continually to punish, but never subdue. Few schools can survive such discipline. Let the words of reproof and threatening, and the blows of correction be few. Let these few be well chosen, significant and in earnest, and the scholars will be glad to have them few indeed. The rod should be the last resort, ordinarily the less it is used the better. But with it, or without it, order must be secured and the school governed. But can every one do this? Can every one, with com. petent learning, who desires a love of study in his scholars, and with clear insight into the characters of all, rule them with easy, but absolute control? By no means. Not every one is born to teach school, any more tban every one is born to command an army or rule a State. The qualities that combine to make the successful teacher, are among the highest and rarest in human character. They are a special gift, and he that has them not, will hardly acquire them by anything that can be said, and should be dissuaded from attempting the work. He that has them, will profit by every hint, and should be encouraged to make the teacher's calling the work of his life. A well-lisciplined, study-loving school, is one of the pleasantest sights in the world, and one of the richest blessings to any community, and the master or mistress of it, is worthy of the highest honor and the largest reward. C. C. P. What is it to be a gentleman? It is to be honest, to be gentle, to be brave, to be wise, and possessing all these qualities, to exercise them in the most graceful outward manner. Ought not a gentleman to be a loyal son, a true husband, an honest father? Ought not his life to be de. cent, his bills to be paid, his tastes to be high and elegant, his aims to be lofty and uoble ?-W. M. Thuckeray. “ Piety stimulatės the whole man to action, makes him consciously responsible to God for the use of his powers, and brings him in contact with truths and influences of the most elevating character." ** SUCCEED OR DIE” Teacher, was that thy creed? “ Succeed or die!" But for the next, D. P. Page, A. M., who had been for a long time a successful Teacher in Newburyport, Mass., was appointed the first Principal of the State Normal School at Albany, N. Y. On accepting the appointment he was heard to say in view of his responsible position, “ I will succeed or die.” He entered upon and prosecuted his work with the same determined spirit indicated by this expression. The enterprise was new and unpopular in the State, but under his judicious management, and with his enthusiasm and perseverance, the school was a perfect success. He had accomplished his object and gained an enviable position as one of the leading educational men of the age. But excessive labor and crushing cares at length proved too much for his feeble constitution and he sank to'his rest. He did " succeed” and he did “ die.” The above beautiful lines by Mrs. Sigourney, were written as a tribute to his memory, soon after his death in 1848. 0. MATHEMATICAL DEPARTMENT. ERNEST C. F. KRAUSS, A. M., EDITOR. Having been invited by the gentlemen who have thus far conducted this journal alone, to join them as co-editor by furnishing articles on Mathematics, I gladly accept this invitation and herewith respectfully introduce myself to our readers. The mathematical department in similar periodicals generally offers problems and afterwards publishes the best solutions sent in. I shall deviate from this custom, and, since the advantage of these problems seems to me very problematical I shall offer but few if any. What I propose and hope to do, is, to give a slight assistance to any teachers who may need and be willing to accept it. During several years of practical teaching, I have made the experience that there are some matters in mathematics (particularly in Algebra, of which I shall principally speak), in regard to which all our class-books are sufficient only for teachers who have had ample time and opportunity to make themselves very familiar with this special science, whereby they are enabled to supply by oral tuition what is wanting in the book, but too brief for most teachers of common schools, Academies, &c., who have to teach such a variety of branches that it is in general an impossibility for them to acquire this degree of familiar. ity with any one of them. My object, therefore, will be to speak of some of the more obscure points and to furnish teachers with means of making them plain, by giving the result of my own meditations and preparations for the explanation of such points. As an introduction I shall however first lay before our readers a short sketch of the various branches of mathematics. Mathematics is the science which treats primarily of the relations and measurement of quantities; and secondarily, of the operations and processes by means of which these relations are ascertained. It is the science of quantity. But it becomes an art by applying the laws which the science has stated, to practical purposes. As science, it is called pure mathematics; as art, mixed mathematics. The science of Mathematics is divided into three branches : I. Arithmetic is that branch of Mathematics which treats of the properties and relations of numbers expressed by the aid of figures and combinations of figures; it is the science of numbers. II. Geometry has for its object the investigation of the properties, relations and measurement of magnitudes, i. e., of lines, angles, surfaces and solids (volumes.) III. Analysis generally embraces all that part of Mathematics in which the quantities considered are denoted by letters and the operations to be performed are indicated by signs. Analysis has three branches : 1. Algebra, which investigates the relations and properties of numerical quantities analytically, by means of symbols. 2. Analytical Geometry, which has for its object the analytical investigation of the relations and properties of geometrical magnitudes. 3. Calculus, which treats of the form of functions. Algebra has again two subdivisions. a. Elementary Algebra, which teaches 1st, the principles of the ordinary operations of Addition, Subtraction, Multiplication, Division, Involution and Evolution, and 2d, the investigation of the nature and properties of Algebraio Equutions, i. e., of those in which the relations between the known and unknown quantities are expressed by these ordinary operations. b. Higher or Transcendental Algebra, which treats 1st, of quantities which cannot be expressed by a finite number of algebraic terms, and 2d, of Transcendental Equations, i. e., of those in which the relations between the quantities are expressed by the aid of logarithmic, trigonometrical and exponential symbols. In regard to Algebra I would add a few remarks: Elementary Algebra may also be called a universal Arithmetic, for it is based upon the same principles and makes use of the same operations, but its solutions have a more general character by the use of symbols. In Arith. metic the solution of an example answers only to the particular numbers which have been considered and there. fore only to one case. In Algebra, by the use of letters, we get relations which will answer to any other quantities which bear the same relations to each other.' Thus Algebra furnishes us with formulas, i. e., algebraic expres. sions of a general rule and principle. Another advantage of the use of letters in Algebra is, that the different quantities taken into consideration are preserved in strict distinction from each other and may tbus be traced from the beginning to the end, which in the calculation of numbers only cannot be done. The particularly analytical character of Algebra, which offers a further difference of it from Arithmetic, lies in the use of unknown quantities, while Arithmetic operates only in known quantities. Daniel Webster said: “If we work upon marble, it will perish ; if we work on brass, time will efface it; if we rear temples, they will crumble into dust; if we work upon immortal minds, if we imbue them with high princi. ples, with just fear of God and of their fellow men, we engrave on these tablets something which no time can efface, but which will brighten to all eternity.” A bevy of children were telling their father what they got to school. The eldest got reading, spelling and definition. “And what do you get, little one?” said the father to a rosy cheeked little fellow, who at the time was sliły driv. ing a ten-penny nail into the door panel. • Me ? Oh, I gets readin', spellin' and spankin." |