox2, or 47.04: 42::11.22: 112 the square root of which is 10.583+=ox, or the required perpendicular. In the same manner we find Cx=7.947+, which satisfies the conditions of the question or nearly JOHN FETHERSTON.

so.

Solution of Problem 45.-The stump, the part broken off and the distance from where the top strikes to the base of the stump form a right angles triangle, the base of which is 80 and the sum of the hypotenuse and perpendicular is 200. Now, since the square of the base equals the difference of the squares of the other two sides and since the difference of two squares equals the product of the sum of the roots into their difference, dividing 80' 6400 by 200, we have 42, the difference of the hypotenuse and perpendicular, hence the hypotenuse i. e. the part broken off 200÷2+32÷2-116. Ans.

=

I think the geometrical theorem that the square described on the hypotenuse of a right angled triangle is equal to the sum of the square described on the other two sides, or something equivalent to it, is essential to the solution of the problem. The second theorem used, I would

demonstrate thus.

Let it be required to multiply the sum of any two

numbers, as 4 and 2 by their difference.

4+2

4-2

42+4x2

22+4x2

42-22

First we multiply the sum by the greater number and observe that the product consists of two parts, viz: the square of the greater number and the product of the greater into the less; but the multiplier which we have used is too great by the less number, hence the product is too great by as many times the multiplicand as there are units in the less number, thus multiplying by the less number, we have a product consisting of the square of the less, and the product of the greater into the less. Subtracting this from the former product, we have remaining as the true product, the square of the greater number to be diminished by square of the less, Q. E. D.

the

As the form of the product does not depend upon the value of the numbers this demonstration is general. E. C. BEACH.

Albion Academy, May 17th.

Solution of Problem 46.-a, b and c are the 3 given perpendiculars and the three sides are represented by x, y and z. According to the well known property of triangles, "double the square of a line drawn from any angle of a triangle to the opposite side, together with double the square of half that side, is equal to the sum of the squares of the other two sides," that is

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By taking the former of these equations from twice the sum of the two latter we have, 4x2 + 1x2=2(262+2c2—a2) consequently

x= √(b+2c2-a2)and y=√ (2a2+2c2-b2) and z= √(2a2+2b2—c3) Dodgeville, Iowa Co. SAMUEL CLEGG.

Problem 53.-At what distance from the equator must a line be drawn parallel to the equator so that its length will be 21600 statute miles; that is, where will one degree contain sixty statute miles? M. C.

EDITORIAL MISCELLANY.

TEACHERS' ASSOCIATIONS.

By request, we offer a few hints in regard to Teachers' Associations. First they may appropriately be distinguished from Institutes. The latter are official, required by law, and now under the control of the County Superintendents. County or Town Associations are voluntary. The Co. Supt. may encourage their formation, may appropriately always be present to aid in their exercises, but he has no official cognizance of them.

ORGANIZATION-Every county should organize, if it has not done so. Let a call issue from a few leading teachers; let a central place be named, where the people take a lively interest in schools, and will entertain those who assemble. A brief constitution may be presented by a committee who will readily find existing constitutions to serve as helps in drawing up one. We print below, a form which seems to be a good one, copied from Mr. Bates' little book, slightly altered * Let meetings be held, if possible, quarterly; if the county is large, they may be held in different parts of the county, from time to time, to accommodate all.

EXERCISES.-A judicious selection of illustrative exercises in modes of teaching, short practical essays, pointed, good natured discussions, interspersed with singing and physical exercises, will be found most serviceable. Long winded, irrevelant lectures from gentlemen who get themselves invited, are not of much account. A good practical instructive lecture is of course a good thing; but don't get bored. A really superior recitation or declamation or two will not be amiss, but common, school-boy performances will not be profitable. If a truly model recitation with a trained class, can be introduced now and then, it will be eminently useful. In the arrangement of exercises, much depends upon the energy, tact and good sense of the Executive Committee. The Presiding Officer should also be a dignified and discreet person, having some knowledge of parliamentary rules. The Co. Supt. may be elected President, if thought proper, but in that case he presides, not in his official capacity, but is elected as a leading educator in the county.

RECESS AND SOCIALITY.-This should not be overlooked. The following from the pen of Alex. Clark, editor of the School Visitor, is much to the point:

"I attended an Institute not long since, where about one hundred teachers were assembled. Very few had ever met before in the same relations. The several lectures were able, and somewhat practical. The teachers seemed to be

* METHOD OF TEACHERS' INSTITUTES, and the Theory of Education. By Sam'l P. Bates, Deputy Supt. of Schools in Pa., and author of "Institute Lectures." Published by A. S. Barnes & Burr, New York. Sold by Geo. Sherwood, 118, Lake St., Chicago. We have borrowed several hints from this book, which is equally applicable to the exercises of "Associations" or "Institutes."

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