The committee on nomination of officers made the following report, which was accepted:

President J. B. Pradt, Sheboygan.

Vice Presidents-M. P. Kinney, Racine; Geo. Gale, Trempeleau; J. J. McIntyre, Berlin.

Secretary-James H. Magoffin, Waukesha.

Treasurer-E. S. Green, La Crosse.

Councillors-A. J. Craig, Palmyra; J. L. Pickard, Platteville; E. C. Johnson, Fond du Lac; E. P. Larkin, Milwaukee; T. J. Conatty, Kenosha,

The Association proceeded to ballot for officers, when the persons nominated by the committee were duly elected.

Chancellor Barnard then addressed the Association, explaining his relation to the public schools of the State, as agent of the Board of Normal Regents, and stating what he hoped to accomplish through lectures and teachers' institutes if supported by the hearty cooperation of teachers and friends of education.

J. L. Pickard made a few remarks with reference to the early history of the Association, his connection with it, and the educational movements of the State. Rev. M. P. Kinney stated that 20 years had elapsed since he commenced teaching in this State, and that he was probably the oldest teacher belonging to the Association.

Rev. M. Adams, of Racine, offered the following resolution, which was adopted: Resolved, That Mr. J. L. Pickard be requested to write out the history of the Association from its organization to the present time, for publication in the Journal of Education.

Mr. McKindley, from the committee appointed to consider the subject, reported in favor of the oppointment of a State Agent to cooperate with Chancellor Barnard in awakening an interest in popular education, and that he had already obtained over $700 in subscriptions towards paying the salary of such agent.

Chancellor Barnard spoke of the good which such an agent could accomplish. He would willingly pay one half of the salary necessary out of his own pocket. He then spoke in the highest terms of the services which Wm. S. Baker, of Massachusetts, who was now in this city, had rendered in a similar capacity, and said that if he could be induced to accept the place, he knew of no man who could accomplish so much good as that gentleman.

Voted that all moneys remaining in the treasury after providing for the expenses of the current year, be appropriated towards the expenses of a State Agent.

M. J. Ford, of Milwaukee, offered the following resolution, which was adopted: Resolved, That we cordially invite and earnestly request Mr. Wm. S. Biker to act as traveling agent, and co-operate with Dr. Barnard in his work of visiting the State.

Mr. Conatty, from the committee on resolutions, reported the following additional ones, which were adopted:

Resolved, That we would express our renewed confidence in the Wisconsin Jonrnal of Edu. cation, and trust that the teachers of the State will make earnest efforts to extend its circals. tion and influence during the ensuing year.

Resolved, That the thanks of this Association be tendered to D. Y. Ki gore, Esq. for his efficient services in completing arrangements for our present session.

Resolved, That we tender our cordial thanks to the citizens of Mad'son for their generous hospitality; we shall long cherish pleasant memories of the noble hearts and happy homes of their beautiful city.

Resolved, That we tender our thanks to the Faculty of the Wisconsin State University and I to the managers of the Madison Horticultural Exhibition for courtesies extended to the Asso·

ciation.

Resolved, That we are under renewed obligations to the officers of the following Railroads: Milwaukee & Mississippi, Chicago & Milwaukee, Milwaukee & Minnesota, Chicago & Nor h western, Racine & Mississippi, Milwaukee & Baraboo Valley, and Galena & Chicago, for their liberality in furnishing free return tickets to members of the Association.

The following resolution offered by Prof. Conover of Madison, was adopted: Resolved, That the Association recommend to the executive committee that in making arrangements for the next meeting, they provide for exercises of a more practical character than have usually characterized the meetings of the association.

Rev. M. Adams offered the following, which were likewise adopted:

Resolved, That the thanks of this Association are tendered to the President for the impartial and efficient manner in which he has presided over the deliberations of our meetings. Resolved, That we tender our thanks to the editors of this city for the interest they have manifested in so fully and correctly reporting the doing of this convention during the present session.

Invitations were received from Hon. L. C. Draper, inviting the Association to visit the rooms of the State Historical Society, and from G. B. Griffin of the Lake Side Retreat, to make a trip on the steamer Flora, at 2 o'clock P. M.

After singing the doxology to the tune of Old Hundred, and prayer by the Rev. Mr. Kinney, the Association adjourned to meet in Milwaukee, at such time as shall be designated y the executive committee.

A J. CRAIG, Secretary pro tem.

A PICKETT, President.

TEACHERS' EXCURSION ON STEAMER FLORA.

In compliance with the invitation received from the proprietor, G. B. Griffin, Esq., about seventy five of the teachers embarked on the steamer Flora, at 23 P. M., Friday, and paid a visit to the "Lake Side Retreat." After an hour agreably spent, the party re-embarked and returned to the city. While on the return pass age the following resolution was unanimously adopted:

Resolved, That the excursion of this afternoon is a delightful and fitting finale to the throngpleasures of the week, and that we, therefore, tender to G. B. Griffin, Esq., our most hearty thanks for his generosity in affording us a free passage on the Steamer Flora to the beautiful grounds of Lake Side Retreat, thereby rendering complete the enjoyments afforded us by the people of Madison.

[The above, though no part of the regular proceedings of the Association, deserves a place in our pages, and we also feel it to be our duty to notice and commend the conduct of the gentlemanly Superintendent of Public Property, Hon Rufus Parks, who had the Assembly Chamber prepared for the use of the Association, furnished desks and stationery for clerks and reporters, iced water for the thirsty, and did all in his power to make the meetings pleasant.-ED. JOURNAL.]

Superintendent's Department.

TO THE ELECTORS OF SCHOOL DISTRICTS.

As the time is approaching for the election of a District Clerk for a term of three years, for each school district in the State, I deem it of so much importance to the cause of education as to venture to call special attention to the subject, and urge your attendance at the annual meeting.

These school district elections are too generally disregarded, while none so vitally and intimately concern the dearest interests of the whole people. It is this criminal neglect that enables a few-and these not always the most discreet and intelligent—to foist upon the districts men utterly unfit for school officers, however good citizens in other respects; and thus the whole school system, from its improper administration, is frequently brought into disrepute, bitter quarrels and vexatious litigations engendered, unworthy teachers employed, and the children deprived of the proper facilities for acquiring an education. When there is scarcely one in every one hundred of our youth who ever enjoy the higher advantages of our Universities, Colleges and Academies, how very important it is that our Common Schools should be watched over with jealous care on the part of the people, and only the very best men chosen for their supervision and management. Spend, then, fellow citizens, a few hours, if need be, in the faithful performance of this high duty-select a judicious and competent man for clerk-one who will serve his district with an eye single to the best interests of the people and the Cause of education-one who will not seek to make use of his position to force upon the district a sister, a son, or a daughter for teachers, when a better selection could and should be made-one, in short, who will not seek the office for the promotion of selfish ends or pecuniary considerations.

In making choice of so important and resposible an officer, I entreat you to lay aside every improper influence-every political and sectarian partiality-and select for Clerk the man best fitted in the district for the position. Then will your schools be improved, and your children properly educated. There are persons in every district, who, if not entirely competent for the office at least comparatively so-honest, intelligent, and well-meaning; let such be sought out and elected on the last Monday in September, and then no one will be disposed to complain because he has been earnestly urged to a performance of this duty. Very respectfully,

of Clerk, are

MADISON, August 1, 1859.

LYMAN C. DRAPER,

Supt. of Public Instruction.

TEACHERS' INSTITUTES FOR 1859.

THE undersigned will appoint, in different parts of the State, as many Institutes to continue in session from Monday evening to Friday evening of the weeks named, in the months of September, October and November, as he thinks he will be able to attend in person and secure the requisite help in conducting, as soon as he receives reasonable assurances on the following points:

1. A desire on the part of at least thirty teachers to have such an appointment made.

2. A pledge on the part of the committee of the individuals asking for the appointment, to give due notice through the press of the neighboring towns and counties, and make all local arrangements.

3. Accommodations for as many teachers, or persons intending to teach public schools the ensuing winter, as may report themselves on Monday evening or Tuesday morning. No favors are asked for the loiterers.

4. The free use of a suitable place for the sessions of the institutes during the day, and for public addresses in the evenings.

Applicants will promote the success of the proposed meetings if they will designate their first, second and third choice as to the week in the month preferred, and also name the week in which, for any reason, the Institute should not be in their respective counties. HENRY BARNARD,

MADISON, July 28th, 1859.

Ag't of Regents of Normal Schools.

Mathematical Department.

EDITOR JOURNAL:-Dear Sir:—In the April number of the Journal, I pointed out some errors in Mr. Whitcom's solution of problem 6, very briefly, and without attempting to be "profound," as the errors alluded to are so apparent that I supposed a bare reference to them would be sufficient: but as Mr. Whitcom has attempted, in the June number, to fortify himself in the false position which he had taken, I will, with your permission, point out more explicitly, and at length, wherein his solution is erroneous.

I stated, in my article alluded to above, that if the equation y2=(x2—a3) tan. A tan. A1 be the equation of a hyperbola, tan. A tan. A1 will be equal to the sqare of the ratio of the semi-axes; that is, constant. Mr. Whitcom thinks it sufficient proof that the factor tan. A tan. A' is constant that the equation already contains two variables, viz: x and y, and asks if I am "ignorant of the fact that every equation between three variables must refer to, and only to, a surface?" Every equation between three variables, two of which are independent, referred to three

axes, is the equation of a surface; but an equation of a line referred to two co-ordinate axes, may have any number of variables, provided they are all functions of x or y. For instance, the equation of the parabola

1

1

=2, we

y2=2px may take the form y2=2p Making xa—w and shall have for the equation of the parabola y2=2pwz, an equation containing three variables, all of which are functions of x. In the circle, also, if the origin of co-ordinates be taken at the extremity of any diameer, and distances equal to the radius be measured off from the origin in opposite directions on the axis of X; and if from these points lines be drawn to any point of the circumference, we may have, representing the angles made by these two lines with the diameter by A and A1, Mr. Whitcom's equation of the hyperbola, viz.: y2=(x2-R') tan. A tan. A1 √2Rx-x2 √2Rx-x2 x -R x+R

(1). In this case tan. A=

; and tan A'=·

; there

Substituting this in equation (1) we have

the equation of the circle, viz.: y3=2Rx-x*. In a similar manner we might find the equations of other curves by first finding the value of tan. A tan. A1 in terms of a and constants and substituting them in equation (1); but generally the equation of curves may be obtained more easily by other processes.

That dis

The second objection which I made to Mr. Whitcom's solution, viz.: the confounding the co-ordinates of a particular point with the general co-ordinates of the curve is a valid one, and Mr. Whitcom's numerous references to Prof. Davies' Analytical Geometry prove it to be so. tinguished mathematician always represents particular co-ordinates by particular symbols: either by x or y, accented, or otherwise marked, or by other characters, and this is the universal custom of all writers on Analytical Geometry. Had there been no other error, however, in Mr. Whitcom's solution, this would not have affected the numerical result. In the course of Mr. Whitcom's investigation, he gave this formula for

√/b*+b3y2+a*y2

a2y1

finding the length of an arc of a hyperbola, viz.: z=xV With reference to this expression, I remarked that if we make y=0, the value of z will be infinite, instead of 0, which is its true value; and if we make x=0, z= —a. Mr Whitcom says that these objections are not well founded. If he means by this that the values of z given above are not its true values under the suppositions there made, why does he not point out the error and give the true values? I also remarked that the above formula was obtained by considering the co-efficient of da in the