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THE FOURTH NORMAL SCHOOL. We congratulate the friends of public education, particularly in the northwest portion of our own State, that we are able to expect at no distant day, a fourth school for training teachers, at River Falls, in the beautiful St. Croix valley. To Regent WELD, who has looked and labored so long, and so unselfishly, to this end, we especially tender congratulations. Other localities presented strong claims, but on the whole the feeling seemed to be that as this portion of the State is so removed from all our educational centers, and is to gather, apparently in a short time, so large a population, it was quite right to anticipate a little the unfolding of the future. No section of the newer portions of the State is more inviting than the valley of the St. Croix. It is drawing to itself an enterprising and intelligent population. The establishment of this school there will increase this tendency, and we hope great things from its influence.
PROF. WERNLI.-In a recent report of the committee of examination appointed to attend the semi-annual closing of the German, English Normal School, Galena, I!l., which is in charge of Prof. JACOB WERNLI, formerly in the Platteville Normal School, they pay him the following compliment :
“In an Institution where all the departments are so nobly sustained, it might seem invidious to make comparisons, but we are led to express our special pleaswe with which the Normal class has been instructed. They left the impression that, if called upon to teach school, they will be workmen that need not be ashamed.' Indeed, we do not see how it could be otherwise, when in Prof. Wernli they have a living model of what a teacher should be. The school is large and cramped for room, which necessitates working under a great disadvantage. They have the foundation laid for a new hall, and additional recitation rooms, and we trust that the hopes of the Principal will be realized in seeing the superstructure completed before the close of the close of the next term.”
We are indebted to GEORGE M. BOWEN, Jefferson, for solutions of problems 43 and 47, and to T. E. ARCHER, Wausau, for solutions of 47 and 49, but have not room for them, as they have already been solved.
57.-Clear solutions of this question were furnished by J. BR., New Holstein, and THOMAS HALPIN, Cedarburg, in addition to those published last month, and were sent to the printer, but were crowded out by press of other matter. It seems not worth while to publish them now.
58.-Demonstrate that in any right-angled triangle the square of either side about the right angle divided by the sum of the hypothenuse and the other side is equal to the difference between the hypothenuse and side used with it in the divisor. Let ABC be a right-angled triangle, right-angled at B, it is required to prove that BC2
=AC-AB. To prove it algebraically we have AC=AB2 + BC?, or ACPAC + AB AB?=BC2. Factoring, (AC+ AB)(AC-AB)=BC?; and dividing by AC+AB, we
AC + AB=AC-AB. To prove the same geometrically, from the point A, with
a radius equal to AB, describe a circle cutting AC in D; produce CA until it cuts the circumference in F; now CB is a tangent, and CF a secant drawn from the same point, hence, CF : CB:: CB : CD. But AB=AF, hence, CF=AC+ AB; and
BC? since AB=AD, DC=AC-AB. Hence, AC+AB : BC:: BC : AC-AB, and
AC + AB =AB-AB.-Q. E. D.--LAMBDA.
A good solution was also received from B. R. A., but defaced, in using matter on the other side of the sheet.
61.–A tree 100 feet high is broken in the wind; in falling, the broken end rests on the stump, while the top rests on the ground 30 feet from the foot of the tree. Required the height of the stump.-W. H., Lowville.
Solution.-Height and hypothenuse squared:
ft. ft, in.
Second Solution.—Let x equal height of stump; we have given now the base and perpendicular to find the hypothenuse—which, according to rule, is equal to
22 +900. If x equals height of stump, 100—~ must equal length of the portion broken off. Placing the two equations, equal to each other, we have, Næ+ 900 =100—X; or, *2 +900=10,000—200x+x2. Transposing and collecting we have, 200x=9,100, and x=4572, height of stump.
62.-Three men are to carry a stick of timber 100 feet long, and of uniform size throughout. Each is to carry one-third of the stick, and two of them are to carry together. If the man who carries alone is at the end of the stick, how far from him must the others be that they may carry their share?
As three men are to carry a stick 100 feet long, one man at an end of it is to carry one-third of it, or 3314 feet; the other two to carry together the balance, or 66% feet. Were the latter to go to the other end, they would carry but one-half the stick, or one-sixth less than their part. Now, in order to carry this, they must come towards the other man, a distance equal to one-sixth the length of the stick, or 16% feet. Hence the two men together are from the man alone, 100-16%, or 8344 feet.—T. HALPIN, Cedarburg.
63.—Why is a body heavier at the poles than at the equator?
1st. It is nearer the center of gravity. 2d. The centripetal force is diminished at the equator, as a consequence of the earth’s revolution.
65.-Suppose an opening to be made directly through the center of the earth, and a cannon ball to be dropped into the abyss, where would the ball come to a state of rest?
A body falls toward the center of the earth, because the greatest amount of attractive matter lies in that direction. But when it descends beneath the surface the attraction in one direction must decrease until the center is reached, when it becomes equal in all directions—hence, a body at the center of the earth must weigh nothing. As a material substance must have weight in order to have motion, the ball must necessarily stop at the center.-W. H., Lowville. 68.-CORRECTION.—Problem 68 should have been given thus: (22+y=11;
To find the value of x and y. 132 +x= 7;)
A. S. 8. Will B. R. A. furnish a solution to this again, as corrected?
70.-Would it not be more interesting to devote a few pages of the JOURNAL to school exercises, declamations, dialogues, etc.
In answer to this question, I should say let them be limited; journals are apt to run to such subjects, if once started; but comparatively few really want them, and we already have journals devoted to that branch of school literature.-I. N. S., Waukesha.
71.—Please, if convenient, inform the readers of the JOURNAL, of the names of the several Territorial and State Governors of Wisconsin.
The Territorial Governors were:
The State Governors have been:
The names of the Governors were also furnished, as above, by Mrs. S. C. SIRRINE, Plainfield.
72.—The worm of which H. CROUSE speaks, is called “ centiped,” (a general term for insects having a great number of feet,) and belongs to the genus Scolopendra, of the order Myriapoda. There are several species, of which the large ones in the tropical countries are dangerous, on account of their venomous bite.. P. S., Gibbsville.
JOHN ALDER, of Eastman, Crawford county, also sends a similar answer, and refers to the word “ centiped,” Web. Un. Dic.
NEW QUESTIONS. 73.-Will some one parse the indicated words in the following? “ And God said unto Moses,' I am that I am.'” (Ex. III. 19.) “For was and is and will be, are but is.” (Tennyson—The Princess.) J. W. B., Janesville.
74.—What is the width of the Frigid Zone, and why are the Tropics of Cancer and Capricorn su called?-A. CRAVEN, Sussex.
75.-If one cow and one ox cost $57, and twenty cows and thirty oxen cost $1,500, what is the cost of each per head? Solution by arithmetic.-H. C., Reedsburg.
76.—Wanted to know the name of the person, the official title, and the time when he performed the duties of acting President of the United States during the absence of the President and Vice President.
76.—Wanted to know the names and respective terms of office of the several Chief Justices of the United States.
78.-If three is one-third of six, what will one fourth of twenty be?-E. H.
79.-A man and son can drink a barrel of water in 5212 days, and it will take the son 1014days more than the father to drink it alone. In what time will each one drink it alone?-W. H. F., Toland's Prairie.
80.—What is the best substantiated theory in regard to solar heat-do we actually receive heat from the sun?–M. H., Rocky Run.
81.–Will some one please give the characteristics of each Governor of Wisconsin?-S. C. SIRRINE, Plainfield.
82.–What is combustion, and what causes it?
83.—The centers of two given spheres are at the extremities of a given right line; required the locus of a point from which the greatest portion of spherical surface is visible.-L. C., Door Creek.
84.-Alice is one-third as old as her mother; five years since slie was but onefifth as old; in how many years will she be one-half as old?—B. R. G.
(We received several other arithmetical questions with the preceding one, but have not room for them.)
DEFINITIONS. For the purpose of encouraging a bill of fare, not so exelusively mathematical, I submit the following grammatical definitions as being better than those usually given, if they stand criticisne, which of course they invite:
(1.) CASE.—Case is a modification of substantives, used to indicate their relation to other words in the sentence.
(2.) PREPOSITION.—A preposition is a word used to indicate the relation of a substantive, usually called its object or subsequent, to some other word in the sentence and with this subsequent to form a phrase which modifies the antecedent term of the relation.
(3.) INTERJECTION.-An interjection is a word that, like the sentence, expresses a complete thought or emotion, and consequently has no dependent construction.A. F. N.
QUERY IN EQUITY. Dear Journal—The following question has arisen, and as it is likely to become one of general interest, I beg you will answer it as early as possible:
A teacher is engaged in the usual manner to teach the public school in a certain district, say for the term of ten months (twenty-two days to the month). Nothing is said about vacations or holidays; Christmas conies on Monday. But at the close of the week previous to Christmas the Board inform the teacher that they propose to give a vacation, extending over Christmas and New Years, school to commence again January 2d. The teacher accepts the position and announces the vacation. At the end of the term, can the teacher include Christmas and New Year's among the days taught ? That is, shall he be allowed for them ?-B. R. A.
The JOURNAL's opinion is, the teacher ought in fairness to be allowed the two days, Christmas and New Years, because he was originally entitled to them, and perhaps makes some sacrifice in consenting to the vacation. The case would be different, of course, if the original agreement provided for the vacation.
QUESTION IN ALGEBRA. On finding the greatest common divisor of polynomials' we divide the greater ploynomial by the less, after suppressing all mononial factors, and if the first term of the dividend will not contain the first term of the divisor, we multiply the first
polynomial by such a factor as will make its first term divisible by the first term of the second polynomial. Now why can we multiply by this factor.-W. H. SMITH, LeRoy, Dodge county.
DRAWING—A QUERY. Supposing that every public where drawing, map-drawing and ornamental penmanship is taught, were to send, from time to time, a few choice samples of work executed by pupils of such schools-said samples to be neatly bound and containing the names of the school, the teacher and the young“ artists,” and the date of presentation—to our State Superintendent, to furnish him with evidences of progress in those branches, would the Superintendent be authorized in receiving and placing such samples on file in his office? And would it act as a healthy stimulant to acknowledge the receipt of such gifts in the JOURNAL, adding, perhaps, a friendly note of criticism?—PENN.— Yes, by all means--Editors.)
WANTED—AN ANSWER.-Suppose it to be one hundred miles from Boston to Portland. A locomotive starts at twelve o'clock from Boston, going fifty miles the first hour, twenty-five the second, and twelve and a half the third, and so on each hour traveling half the remaining distance, when will it reach the depot at Portland? A reward of $1,000 awaits any person who, by a mathematical calculation, can arrive at the exact hour.-Boston Times.
What word of one syllable can be pronounced quicker by adding two letters? What word can be pronounced easier by adding another syllable?
STUDY OF CIVIL GOVERNMENT.. The following intelligible answers were given by would-be-teachers, while under. examination:
Question. What is the Constitution of the United States? Answer. “ The Constitution of the United States are the laws made by the chosen people.”
Q. What are the conditions of eligibility to the United States Senate?
A. “The conditions of membership of United States Senate, is a well calculated theory of advancing and promoting and enforcing all laws sustained by the nation."
Q. How may the Constitution of Wisconsin be amended?
A. “Wisconsin laws may be amended by the signature and great seal of United States approved.”
Q. What is meant by suspension of writ of habeas corpus?
A. “ The suspension of the writ of habeas corpus is the death of the United States Federal Government."
The following is a specimen of communication between a teacher and a school board:
“I formally resign my position as teacher of school of this account of the duties of the place being too arduous for the capacity of my ability to fill.
We make some extracts, which the writer will pardon, from a private letter:
“Since people may labor in so many different ways to the same end, you will pardon me for assuming myself to be in your field, by giving just a thought in reference to an article I have this moment read in your JOURNAL, December 1871, entitled “Physical Education.'
“In the first line, Herbert Spencer is spoken of as 'one of the ablest writers of our (?) country.' Question. Who can say that out of the maze of his ‘unknowable' and knowable,' an American thinker is safe in accepting that order of duties and activities of which the third, 'parenthood,' stands in front of all undetermined social problems?