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of nature's laws as certainly as effect follows cause; and I venture that seven-tenths of the people of Wisconsin know little, if anything, of the causes of ill-health; and all because the study of man, in any form, is entirely disregarded in our common schools.

Now, I would like to see a book, furnished in the same manner as the " Constitutions” are, used in our common schools. It should be brief, especially the anatomical part, while the physiological part might' be more extended, and the hygienic rules should be given very explicitly and so as to be easily understood.

Will not some of our legislators, interested in the cause of education, introduce this subject into the Legislature the present session?

I would like to see some move in this direction, for I am satisfied that physiology should be taught in the common schools.

PROPERTIES OF SQUARE NUMBERS.

(CONTINUED.)

BY L. CAMPBELL.

2

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(A'#D")-(4'7D") (A'#D)-(4'D")"

2

(2B»= (BP4d") - ( Brza) Substituting this value of (2B)" for (A #

[A*

2

We have seen when A=B'- and B-C=D,
That A' =

A'+D? A-D'
2D

2D Multiplying by four we obtain

A'+D A'D:
'
D

D
A'+D
In which

=2B.

D
In like manner, when B’=M'-N’ and M–N=d, we find

B’-
d

d
A'+D

in equation (2),

D and transposing, we have AP-D

B-a? B'+d??
(2A)' +

+
D
d

d
Assume D=d=1, then
(2A)*+(A?-1)+(BP-1)=(B2+1)

(r) In which B=

A2+1

; and B will therefore be a whole number when

2 A is taken equal to any odd number whatever.

Make A successively=3, 5, 7, etc., then B=5, 13, 25, etc., and equation (r) gives, 6° +8° +24=26'

10° +249 +168'=170° 14? +482 +6242=6262

182 +30° +1680=16822 22+120° +3720o=37222 26° +160+ 72242=72262 etc.

etc.

In each of these equations the numbers whose squares are indicated, may be regarded as the three dimensions and diagonal, expressed in whole numbers, of a rectangular volume, the first number of each representing the sum of the squares of the three dimensions and the second number the square of the diagonal.

A+D AP-D The expressions

and will always reduce to positive. D

D whole numbers when A and D are whole numbers and D a iactor of A.

Suppose A=6, then since 6 is divisible by 1, 2 and 3, if in equation (2) we assume D=1, 2, 3, we shall have, when

D=1, 122=372 — 35%;
D=2, 12'=209-16',

D=3, 12'=15'-9'. Hence 129=372-359=202-16=15-9', which shows that 12 is the common base or perpendicular of three right angled triangles whose sides are expressed whole numbers.

In general if A be any whole number containing n integral factors, each of which is less than A, then 2A may be taken to represent the common base or perpendicular of n right angled triangles whose sides may be expressed in whole numbers.

Place A=12, and D successively=1, 2, 3, 4, 6, the entire factors of 12, then equation () gives,

24=1452_143?=742–1702=512_452=402-32=30—182. We find in like manner,

282=1972—195?=1002—969=352— 21”;
329=2572— 255?=130?—126'=68?—60o=40?— 24”;
369=3252_3232=1642–160o=1112—1052=60?–482=452 — 272;

402=4012-3992–2022 -1982=1042-962=8575-50- 30%. If we assume D=, Æ, &, etc., we shall find,

(2A)=(**) —(4)=(194) 2—(-4)=(124) ?-(134)=etc. When A=1, 2+=()-(3)=(1)-(3)=(43)-()=etc.

A=2, 4=52—3=(29)-(44)=(12)-(15)=etc.

A=3, 6'=(15)-(x)=102—82=(31)?—(45)'=etc. This shows that any number of right angled triangles may be found, having a common base or perpendicular, whose sides are expressed in rational numbers, whole or fractional.

THE SUBLIME is generally monotonous. It is the height, depth, and length of one thing, or attribute, which constitutes sublimity. The beautiful is varied. It lives in motion, flashes in colors, and glides and dances in changing melodies.

A PEBBLE and an almond seem equally hard and forbidding from the exterior ; but when both are broken, the almond is found to have “reserved ” a sweetness of which it gave no outward sign, while the pebble is the same throughout.

THE SCHOOL MONTH.

BY M. LEVIS, DISTRICT CLERK, DISTRICT NO. 2, ALMA.

There is an error which prevails to some extent among school district officers through our part of the state, which, for the welfare of the schools, and justice to the faithful teacher, requires to be corrected. And that is, “the Legislature of 1871 made some material changes in the Wisconsin school code." One of the changes (it is said), is, instead of the instructors teaching twenty days for a month, as heretofore, “ they shall hereafter teach twenty-two days, and no Saturdays.” The district board having no power to contract with a person to teach twenty days per month, and upon no reason whatever to ailow the teacher time for school taught on Saturday. In consequence of this version of the law, I am personally knowing to instances where districts have failed to employ the teachers they desired. And a number of instances where teachers have taught twenty-two days for a month, and allowed no Saturdays. One instance, viz: A teacher is employed to teach five months at $50 per month, board at $3 per week. Now at twenty or twenty-two days for a month he should receive clear from toard, $30 per month.

The school board are convinced by past experience that the “twenty day system” has resulted in far more good to the district, giving the pupils time to rest on Saturday, and to be prepared to attend regularly through the week. “But the late change in the law will not allow clerks to employ for less than twenty two days and teach no Saturdays.” And so the instructor after teaching five months, has still iwo weeks to continue school, for which he receives no remuneration, and also two weeks board to pay; coming about as near as possible to “ work for nothing and board yourself.” This extra time and board amounts to $31. So this monthly wages, instead of netting $38.00, is but $31.80. Any perscn taking reason for their guide, will see at once the injustice of this. If I am rightly informed, the late change in the school code in regard to this subject, amounts to very little, if anything. “Twenty two days for a month unless the contract specifies otherwise,” is as it always has been in our school law. A large number of the districts throughout the state (believing it to be better for all concerned,) contract for twenty days per month.

An attempt was made in the legislature to have it uniform through the state, twenty days to constitute a month, and five days' school per week, but the law remains unchanged, except there is to be no school taught on Saturday unless the district is willing, which is really as it has been heretofore. This constitutes the change in the law.The school board, and more particularly the clerk, are the law on this subject. If it is considered better to have no school on Saturday and twenty days for a month it is the clerk's duty and right to contract to that effect. But if it is thought better to have twenty-two days for a month, then in the light of reason, and without any violation of law, allow the school to be in session every other Saturday; and if a day or two is lost through sickness or other good cause don't be afraid of breaking the “ lawif you allow the teacher to make it up by teaching on Saturday.

ORDER IN SCHOOLS. “We cazinot have a good school without ɔrder."

Nearly every teacher we meet agrees with the above proposition, and, if questioned on the subject, probably every one would give a different answer as to what constitutes good order in a school. All agree that order is requisite; but, in what does it consist?

We enter a school room. Not an eye is raised, not a muscle moves, and we hear the old clock ticking with painful distinctness; everything is in “apple pie ” order; not a smile is seen, and if any one is so unfortunate as to sneeze, he receives a severe reprimand for disorderly behavior.

We must admit that this is an orderly school; but, is it necessary, to attain this end, that all the youthful life and exuberance of spirit be crushed out of the children? We always feel as though we had entered a graveyard when we go into a school of this stamp. There is a sensation of something dead, something buried beneath this statuesque exterior, which needs a resurrection.

It seems as though teachers are getting to attach more and more importance to the appearance of their schools, and, as a necessary consequence, neglecting other matters. So much time is spent (we will not say wasted,) in enforcing the observance of numerous forms and petty rules; which, probably, the next teacher will omit entirely. If one teacher would remain in a school for any length of time, these observances might be beneficial; but, as things now stand, each term generally bringing a change of teachers, it seems to us that much of this time is wasted.

How, then, shall we gain this order which is so indispensable. That depends a great deal, of course, on what our ideas of order are; but we think that one thing is indispensable. The children themselves must have their interest and sympathy enlisted with the teacher; they must be brought to see how much more can be accomplished when there is nothing to detract the attention from lessons; their pride and ambition should be roused to make their schools the best; and when they feel that the teacher is really interested in their progress and general welfare, there will be few instances of wilful disorder; and, in this way, we shall soon find that the school is far more orderly and pleasant, than when the pupils were restrained, merely through the fear of punishment.—M. C. G., in Kenosha Telegraph.

SUPERFICIAL EDUCATION.—There is too much truth in the prevailing opinion that the education of the masses is tending to superficialism. Perhaps this condition arises, in a great degree, from an unwise and overweening disposition, on the part of parents, to see their children apparently advancing, regardless of actual accomplishment. The conscientious teacher often finds himself compelled to incur the displeasure of both parent and pupil, that he may advance the interests of the latter. Higher branches are too often undertaken without primary fitness. It requires much judgment and fairness in the pupil to say: "I do not understand the primary principles of this science.” The unscrupulous teacher who continually flatters both parent and pupil, is welcomed everywhere; and thus the work of superficialism goes on.-B. R. A., in Kilbourn City Mirror.

NORMAL—There is a prevailing idea that a peculiar method of teaching exists, known as normal. Normal is derived from the Latin norma, which signifies rule, model or pattern, and a normal school is therefore one in which the instruction given is supposed to be a model by which the pupil, afterwards a teacher, is to be governed in imparting knowledge. But there is no particular method in teaching, known as the normal. The chief excellence of normal training developes itself in the organization of schools and classification and arrangement of recitations. But so far as educating is concerned, we think the teacher will find no theory or rule to supersede tact and judgment; and when he becomes a devotee of some particular theory, he has sacrificed judgment and self-reliance to this special system.-Ib.

THE TOWNSHIP SYSTEM.-Ought each town be made to support its own schools without any regard to its ability? In some towns this will require a tax of four or five cents on the doilar; in others, a tax only of so many mills. Education is said to be a matter of State concern; hence all the schools ought to be supported by a Stałe tax. The township system is on too small a scale. It may work well enough in old and thickly settled counties, where there is a good deal of wealth, and it ought to be fairly tried here, and if not found practicable, let it give place to something better. Let some of the best towns in Monroe county try it. Get up your petitions, signed by ten legal voters, asking the board of supervisors that the question be submitted to the people to be voted for at the spring town meeting.-G. B. H., in Sparta Herald.

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