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SUMMARY OF SCHOOL STATISTICS.

The following Summary from Mr. Pickard's Report for 1862, is more full and varied than heretofore, and much pains has been taken we believe to make it accurate. We defer remarks till the issue of the whole Report; which will we think prove to be an educational document of more than usual interest:

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Number of parts of districts.

775

2

.....

...........................

3,787

..........

1,764

Number of districts, reckoning 2% parts equal to a whole district..........
Number of districts not reporting

4,571

164

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Number of female children between 4 and 20 years of age............
Total number of children between 4 and 20 years of age.
Excess of males over females........

Increase since last report....

Number of districts maintaining school more than one term.......................................
Number of male teachers employed during the winter term..........
Number of female teachers employed during the winter term..........
Number of male teachers employed during the summer term...........
Number of female teachers employed during the summer term..
Number of different persons employed in teaching during the year.....
Number of pupils registered during the winter term...

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Whole number of days' attendance of pupils during the winter term....
Whole number of pupils registered during the summer term..

5,886,890

129,900

Whole number of days' attendance of pupils during the summer term....
Who e number of pupils attending during the year..

4,690,943

191,366

Number of children under 4 years of age who have attended school...
Number of children over 20 years of age who have attended school...
Whole number of days' attendance of pupils during the year......
Number of select and private schools..

Number of pupils reported attending them................ ............................

2,420

2,049

10,577,833

189

2,049

Average wages paid male teachers per month during winter term....................
Average wages paid female teachers per month during winter term.......
Average wages paid male teachers per month during summer term..........
Average wages paid female teachers per month during summer term.......
State fund apportioned during the year
Tax levied by county boards......
Tax levied by towns...

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District taxes for teachers' wages...................................................................................
District taxes for school houses..

District taxes for maps, charts and apparatus.......
District taxes tor other purposes...

Total school taxes raised................

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2,865 51

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Number of sites containing less than one acre
Number of sites uninclosed......

Number of school houses without blackboards..................................

Number of school houses without outline maps.......

Total valuation of school houses..................

Highest valuation of any one school house.................
Lowest valuation of any one school house......

Average valuation of school houses.....

Number of district libraries.............
Number of volumes in the same..

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MATHEMATICAL DEPARTMENT.

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Solution of Problem 55.-Represent the two greater sides of the triangle by a and b, and the area by 1; then, since "two triangles having an angle in each equal, are to each other as the rectangles of the sides which contain the equal angles," we have 1 : 1 :: ab : x2; x= • the distance to be measured on a and b from the vertex of the smallest angle of the triangle. J. T. DODge.

Monroe, Green Co., Nov., 1862.

N 2

=

Solution of Problem 56.—The extremity of the minor axis will be the point required.

Monroe, Green Co., Nov., 1862.

Explanation of Rule for Reducing rods, then by the rule, 16.5 x =

99 x 6

J. T. DODGE.

Rods to Feet-Let x = number of 100 x 2 100 x By reducing, 6

=

6

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= 16.5x = true number of feet. Or, since we multiply by 100,

we take 6 times as many feet, + 1, as there are in each rod; hence, by deducting one foot for each rod, we have the true number of feet × 6. Monroe, Green Co., Nov., 1862. J. T. DODGE.

Answer to the Question about the difference between two numbers consisting of the same digits.-Since the difference between any number of units of the 1st order and the same number of units of the 2d order is such a multiple of 9 as is expressed by the number of units, and since by inverting the digits of a number we add as many units of the second order as we subtract of the first order, or conversely, the difference must be some multiple of 9, and therefore divisible by it.

Monroe, Green Co., Nov., 1862.

J. T. DODGE.

SUBTRACTION-THE TWO METHODS.-Let it be required to subtract 46 from 83, where the unit figure of the subtrahend is greater than the unit figure of the minuend. There are two methods. By the one, we decompose the minuend, calling it 7 tens and 13 units; then, from these two parts we subtract respectively 4 tens and 6 units. By the other method, we equally increase both minuend and subtrahend, by adding 10 units to the one, and 1 ten to the other. Which is the best for the learner? Your correspondent, "L. K.," prefers the former. I prefer the latter, and for this preference offer the following reasons:

1. The two methods are equally simple as respects the combinations of numbers made in subtracting. In the one case, we take 6 units from

13 units, and 4 tens from 7 tens; in the other case, we take 6 units from 13 units, and 5 tens from 8 tens.

2. Whichever method we pursue, we call the 3 units of the minuend 13 units. But by the second method we compensate for this sooner in the subsequent part of the operation. Thus, after subtracting the 6 units from the 13 units, the attention passes first to the tens of the subtrahend, then to the tens above in the minuend. Here are two steps in the intellectual process. By the second method, the compensation is made at the first step, by calling the 4 tens, 5 tens. By the first method, the compensation is deferred till we reach the second step; and every one must admit that this increases the liability to mistake. It is better for the child, whose mind is laboring under the task of numeral combination, to have done with the compensatory part-the "carrying”—as soon as possible. When the learner, in an example of addition, has added one column, do we not require him to carry the tens when he begins the addition of the next column, telling him that if he waits until he has finished adding this column, he may forget the carrying? This principle applied in subtraction will certainly compel us to discriminate in favor of the second method.

3. I cannot agree with "L. K.," that the second method is more "circumlocutionary" in respect to the reasoning process. The explanation of the first method is, that the 83 is decomposed into 70 and 13. The explanation of the second method is, that the difference of two numbers is not altered by equally increasing the numbers. Says "L. K.:" "To be entitled to add 10 to any figure in the minuend, I must borrow 1 of the next left hand figure in it." Not necessarily; for we acquire just as clear a title to do this, by adding 1 to the next higher figure in the subtrahend.

By reference to Robinson's Progressive Practical Arithmetic, page 31, the reader will find the analysis of each method, successively given. The two analyses are about equal in length, that of the second method being a little shorter, and, I think, a little the plainer to the learner's X. comprehension.

The question below is referred for solution to the Mathematical Editor by a teacher's institute. We number it according to its order and annex an algebraic solution.

Problem 57.-"Where should a lever be placed under a stick of timber 30 feet long and of equal size from end to end, in order that three men, two at the lever and one at one end of the stick, may each carry one-third of the weight?"

Solution.-Let the line A B represent the stick of timber, A

A

B

P

the end at which one man carries, and P the point where the "lever" is applied. Put a eqal to the number of feet in PB, and w equal to the weight of 1 foot of the timber; then will 30 x= AP, and 10w will exerted by the man at A, because he carries }

represent the lifting force of the stick.

We may regard a part of the stick equal to 2x, as balancing at P, and the remainder, 30 x, as being lifted by the man at A around P as a fulcrum. The weight of the latter piece may be considered to be at its center of gravity, that is, its middle point.

Now by the conditions of equilibrium in a lever, which are that the product of the power multiplied by the distance of its point of application from the fulcrum, equals the product of the weight multiplied by the distance of its point of support from the fulcrum, we have the equation

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Dividing by w, performing the operations indicated, transposing, and dividing by the coefficient of x, we obtain x= 7

The bar by which the two men lift should therefore be placed 71 feet, or one-fourth the length of the stick, from B.

Problem 58.-What is the square root of the decimal .9 ?

Problem 59.-A surveyor runs a trial line north to the shore of a pond, and wishes to ascertain the position of a corner concealed under the water on the opposite side. From the corner a tree on the bank is known to bear N 49 W 4.68 chains. This tree bears N 7° 30' W from the point where the trial line ends. From this point he measures a line S 64° 30' W 13.00 chains, and then finds that the tree bears N 17° 15′ E. How far is the end of the trial line from the corner, and on which side, and at what distance from the corner would it fall if produced?

Problem 60.-Suppose a point, A, on a wheel four feet in diameter, rests on a level plane, through what length of space will A pass while said wheel by rolling on said plane makes one revolution? Wyocena.

P. BRONSON.

"Mother," exclaimed a learned youth from the Academy, who wished to inform his maternal parent that the cow had got out of the yard and gone off, "our bovine lacteal provider has ruptured the enclosure, passed her prescribed boundaries, meandered away, and taken a nocturnal excursion."

SUPERINTENDENT'S DEPARTMENT.

OFFICE OF SUPERINTENDENT OF PUBLIC INSTRUCTION,
Madison, December 17, 1862.

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Edr. Journal:-The following reports were received too late to be included in the Annual Report, for which they were designed. Please insert them in the Journal. Yours, truly, J. L. PICKard.

GREEN LAKE COUNTY.

I submit to you, at this late hour, a few brief remarks, as a supplementary Report, according to your wishes, as expressed in the October number of the Journal of Education.

At my meetings, held last spring, for the examination of teachers, 96 applicants presented themselves for inspection; 86 received Certificates, one of the First, and 85 of the Third Grade. Of this number, 70 taught during the summer term, and, so far as I can learn, with better success than I had anticipated, giving almost universal satisfaction throughout the County. It could not be otherwise, as the new system, in the examination of teachers, requires written answers to the questions on the different branches taught in our schools. It is evident that a qualification for such examinations prepare the teachers to elevate our common schools.

We have become satisfied that where parents visit the schools often, it inspires the teachers with confidence in their calling, and the children wake up to new life and energy in their studies.

If parents could be led to see the advantages to be derived from commodious and well-arranged school-houses, both to the physical health and intellectual growth of their children, I think they would have a different class of school-houses.

The war has had its effect, in taking from us many of our best male teachers, leaving only 20 who have been licensed to teach the coming winter; and about one-third of this number were from other counties.

The greater number of our schools, the coming winter, will be under the instruction of females; and if that class of teachers do as well as they did last winter, we feel assured that success will crown their responsible labors.

There were not many teachers present at our Institute, this fall; and the causes that contributed to make it so were probably the same as those which affected Institutes in other counties.

Yours, respectfully,

N. C. HOIT, Co. Supt.

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