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Solution of Problem No. 17.—Let x, xy, xy’, xys represent the four numbers. Then by the conditions of the problem æy: —&y=24, and xys +x : xy + xy :: 7:3, or y*+1 : yo+y::7:3. Hence, (dividing the first couplet by <+1, yé-y+1:y::7:8, and by cumposition y* +1:y::10: 3. Hence 3y +3=10y, hence ye
1-1, hence y=3 and by the first equation, 272-3x=24, or x=1, and the numbers are 1, 3, 9, 27.
=0. O. B.
Problem No. 22.—The base of a right angled triangle is equal to the perpendicular diminished by its squaro-root, and the area is equal to one acre; find the base and perpendicular.
Problem No. 23.-Required the greatest rectangle, that can be cut from a triangle, whose sides are respectively 13, 14, and 15 feet.
Problem No. 24.—Required the greatest cylinder that can be cat from a given cone.
Problem No. 25.-A hollow paraboloid whose height is 19 inches, and whose greatest diameter is 7 inches, contains 60 cubic inches of water, Required the diameter of the sphere which will just be immersed in the water,
Problem No. 26.-A, B, and O carry a stick of timber of equal size from end to end. A and B carrying together by a bearing pole and O alone at the end. Where must the cross pole be placed that each may carry his proportion of the the timber.
Problem No. 27.--The altitude of a cone is to the radius of its base as 4 to 3, and the entire surface is to its solidity, as 1 to 80; required the altitade.
Problem No. 28.–A thin triangular plate, of uniform thickness, is supported in a horizontal position by three props at the angular points. Required the pressure upon each prop in terms of the sides of the triangle.
[We are obliged to get our engraving done in Milwaukee, and we failed to get the diagrams illustrating the several solutions which we have on hand in time for this Number. They will appear in our next issue.Ed.]
Town LIBRARIES.— The able exposition of the advantages of the town over the district library system in the present Number, by the State Superintendent, Mr. Draper, is worthy of the careful consideration of every friend of popular enlightenment. That the old system was a failure, so far as nine-tenths of the State is concerned, is evident to all, and that the township system has succeeded in other States, and secured the best results wherever established, is conclusively shown by the ablest educators East and West.
That there will be opposition to the system in some localities, on account of the increase of taxation consequent upon its establishment, is to be expected, yet we think when the whole matter is carefully considered, the real benefits estimated, and the smallness of the tax on individuals taken into account,* all opposition will cease, and the Town Library Law will be looked upon as a most wise and beneficent measure, and the hopeful anticipations of the Superintendent be participated in by all who believe that intelligence and virtue are the basis and safeguard of our institutions.
New School Law.—The bill prepared by Mr. Pickett, and which was introduced into the Assembly too late in the session for any definite action to be taken upon it, proposed an entire change in the system in the following respects :
First, as to the division of territory into districts. The present district is to be retained, for the purpose of electing, annually, an officer styled director.
Each organized town, and every city and village containing a certain number of children over 4 and under 20 years of age, constitutes a union district.
Each county (as near as practicable) constitutes a Superintendent district, and finally the State at large is considered as a single district for school purposes.
Second, of School Boards.
SEC. 5. There shall be elected in each school district, as hereinafter proyided, one officer to be called Director, and in certain cases one or two Associate Directors.
SEC. 6. For the management and control of schools in the union districts there shall be organized in each a Board to be called the School Board, which shall be composed of the Directors, or Directors ar Associate Directors of the School Districts or district situated therein, and & School Inspector who shall be ex-officio Secretary of the said School Board.
* Only ten cents on one thousand dollars,
Sec. 7. To promote the interests of education in the Superintendent District there shall be constituted a board to be called the Board of Education, which shall be composed of the several School Inspectors of the Union Districts situated therein, and a County Su perintendent, who shall be ex-officio Secretary of said County Board of Education.
SEC; 8. To promote the general interests of education in the State, there shall be organized a State Board of Education, which shall be composed of the several County Superintendents and the State Superintendent,who shall be ex officio Secretary of the said Board, and the Chancellor of the State University, and the Principal of the Normal Department shall be ex-officio Members,
SEO. 9. The Board of Supervisors of the several towns, the City Councils of the several cit. ies, and the Boards of Trustees of the several villages, constituting Union Districts shall each for the purposes of this act, be termed a Board of Controllers, and shall perform such duties 88 hereinafter provided.
It will be seen at once that the bill proposes to take the control of the schools from the annual district meeting, and give it to a board composed of the Directors of the Town or Union Districts. These directors are organized into a School Board for the whole town, the secretary of this board, called an Inspector, being their executive officer, and taking the place and performing the duties of the present Superintendent.
The Secretary of the County Board is Superintendent of the County District, has a general supervision of the schools, holds institutes, examines teachers, etc.
In brief, the system comprises a State, a County, and a Town Board of Education with definite powers and proper executive officers to put in operation and supervise the system, each part of which is adapted to every other part, and the whole intended to secure a harmonious development of our educational resources, and the best and highest education for all our children.
Further explanations, and reasons why the system should be adopted, will be given hereafter.
WATERTOWN.—Lectures on Anatomy, and Physiology were given in the Second Ward School of this city, during the winter term, by Dr. L. S. Ingman; a good example for other places.
WOMAN'S RIGHTS IN MINNESOTA.-W. P. Underwood writes us from Richland, Fillmore County, Minnesota claiming “the banner” for the young and thrifty State, so far as the recognition of woman's rights, and provision for the cause of edncation. He sends a copy of a section of the school laws of Minnesota, in the following words:
" Every inhabitant over the age of twenty-one years, who shall have resided in any school district for three months immediately preceding any district meeting, and who shall have paid, or shall be liable to pay any taxes, except road tax in said district, shall be allowed to vote at such meeting," and remarks: "This gives taxable women equal “privileges with men to vote and hold office, as sex is not named any where in the school laws.
“Every sixteenth and thirty-sixth section of every township is appropriated to schools, so with judicious management the cause of education will prosper."-Life Illustrated.
GLOBES.- A few years since a globe in a school-room was a great curiosity, a costly rarity in which few schools could indulge, and even now, notwithstanding the decrease in price, and the superiority of those manufactured at the present day, but few schools are supplied with those useful assistants in the study of geography and astronomy. For the purpose of calling the attention of teachers and school boards to the matter, we insert the following article, originally published in the Pittsburg Gazette.
"There is quite an active movement just now among the friends of education, in favor of introducing artificial globes into all the common schools. It is indeed time. Both our English cousins and ourselves have hitherto neglected these valuable aids to education. We have been too much in the habit of regarding globes as suitable only for the higher institutions of learning. The reverse of this is now being recognized as the fact. Thanks to the French and Germans—especially the latter-for the change. They have proved to the world that no child, learning even the rudiments of geography—not to mention astronomy—is too young to derive advantage from lessons on the globe. The experience of the best teachers show that much time is gained by the early use of these veritable keys of knowledge. The maps are very good in their way. They give a tolerably correct general idea of the boundaries, bearings, etc., of any particular country of limited extent. But if we require to know the relative positions of different countries situated at considerable distance from each other, they are apt rather to mislead than direct us; whereas a mere glance at the terrestrial globe gives the necessary information at once, without further trouble, and so impresses it on the mind that it is likely to be retained through life. But it is not alone to students that globes are useful, They are so to all who read. It is incredible to those who are unacquainted with their use what important aid they afford even in the perusal of the daily journals or the Bible. True, a good pair of globles cost a pretty round sum; but so do any articles which are useful—which economize time, and which require labor and skill in their production. They do not, however, cost one-third as much now as they did some seven years ago. Then all, or mostly all, had to be imported from France or England; whereas, neither of those countries export better or imore beautiful globes than are at present manufactured in our own country by the Messrs. Moore & Nims, of Troy, N.Y. I have recently had the pleasure of examining a whole series of these—in eight different styles and sizes -and in commencing this epistle, it was my intention to give your readers a brief description of them. I can only say now, that the sixteen-inch bronze pedestal stand globes of Troy manufacture surpass in accuracy, beauty, and elegance of finish
any similar articles it has eve been my privilege to examine."-Pittsburgh Gazette.
The price of the above globes may be learned by examining our advertising columns.
A POPULAR ERROR. —One of the most common and fatal mistakes made by ardent friends of education, is the indulgence of unreasonable hope, and the main. tenance of extravagant views as to what they can effect by the means of it. It is often supposed that great results can be produced in a single term of twelve or fifteen weeks. Both teacher and committee aim at this rapid mode of manufacture. True education is that which aids the slow and healthy growth of the mind-the incorporation into it of principles, and the formation of tastes and habits, the full value of which will appear only after mature years have developed their tendencies. The highest and best parts of education are incapable of exhibition. The show made at the cluse of a term is well enough to amuse children and their fond parents, but is often like that of a newly dressed pleasure grounds, adorned with trees and shrubs fresh from the nursery, having a show of vitality in the foliage, though as yet drawing no sap from the root. Such frost-work of the school-room is soon dissolved, and generally passes away with the occasion. All attempts at such premature resnlts of education are entirely useless, and yet our system of employing teachers by the term renders it almost necessary for a teacher who is ambitious of distinction, to lay his plans for that kind of superficial cul. ture and mechanical drill which can be produced in a few weeks, and shown off as evidence of marvelous skill.Sears.
MADISON.-D. Y. Kilgore has been re-elected Superintendent of Schools by the Board of Education of this city. Mr. Kilgore has held the office for several years, and discharged its duties with much acceptance.—Madison Journal.
W. C. Sanford, formerly of Watertown, and late of Columbus, in this State, has gone to Vermont, and is engaged in a select school at Orwell, in that State.
MILWAUKEE. - Rufus King, Esq., the able editor of the Milwaukee Sentinel, has been appointed City Superintendent of Schools, with a salary of $2000.
PALMYRA. --E. B. Gray has resigned his situation as principal of the public school in this village on account of poor health. He has labored assiduously and successfully while in Palmyra, and made many warm friends. His address in future will be Whitewater, Wal. Co., Wis., to which place he has removed with the ntention of making a permanent home in that pleasant and thriving village.
FOND DU LAC.---We learn from the Commonwealth that the High School in this city, under the charge of Mr. E. C. Johnson, is in a highly prosperous condition, and gives complete satisfaction to its patrons.
The examination at the close of the winter térm reflected great credit on both teachers and pupils. The executive committee, in their report, say that they