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Editor's Table .
WHAT IS DIVISION ?
NE of our Western correspondents, a practical teacher, residing in Illinois,
teachers, and also the modes of illustrating the various branches taught in common schools. He is a thinking teacher, and one not satisfied with stereotyped forms, even though found“ in the book.” He has recently favored us with a few queries concerning Division, which we shall present in this connection. They are more properly suggestives than substitutes for other formulas. Of them the writer modestly says: “I do not know that the distinction made in the following examples is recognized in any of our text-books. It is submitted for the consideration of teachers.”
What is Division ? “ Finding how many times one number contains another,” say our text-books.
Well, how many times does 17 contain 8? Why, 2} times. But what do you mean by of a time? I mean that 8 is contained in 17, 2 times and } of another time.
But $ of a time is f of something very indefinite. It can only be explained thus : either, 8 is contained in 17, 2 times, and of 8 is contained once in the remainder, or 8 goes in twice and f in again, leaving & out. Into 5, 8 could not get, but it could get f in, leaving & out.
Is not dividing 17 by 8 finding how many eights there are in 17 ? And would not a better definition of Division be, Finding how many of one number are contained in another ?
But this is not all. For 12 cents you can buy as many oranges as there are 4 cents, the price of one orange, in 12. But we can not say that one orange will cost (if 3 cost 12 cents) as many cents as there are 3 oranges in 12 cents. And if we drop oranges and cents, and say that one orange will cost as many cents as there are threes in twelve, although the process will always be true, yet there is a link of logical reasoning dropped. Are we not searching to find what number of cents are contained 3 times in 12 cents ? If so, our reasoning should show that the number when found will equal the number of threes in 12. This may be done by a tedious process. We conclude that Division sometimes, then, is finding what number is contained in another a given number of times. This number will be found by separating the given number into equal parts.
The examples in Division naturally fall, then, into two classes, each of which requires a separate formula for its solution. The first answers to the old definition, and is the one, under some modifications, used by nearly all teachers. The second requires the use of a fraction. Would not the following be improved formulas for Division ?
1. At 7 dollars each, how many chairs can I purchase for 56 dollars ?
Formula. As many chairs as there are 7 dollars in 56 dollars ; there are 8, Answer, 8 chairs.
2. James divided 30 apples equally among six boys. How many apples did each boy receive ?
Formula. Each boy received 1-6 of 30 apples, which is 5 apples.
SOMETHING FOR THE LITTLE FOLKs.—Returning from our dinner a few days since (editors eat dinners), we were pleased to find, on our office-desk, a whole
Library for Children,” and, what is more, it was neatly put up in a little case. On removing the books from the case, which was made of pasteboard, we found the library to consist of six numbers of the Eagle Primer, by our old friend, J. S. Denman. Eagle Primer No. 1, is a treasury of pictures, representing a great variety of birds, animals, children playing, shops, cars, houses, and many other things. It is designed for the use of children while they are too young to learn to read. No. 2, contains the alphabet in fancy pictorial, and other letters, and a few easy lessons, illustrated by numerous engravings, designed to be used by children in learning the first principles of reading. Nos. 3, 4, 5, and 6, each contain easy, instructive, and progressive lessons, all beautifully and profusely illustrated, and so arranged as to lead the little learner forward by simple and regular steps from one lesson and book to another, through the whole series. Each number of the Primer contains 32 pages.
If any of our readers wish some useful primers for their little brothers and sisters, or parents desire to procure such for their children who are too young to read in THE STUDENT, we commend to them “ Denman's Library for Little Children.” If desired, we will send the whole by mail, including case, postage paid, for 40 cents.
MICROSCOPIC WONDERS.—The world is full of beauty, and of interesting ob jects which are overlooked by the multitude. Now and then some lover of nature reveals new wonders to us by means of the microscope, and we are shown a thousand curious objects which we never imagined to exist in earth, air, or water. The articles by Uncle George, published monthly in THE STUDENT unfold to the readers a great amount of interesting information concerning the beauties and curiosities of the microscopic world. If any of our readers have neglected them, we trust they will do so no more after reading one or two numbers. Brocklesby, in his “ Microscopic World,” has revealed a multitude of beauties. It is a highly interesting work, profusely illustrated. To its publishers, Messrs. Pratt, Woodford & Co., New York, we are indebted for a few of its illustrations used in the articles by Uncle George. Should any of our readers desire that work, we will send it by mail, postage paid, for 12.
Our Museum. .
EPTEMBER is so called from its being the seventh month of the old Roman
month of our calendar. Several of the Roman emperors gave names to this month in honor of themselves; but the name of September has outlived every other appellation. On the 23d of this month our days and nights will be of equal length, when the sun will rise and set at six o'clock.
THE GRAMMAR (unpublished of course) of the schoolmaster who made an unsuccessful tour to the mines of California adopts the following mode of comparison : positive mine, comparative miner, superlative minus.
A RECOMMENDATION given to a servant girl, by a person who meant to compliment her very highly, read as follows: “ This is to Certify that Isabel Weir served with us during the last half year, and found her in every respect Cred ible, and free of Nothing that was rong.” Rather a doubtful character.
PENNY is derived from the Latin pecunia, money. Previous to the time of Edward I. the penny was struck with a cross, so deeply indented in it that it might easily be broken into two parts, which were called half-pennies, or into four parts, called four things, or farthings. Edward I. commenced the coinage of round half-pence and farthings.
MEASURES AND WEIGHTS.-While learning the tables of measures and weights found in Arithmetics, we often wondered how people ever came to have any such tables, and who made them at first. It is not so much of a mystery to us now, how there came to be such tables, though we have never learned who formed them.
When we remember that the early inhabitants of the world must necessarily have had occasions to express to each other some ideas of distances, and also of weights, we perceive that it must have been natural that they should select as a measure something common to every person ; accordingly we find that the length of the arm from the elbow to the end of the middle finger became a universal measure, and was called, a cubit. Besides these were hand-breadths, the width of the hand, and the foot, the length of a man's foot. In time, it became necessary to have shorter and also longer measures, and we find the length of the first joint of the thunib used as an inch, and the inch divided into three barley-corns, being equal to the length of three grains of barley. Thus came the first forms of measurement, which have been modified and improved by succeeding generations till we have our present “ long measure.”
Measures of weight, again, had a like derivation. Seeds seem commonly to have supplied the unit. The original of the carat used for weighing in India is a small bean. Our own systems, both Troy and Avordupois, are derived primarily from wheat-corns. Our smallest weight, the grain, is a grain of wheat. This is not a speculation, it is an historically registered fact. Henry III. enacted that an ounce should be the weight of 640 dry grains of wheat from the middle of the ear. And as all the other weights are multiples or sub-multiples of this, it follows that the grain of wheat is the basis of our scale.
So natural is it to use organic bodies as weights, before artificial weights have been established, or where they are not to be had, that in some of the remoter parts of Ireland the people are said to be in the habit, even now, of putting a man into the scales to serve as a measure for heavy commodities.
While speaking of this subject it may be well to add that at the present day we have a standard for linear measure which has been fixed with great accuracy. It was determined from the length of a pendulum which will vibrate seconds in a vacuum at a temperature of 32°. Experiments were made at Columbia College, in New York city, and the length of such a pendulum was di. vided into 39,101,688 equal parts, and 36,000,000 of these parts were adopted as the standard length of a yard by the State of New York; and this corresponds with the standard yard of Great Britain, which was determined by a similar process. As a yard is divided into 36 inches, it is easy to arrive at an accurate measurement of an inch. And should the standard length of a yard
ever be lost it could be recovered by resorting to this experiment with the pen. dulum.
A TURKISH Will.—How to divide seventeen horses among three persons, giving the first one half, the second one third, the third one ninth. A Turk left to his eldest son one half of his horses, to his second son one third of his horses, to his third son one ninth of his horses. He had seventeen horses in all. The executor did not know what to do, as seventeen will not divide by two, by three, nor by nine. A Dervish came up on horseback, and the executor consulted him. The Dervish said : “ Take my horse and add him to the others.” There were then eighteen horses. The executor then gave to the eldest son one half, 9; to the second one third, 6; to the third son one ninth, 2; total, 17. The Dervish then said : “You don't want my horse now, I will take him back again.”
CLASSICAL PUN.—The completest pun on the records of literature is produced in the following words, which were inscribed on a tea chest: Tu Doces, which is the second person singular of the verb doceo, to teach ; and when literally translated, becomes Thou Tea-chest.
ALLITERATION, OR THE SIEGE OF BELGRADE.
An Austrian army awfully arrayed,
Et cetera, et cetera, et cetera.
Items and Events.
COLAR PHENOMENON.-On the morning of the 11th of August there was witnessed in New York and vicinity an unusual and beautiful solar phenom
The sun appeared to be surrounded by several rings of different shades. Two rings, with the sun nearly in their centers, appeared, and intersected each other at two opposite points. The inner circumferences of the rings within the points of intersection were dark, but beyond the points of intersection they were luminous. Several other circles and arcs of circles appeared with the sun either in their circumferences or near one side. Under the sun was the
appear. ance of an inverted rainbow. The phenomenon was exceedingly curious and interesting. The appearance is very unusual in this latitude. This phenomenon is believed to be caused by the refraction of the sun's rays as they pass through crystals of frozen vapor floating in the upper regions of the atmosphere.
DEATH OF “ UNCLE Sam.”—During the war with England in 1812, Messrs. Samuel and Ebenezer Wilson, active and enterprising citizens of Troy, N. Y., being extensive dealers in pork and beef, furnished large supplies for the northern army. Samuel Wilson was commonly known and spoken of as “ Uncle Sam.” On the heads of the barrels designed for the army he had branded the letters “U. S.,” denoting that they were for the government of the United States ; but the workmen were not accustomed to that name, or its abbreviation, and they at once supposed it to mean “ Uncle Sam” Wilson. This interpretation soon became common throughout the army, but finally it lost its local signification, and from that period has been the familiar term for the United States.” A few weeks since this same Samuel Wilson died at Troy, N. Y., aged 84 years.
DROUTH.—During the past month there has probably been one of the most extensive drouths experienced in this country for many years. It has extended over nearly two thirds of the Union, blighting the prospects of farmers. In many sections extensive fires have also raged in the forests, and the mountains, and through the swamps, in consequence of their dry state, destroying much valuable timber, and filling the air with smoke for miles around. Corn, potatoes, and late summer crops have suffered very much. In some counties pastures have dried up, and farmers are obliged to fodder their cattle.
CHOLERA.—This scourge, which has been so extensive in its visitations throughout the entire country, in rural localities as well as in cities, has very much abated, and it is hoped that before the close of the present month it will have disappeared entirely. There has been much less of it in New York city this season than in 1849. The whole number of deaths from cholera in this city during the present season has been a little less than 2,000, and that out of a population of about 700,000.
OBERLIN COLLEGE.—The annual examination of this institution took place during the week, commencing on Aug. 14th. About 600 students were examined Among the graduates were twelve young ladies; one of whom received the diploma of A. B. The abbreviation used to stand for “ Bachelor of Arts,” but we suppose it has become so changed by the“ progress of the age” that it may also now be defined “ Mistress of Arts.” The tuition in Oberlin College is only $e a year. Board $1 25 per week.