entirely opposite points of view, and that art and science flow, as it were, from opposite poles of the mental battery. But we are persuaded that there is not a real antagonism between them, and that the apparent conflict comes merely from the limited capacity of the human mind, in which close attention to one mode of viewing an object usually excludes all other modes. In souls of a larger growth there is found to be no incompatibility, and Art and Science are helpers of each other; Geometry and Optics justifying and sustaining Sculpture and Painting, and they in turn giving new interest and delight to those sciences; while Music and Poetry hold a similar, although more obscure, relation to Algebra. We have treated of the mathematics, in the present article, as though they were isolated subjects; but the remarks which we have made concerning their relation to art warn us that we must never forget the intimate blending of all themes of thought into one great universe of truth. The five branches of the hierarchy are all indispensable, and are all so interwoven that one is well taught only as it is perceived to lie in harmonious connection with the others. For this reason the teacher of mathematics should be prepared, during the whole of the course of instruction, to point out to the pupil the bonds that link his subject with the physical world, with the laws of astronomy, chemistry, botany and zoölogy; with the history of man, of his speculation, and of his action, with mechanical inventions, with art, and with commerce; with the nature of man, capable of apprehending the mathematical thoughts that have guided the Creator of the world in the formation of all things; with the nature of that Being who has made all contained in space, or evolved in time, and subjected them to laws which are a source of such instructive and delightful investigation for his children to pursue, and which, in the forms and appearances they produce, awaken also such manifold sources of pleasure in the beauty and harmony of His works. The principal views which we have endeavored to present in this article may be summed up in three sentences: that geometry should precede arithmetic in the training of a child's mathematical powers,-that in each of these two studies concrete forms should precede abstract language, observation and conception precede reasoning,—and that the cultivation of the power of definite conception by geometry is as truly valuable as the cultivation of the logical power. We cannot agree with the opinion that arithmetic is of more practical utility than geometry; yet, if we were of that opinion, we should still teach our children geometry first, arithmetic afterwards. For a change of occupation is rest, and the boy, who begins with geometry and leaves arithmetic to a later period, develops his powers is a more natural order, achieves his task with less fatigue and, at the age of fifteen, not only knows more of other things, but more of arithmetic, also, than he could have known had his taste for numerical computation been destroyed by a premature and too continuous application to that science. In our next article we propose to consider the proper mode of introducing the young to Natural History. To be Continued. Superintendent's Department OPINIONS, &C., FROM THE OFFICE OF THE STATE SUPERINTENDENT. (Continued from the July Number.) Q, Have the Board, the teacher, or the town or city superintendent the authority to expel a pupil from school for want of punctuality? A. In regard to the powers of superintendents, and the duties of teachers, in the absence of positive statute, custom and precedent have established a quasi law. The teacher has control of the scholars only during school hours, and while in the school house, or grounds. Out of school hours, and at home, parents have, as they ought to have, full and free control; nor does the act of attending school on the part of the child divert or lessen parental authority. The School Board may establish certain regulations for the management and government of the school, as provided for by law. For instance: they may prescribe certain textbooks, and teachers are not obliged to hear scholars recite in any other; or they may prescribe certain duties, such as writing compositions, or declamation, and a persistent refusal on the part of a pupil to comply, would, undoubtedly be a sufficient cause for a suspension from the privileges of the school until the rule was complied with. Or, for continued misbehavior, the Board may peremptorily expel a scholar until obedience is promised, and good behavior guaranteed. The con、 stitution says that the common schools shall forever be free to all children, etc⋅ The Declaration of Independence also classes liberty among the inalienable rights of men. But a man, by his own criminal action, may forfeit his liberty. And so a child, by his own continued misbehavior, may forfeit the right, secured to him by the Constitution of our State, of attending school. The right, then, to suspend to expel for a time, is clearly within the province of the school board. But this power cannot be delegated by the Board to the teacher; nor can the town or city Superintendent, except in case a local law gives him the authority, take this matter into his own hands. Whether tardiness is a sufficient reason for expulsion, or not, must be determined by circumstances. Punctuality of attendance is a great desideratum; but this, like all else in education, must be maintained rather by persuasion than by force. But, although punctuality is thus one of the necessities of a good school, it cannot be that, for an absence required or permitted by a parent, the teacher or School Board can, as a punishment for such absence, peremptorily refuse admis、 sion to the absentee. If a parent keeps his child at home one term, can the School Board refuse the child admittance the next? Or, if the parent keeps his child at home for one day, can the School Board refuse admission the next? Thus whenever absence is the result of obedience to parental authority (command or permission), the authority of the School Board should not inflict a punishment. If punishment is merited, it is by the parent. In case the absence is so long continued as to interfere with the good order of the school, and the progress of those who are punctual, a more severe course may be necessary to prevent its recur、 rence. But, in all cases, it should make a difference whether parental authority sanctioned the absence. We would, therefore, answer the question by saying that the Board cannot expel a scholar for tardiness, but that they may suspend him for a short period when such absence partakes of a criminal character. Q. If districts, in ignorance of the law, at their annual meeting in 1858, elected their officers all for one year, how long will they hold their offices? A. The officers elected at the annual meeting in 1858 will all hold their offices as provided in Section 16 of the School Law, whether such was the intention or not. In cases where there is any dissatisfaction, it would be advisable for all officers thus elected to resign, that the election may proceed with full cognizance of the law. Q. In case of an election at a first meeting, how long will the officers hold their offices? A. The same as though they were elected at the previous annual meeting. Section 16 of the School Law provides "that at the first annual election of district officers after the passage of this act, and at the first election [not the “first annual election,"] of such officers in any newly organized district, the clerk shall be chosen for one year, the treasurer for two years, and the director for three years Thus, in case of an electionat a first meeting, the time between that and the annual meeting must be taken as one full year. S. H. CARPENTER, Assistant State Superintendent. Mathematical Department. 7 EDITOR JOURNAL:-I am desirous of eliciting from some one or more of your scientific readers, information as to a disputed point respecting gravitation; and, with such view, submit the annexed problems, in the hope that some formula and process of procedure to obtain true answers may be supplied. The writer is well aware that it is a conceded point that matter gains in weight by an approach toward the poles, but doubts the sufficiency of the reasoning as to the cause, and submits a proposition in refutation: Proposition:-That if attraction of gravitation is toward the center of a mass; that the force of such gravitation will vary the surface of any mass, not a perfect sphere; and that such variation will be modified by the extent of lateral attraction, and distance from the centers of attraction. Also, that a lateral attraction of 45' will reduce the attraction of gravitation (downward) the one half. corner F-D perpendicular to F: whether the attraction will be greater in Question.-At what point on the earth's surface will matter have the greatest weight, at the Poles, or at the Equator? Centrifugal force not to be considered. The equatorial diameter being 26 miles greater than the polar. N. B.-In "Another solution to Problem 12," in the March No., there seems to be a typographical error. 200 200 200 Problem No. 33.—I have a garden in the form of an equilateral triangle, whose sides are each 200 feet. On each corner stands a tower, whose heights are respectively 30, 40, and 50 feet. What is the length of a ladder that will just reach the top of each tower, and how far is it from the foot of the ladder to the base of each tower? J. C. D. Editorial Miscellany. ABSENCE from our office attending Teachers' Institutes, and a severe attack of inflammation of the eyes, which, for more than two weeks, frustrated all attempts to read or write, must be our apology for the lack of variety in our editorial columns, and for the delay in issuing the present number. TEACHERS' INSTITUTES.-The Institutes held under the direction of Chancellor Barnard during the past month, have been very successful, and will do much in arousing public attention and securing union of effort in the work of improving the condition of our schools, and the qualifications of teachers. The attendance in most cases was large, exceeding the anticipations of the most sanguine, and the exercises were characterised by earnestness and good feeling. Chancellor Barnard was present at most of the Institutes, lecturing upon topics relating to a system of public instruction adapted to the wants of our people, and exercising a general supervision over each. Messrs. F. A. and C. H. Allen, of Pennsylvania, and Mr. John Ogden, of Ohio, were engaged by Dr. Barnard to take charge of the Institutes and conduct the daily exercises, and they have shown themselves well qualified for the performance of the duties devolving upon them, as the success which attended their labors and the hearty approbation of the teachers benefitted by their instructions abundantly testify. At Elkhorn the lady teachers presented Messrs. F. A. Allen and Ogden a set of silver forks as a token of their gratitude and esteem, and at Waupun the ladies presented the same gentlemen a well filled purse as a partial return for benefits received, and the resolutions passed at Sheboygan and other places where institutes were held by Mr. C. H. Allen, show that his labors were highly appreciated by the teachers and citizens in attendance. Mr. C. E. Hovey, principal of the Illinois State Normal School, had charge of the Institute held at Mineral Point, and the complete success which followed his efforts proved his fitness for the responsible post he occupies in our sister State. It is proper to state that the gentlemen mentioned were assisted by prominent teachers of each locality where |