and all alterations of a joint district must be made by the concurrent action of the Saperintendent of all the towns in part embraced in the district. Q. Has the Olerk a discretionary power to call a special meeting, or must be call it upon the request of five voters ? A. The discretion rests with the people. If five voters request the Olerk to call the meeting, it is bis duty so to do. It is not his business to decide upon the propriety of such a course. Q. If the Clerk refuses to draw a warrant on the Treasurer when ordered to by a vote of the district, what remedy has the district? A. The Board can either declare his office vacant, or order an action to be brought against him for malfeasance in office. In most cases the last course would be preferable, as it is not advisable to resort to removal ex. cept in excreme cases. ASSESSMENT AND COLLEOTION OF TAXES. Q. In case a tax is daly levied, and is in the collector's hands, when the district is divided, how must the tax be collected, and how paid over when collected ? A. The tax thus levied must be collected the same as though no division had taken place, and the money thus raised must be added to the assets of the district apon a division of property. A division does not annal any acts of a district wbich have been wholly or partially carried into effect, and the state of the case at the time of the levy of the tax, and not at its collection, will govern. This principle will also apply in cases where there is no division of property. Compiled from the records of the Department, by S. H. CARPENTER, Assistant State Superintendent. NOTICE TO Town SUPERINTENDENTS.—The new edition of the School Law is now ready for distribution. Towns will be supplied upon application to this Department. The Laws of 1859, amendatory to the School Law, will be issued immediately for the accommodation of those having the old edition. BLANKS.—The Blanks have been sent out from this Department for the Annual Reports of District Olerks and Town Superintendents. Those who do not receive them by July 1st, are requested to inform this Department, in which event they will be immediately forwarded. THE JOURNAL OF EDUCATION, sent by the State to Town Superinten dents and District Clerk, mast in all cases be considered as Public Property, and be preserved and delivered to successors in office, or placed in the District Library, as the law directs, In no case will the State furnish numbers or volumes that have been lost through carelessness. S. H. CARPENTER, NORMAL SCHOOLS. Proceedings of the Board of Normal School Regents at their meeting, June 22d, 1859. Board met at 5 o'clock P.M. Present-Hon. O. C. SHOLES, President, Hon. W. E. Smith, Messrs. Bean, Cooke, Chapman, Olarke, Maxon, Robbins, Cary, and Draper. Minutes read and approved. The committee appointed at the annual meeting in April, (Messrs. Bean, Cook, and Draper), to revise the course of study of the Normal Departments, and the system of rules and regulations for their government, and to prepare blank forms for their annual reports, made their report which, with slight amendments, was adopted. A committee, consisting of Messrs. Bean and Cook, was appointed to report in the evering on the duties of the Agent. Adjourned to 8 o'clock. 8 O'CLOCK. The committee on duties of the Agent made their report, with the following Preamble and Resolutions : WHEREAS, The Hon. Henry Barnard has heretofore signified his acceptance of the office of agent of this Board, tendered him at a meeting held on the 5th of Oct. last : --therefore Resolved, That he be invested as such agent with full power of supervision and control over such normal institutions as shall apply for a participation in the normal school fund. Resolved, That as such agent he be instructed to obtain and transmit to this Board full information as to the course of discipline and study in conformity with the resolutions of this Board as he may think best. Resolved, That as such agent, he be authorized to prepare and have printed all necessary blanks and documents for the conduct of his examinations. Resolved, That as such agent, he be authorized to hold Teachers Institutes in vari 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 apon & salary for Dr. Barnard. Messrs. Robbins, Cooke and Cary, were appointed said committee. Resolved, That the Secretary and Agent be and they are herebò 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. 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 & certificate of the Agent as to the time of service and expenses of the assistants. Adopted. 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. FRANOIS C. WOODWORTH, late editor of Woodworth's Youth's Cabinet, died of consumption, on Sunday morning, June 5th, on board the steamship from Savannab, 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. В. E 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 0. Pat A D=2 R=diameter of the sphere, B O 2 x=altitude of the required cylinder, B F=2 y =diameter of cylinder, and S=ils solid contents. Then, y: 2 x a=s. (1.) yö=R'—*, . (2.) Or combining, (1) and (2.) (3.) If we increase x by z, and denote the corresponding cylinder by s', we S' have R*x + R 2-20 3x2—3.222 —28= from which substracting (3), S' - 8 and dividing by 2, we get R’—3x4 — 3x2—29= 22 O If we put 2=0, then S'=S, and the above becomes R?—3x=0; hence 1 This value of x in (2) gives 2y=2R 20, 20=altitude of cylinder=2 RV Or thas: Differentiating (3), and observing that because S is a maximum, &S=0, we get R’dx—3x?dx=0; or, RP-3x –0, as above. A. W. WHITOOM. Solution of Problem No. 22.-Let A B O be the triangle. Place the perpendicular A B-2°, then by the problem ' -~ will equal the base B O. Since the area of the triangle is equal to one acre, or 160 square rods, we have the equation 2*(x*—2)=160, which reduced gives 2 24—29=320. Solving this equation we find X=4,503 nearly. Hence, a?=20,277 + rods =A B and wo_15,774+rods=B 0. L. CAMPBELL. B Another Solution of Problem No. 22.-Lot x=the base, and y the perpendicular. Then by the conditions of the problem 2-Y-VY (1) and xy =320 square rods (2). Sabstituting the value of æ in equation (1) in equation (2) we have y-y Vy=320, which being rolved, gives y=20-2814 rods. Substitating this value in equation (1) we have 2-15•7779 rods. Jas. M. INGALLS. Solution of Problem No. 24.-Let A B O represent the cone, h its perpendicular height, D the diameter of its base, and E F G H the required cylindor. 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 y'(h—2)—the solidity. We may now find the relation between x and y by the following proportion h:D:: * : y. Therefore, y= Dr. Substitating Dx for y, and omitting constant fac B G нс h tors we have xo(h—2)=maximum. Placiog the differential of this expression=0, we find x=h. Hence h-x=th-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 magnituda. Let a—the length of the timber. Since O is to support half as much as the bearing pole, O'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 O's distance-A; hence the pole’s distance- A from the center; or, 1 the length of the stick from the end opposite O. A. W. WHITOOM. Solution of Problem No. 27.-Let R-the radius of the cone, and & the alticade. Then we have x :R::4:3. Hence R-3(1). Also, o R R2x V(x2+R”) + OR? : 3 ::1:80. Hence (2* +R*)+R: :: 1 : 80. Hence 80 V(x2 +R?)+80R- Substituting the value of R given in equation (1) and reducing we have 9x?_4320x–921,600. Hence x=640, and R=480. Jas. M. INGALLS. [We have received from Mr. Ingalls an answer Mr, Whitcom's commanication 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.-E..] |