Зображення сторінки
PDF
ePub

ous parts of the State, to deliver educational addresses; and for the better discharge of his duties to employ, in connection with a committee of this Board, such assistants as may be found necessary.

Which was adopted.

On motion of Mr. Robbins, a committee of three was appointed to confer with a committee of the University Regents, now in session, to fix upon a salary for Dr. Barnard.

Messrs. Robbins, Cooke and Cary, were appointed said committee.
On motion of Dr. Cooke.

Resolved, That the Secretary and Agent be and they are hereby requested to prepare such a brief statement of requirements, etc., as they may deem necessary for the information of such institutions as apply for the benefit of the Normal School Fund.

Adopted.

By Mr. Clark.

Resolved, That the President and Secretary be authorized to draw warrants on the Treasurer in favor of such assistants as may be employed by the Agent of the Board for such amounts as may be found due on a certificate of the Agent as to the time of service and expenses of the assistants.

Adopted.

On motion of Mr. Bean,

Resolved, That an appropriation of $250 be placed in the hands of Prof. Barnard, the Agent of this Board, for the purpose of defraying the contingent expenses in holding Teachers' Institutes.

Adjourned to 23d at 9 o'clock.

JUNE 23d.

Committee appointed last evening, reported that they had had a conference with the committee of the Regents of the University, and reported the following resolution, which was unanimously adopted:

Resolved, That this Board fix the salary of Dr. Barnard as our agent of the Normal Schools at $1,250 be paid quarterly out of the Normal School Fund. Adjourned.

S. CHAPMAN, Sec'y.

FRANCIS C. WOODWORTH, late editor of Woodworth's Youth's Cabinet, died of consumption, on Sunday morning, June 5th, on board the steamship from Savannah, in which city he had been during the winter, for the benefit of his health.

The Board of Education of N. Y. City have resolved by a vote of 21 to 16 to require the reading of the Bible in all the public schools of that city.

The voice of provocation is the voice of God calling us to the practice of patience.-Beecher.

Mathematical Department.

Solution of Problem 21.-Let A BODEF be a section of the sphere perpendicular to the base of the cylinder, and cutting their common center O. Put A D=2 R=diameter of the sphere, B C

2 x altitude of the required cylinder, B F-2 y diameter of cylinder, and S=its solid contents. Then, y2 2 x =S.

[blocks in formation]

(1.)

(2.)

(1) and (2.)

(3.)

F

B

E

If we increase by z, and denote the corresponding cylinder by S', we

[blocks in formation]

and dividing by 2, we get R3-3x2—3xz—z2 = ̄2z □

If we put z=0, then S'=S, and the above becomes R3-3x2=0; hence

2x=altitude of cylinder=2 R√

[blocks in formation]

Or thus: Differentiating (3), and observing that because S is a

maximum, d S=0, we get R'dx-3x2dx=0; or, R3-3x2-0, as above. A. W. WHITOOM.

Solution of Problem No. 22.-Let A B C be the triangle. Place the perpendicular A B-x2, then by the problem x2-x will equal the base B C. Since the area of the triangle is equal to one

acre, or 160 square rods, we have the equation x2(x2—x)=160, which reduced gives

2

x1-x3-320. Solving this equation we find x=4,503 nearly. Hence, x2=20,277 + rods =A B and x2-x-15,774+rods=B C.

L. CAMPBELL.

B

Another Solution of Problem No. 22.-Let x=the base, and y the perpendicular. Then by the conditions of the problem x-y-√y (1) and xy —320 square rods (2). Substituting the value of x in equation (1) in equation (2) we have y-y y=320, which being solved, gives y=20.2814 rods. Substituting this value in equation (1) we have x-15.7779 rods. JAS. M. INGALLS.

Solution of Problem No. 24.-Let A B C represent the cone, h its perpendicular height, D the diameter of its base, and E F G H the required cylinder. Let x=the height of the cone, A E F, y-the diameter of its base the diameter of the cylinder, and h-x- -the altitude of the cylinder. Hence 7854 y2(h—x)—the solidity. We may now find the relation between x and y by the following proportion h:D :: x: y.

Therefore, y Dx.
=

h

Substituting Dr for y, and omitting constant fac

h

E

[blocks in formation]

tors we have x2(h—x)=maximum. Placing the differential of this expression=0, we find x=3h. Hence h-x-1h-the altitude of the cylinder, and y-D-its diameter. L. CAMPBELL.

Solution of Problem No. 26.-The position of the bearing pole will not be varied by supposing the whole weight to be at the timber's center of gravity; which, by the conditions given, is at the center of magnitude. Let a the length of the timber. Since C is to support half as much as the bearing pole, C's distance from the center of gravity must-by the principle of the lever-be twice as great as that of the bearing pole; but C's distance-A; hence the pole's distance- A from the center; or, the length of the stick from the end opposite C. A. W. WHITOOM.

Solution of Problem No. 27.-Let R-the radius of the cone, and ≈ the altitude. Then we have x: R::4: 3. Hence R-(1). Also, R2x

R

√(x2+R2) + R2: 3 :: 180. Hence (x2+R2)+R: R :: 1: 80.

Substituting the value of R given in

Hence x=640, JAS. M. INGALLS.

Hence 80/(x2+R2)+80R➡22.
equation (1) and reducing we have 9x-4320x-921,600.
and R-480.

[We have received from Mr. Ingalls an answer to Mr. Whitcom's communication in the Mathematical department of the last Number, but must postpone it for want of room. We have a number of problems on hand, which will appear in due time.-ED.]

CORRECTION. The following typographical errors occur in Mr. Ingalls' solution of problem No. 6, in the June Number: "Fifteenth line from the bottom, for C F b, read c F b; eighth line from bottom, the sign between ds and dt within the parenthesis should be + instead of -; fifth line from bottom, for ds read s."

Editorial Miscellany.

[ocr errors]

DISAPPOINTMENT.-When the June Number was issued, we thought that arrangements were perfected by which we should be enabled to present the first Number of Vol. 4 in a new dress, but alas for human calculations in this age of dispatch! After waiting and writing, and waiting and telegraphing, and waiting again till near the close of the month, we were obliged to set up the Journal with the same old type, and to borrow cover paper at the last moment, having failed in every attempt to procure the kind we wished. We regret this very much, as we had set our heart on getting out a beautiful specimen number this month; but we must "learn to labor and to wait" another month.

THE STATE UNIVERSITY.

A special meeting of the Board of Regents was held in the Capitol on the 22d ult. Communications were made to the Board by Chancellor Barnard and several of the Professors in relation to special matters of interest to the University. The following resolution was reported by Mr. Tenney, from a special business committee and adopted, to wit:

Resolved, That the Executive Committee are hereby authorized to make arrangements with the Board of Education of the city of Madison, for the accommodation and instruction of students of the University in the Normal and Preparatory Departments, with the pupils of the Public High School in the same studies, provided such arrangements do not diminish the advantages of the University students, and do not impose any additional expense on the University.

A resolution was also reported from the same committee, and adopted, for establishing a Polytechnic School in the University.

Dr. DAVID B. REID of the University of Edinburgh, was elected to fill the chair thus established, at a salary of $1,500 per annum.

The salary of the Chancellor was fixed at $1,750 per annum, which with the sum allowed him by the Normal Regents as their agent ($1,250), makes $3000. The new Chancellor has been cordially received by every one connected with

the University, and it seems to be acknowledged by all that its prospects were never more encouraging. As agent of the Normal Board, Dr. Barnard is preparing a plan of operations calculated to embrace all the agencies which can be made to subserve his purposes in advancing the educational interests of the State. That he will meet with a hearty co-operation on the part of all our people, is not to be doubted, and we look with confidence for valuable improvements and great progress in the right direction as the result of his large experience and devotion to the good work.

THE

WISCONSIN STATE TEACHERS' ASSOCIATION.

SEVENTH ANNUAL MEETING OF THE WISCONSIN STATE TEACHERS' ASSOCIATION WILL BE HELD AT MADISON, COMMENCING ON TUESDAY, JULY 26TH, 1859, AT 8 O'CLOCK P.M.

The Executive Committee have called the meeting one week earlier than usual, that they might thereby secure the attendance of Henry Barnard, LL.D., whose prospective relations to the teachers of the State, as Agent of the Board of Normal School Regents, render it especially desirable that he should meet them at their annual gathering. Dr. Barnard will be inaugurated Chancellor of the State University on Wednesday-Commencement Day-and a part of his inaugural discourse will, by invitation, be especially addressed to the teachers of the State. The opening address will be given by the President, A. Pickett, of Horicon.

A complete programme can not now be given, but it is expected that besides those which may not be definitely announced, addresses will be made as follows:

"Upon the Method of Governing a School so as to Secure Moral Development"-By Prof. E. P LARKIN, Principal of the 2d Ward High School in Milwaukee.

"Upon Mental Development; How Secured"-By E. C,JOHNSON, Principal of the High School in Fond du Laз.

"Upon Religious Instruction in Common Schools"-By Rev. M. P. KINNEY, of Racine. "Upon Physical Geography"-By Prof. E. DANIELS, of Waukesha.

"Report upon the Revision of the School Law"-By Rev. J. B, PRADT, of Sheboygan. "Essay"-By Miss E, L. BISSELL, of Hartford.

On Thursday Evening there will be a Social Gathering at the City Hall, where, as we are authorized to state, the citizens of Madison will be happy to meet the teachers and strangers from abroad.

The annual election of officers will occur on Friday Morning,

Madison offers a cordial welcome to the Association, extending her hospitality to all who may attend, and it is hoped that there will be a large representation of teachers and friends of education from all parts of the State, as we feel warranted in assuring them that all reasonable efforts will be made to secure an interesting and profitable session,

The usual arrangements have been made with most of the R.R. Companies in the State, to Return Free, those who receive the necessary certificate of attendance from the Secretary of the Asssociation.

JAS. W. STRONG, Secretary.

MADISON, WIS., July 1st, 1859.

A, PICKETT, President.

GLOBES!

GLOBESI

The reputation of the Franklin Globes has already outrun the necessity for description. The manufacturers have recently added to their list a splendid thirty inch Terrestrial Globe, the largest ever made in this country. The Franklin Globe Manual is designed to facilitate the study of the Globês, and includes a description of the various terrestrial and celestial phe

« НазадПродовжити »