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into which the integral unit is divided, will increase or decrease in the same ratio, in which their number is decreased or increased. 1-2 is twice as much as 1-4, 1.8 is half as much as 1.4,
1.6, 1-2 “ three times“
third 1.4 " five
"1-20; 1-100“ one fifth 1.20. In short: if we divide the Denominator of a fraction, without altering the Numerator, we increase, if we mul tiply the Denominator, we decrease the value of the fraction so many times as the number contains units, by which in the first case we have divided, in the second case multiplied. To multiply a fraction by a fraction.
Given 3-4 x 2.7. § 8. Our multiplier 2-7 is the 7th part of 2, as was shown in $ 2. 3-4 x 2 6-4, as we have seen in § 3. Having here multiplied by a number 7 times larger than required, the Product must be 7 times larger than it should be, and to correct this we must evidently divide this first Product 6-4 by 7, which we do according to $ 6 by multiplying its Denominator, and obtain 6-28; hence,
3 2 3 x 2 6
4 7 4 x 7 The Numerator 2 of our Multiplier'says, that twice as many parts as there are given, are required, hence we get G parts. The Denominator of our Multiplier says that the parts required are to be only one seventh as large as those given; the paris given are fourths, the parts required must be 28ths, as shown in $ 7.
-- D a Let A B (fig. 4) represent the integral unit, then is Af 1-4, A g 3-4. Multiplying A g or 3-4 by 2, we obtain Al
or 6-4. Dividing this by 7, we have A p, which must be 6-28, as we will show. Ck is as large as A f, i. e. 1-4. Dividing this into 7 parts, Cris 1-7 of Ck (i. e. of 1-4) and therefore 1-28 of C D, i. e. of 1; hence Cq which is as large as A p, is 6-28. Q. E. D.
To divide a fraction by a fraction.
Given 4-5 • 2-3.. Our Divisor 2-3 is the third part of two as explained in § 2. The Numerator 2 of this Divisor indicating, that the parts required are to be only half as large as those given, it follows that there must be twice as many of them in the unit as shown in $8 6 and 7. Hence, instead of fifths we get tenths, and 4-5 = 2=4-10. But we have divided by a number, three times larger than was required, in consequence of which this Quotient will be only one-third as large as it ought to be. Hence, to give it the proper size, we must multiply this first Quotient by three, which we do according to $ 3 by multiplying the Numerator, and thus we have
4 2 4 X 3 12
D q Let A B (fig. 5,) represent the integral unit, A f will be 1-5, A g is 4-5. Dividing C k, which is equal to A f i. e. 1-5 into two parts, Cris 1-2 of Ck, i. e. of 1-5 and 1-10 of CD, i. o. of 1. Further C 1, which is 1-2 as large as A g, is 4-10. Having divided by a number, three times too large, this result Cl is three times too small, hence three times its size, i. e. C q or 12-10, will be the result required.
SCANDAL.-Many a wretch has rid on a hurdle who has done much less mischief than utterers of forged tales, coiners of scandal, and clippers of reputation.-Sheriden.
TIME.—The great rule of moral conduct is, next to God, to respect time.—Lavater.
EDITORIAL DEPARTMENT. To the hundreds of teachers, who are now employed in the District Schools of Vermont, we would address a few words of encouragement. We have already intimated the deep interest we feel in your success. We have a common cause, and would cherish a deep sympathy, in all that interests or troubles you. Allow us, therefare, in a familiar manner, to make a few practical suggestions. And first of all, try to realize the importance of your work. Your position is one of fearful responsibility, and doubly so, at such a time as this. We have reached that period in the history of our noble country, when the strength of our government and the permanency of our free institutions, are to be tested. Every heart not stained by a traitor's guilt, even now, throbs with the deepest emotion. Patriotism is at length aroused, and every man, woman,
and child, has raised the question, “ What can I do for my country ?” Your fathers and brothers are gone, or are ready to go, to the bloody battle field ; your mothers and sisters may be employed to provide for their present and future wants. You are also toiling for your country; they for its rescue from the foul grasp of treason and
you for its future prosperity. Our common schools have more power to secure the future greatness of Vermont, than all the swords and bayonets that have gone forth, or will go from our borders. Your work, then, is important and your responsibility great. A sensible writer has said, ' “ 'The mothers of a country, mould the character of its citizens, determine its institutions, and shape its destiny. Next to the influence of the mother, is that of the FEMALE TEACHER." You see, therefore, that you occupy not only an important, but an honorable position. To you Lelongs a large share of the responsibility and glory of moulding the destiny of a future generation. With what earnestness, then, should you apply yourselves to your noble work.
You should strive to honor your profession. In order to do this, you must have a high standard of qualification ; you should not be satisfied with only such attainments as will meet the demands of the law, but should aim at a larger degree of cultivation, and of scientific and professional knowledge. And you must enter upon your duties, with the 'spirit of earnestness and self sacrifice which the importance of your work demands. It matters not for how small a compensation you are compelled to labor ; how little inter est your employers manifest either in yourself, or your school ; how uncomfortable and ill constructed may be your school house, or how
poor the “tools” you have to work with : you must be an carnest and true teacher or you are unworthy the place you occupy. “To teach, whether by word or action, is the greatest function on earth,” Can you, then, sustain yourself in this high position, or deserve the sacred name of teacher, while you are governed by merely mercenary motives?
We trust, young ladies, that you are all well qualified' and earnest teachers, and will proceed to make some suggestions, as to the manner in which you are to discharge your various duties. You act in the two fold capacity of mistress and teacher ; you must both manage and instruct, every hour of every day of your term. And remember, that upon your management, depends your success, more than anything else. You have already begun your schools, and are now forming acquaintances, and fixing impressions for good or for evil. Every act in the school room and ir: the neighborhood, is telling upon your success or failure. Do you board among the scholars? This time honored custom, which some regard a relic of darker ages, has its advantages, as well as its disadvantages. If
you do not have your home in the district, you should lose no time to form an intimate acquaintance with all your patrons. Visit them at their homes. Interest yourselves in what interests them, in their business, in their children ; in the family, be social, and you will gain the sympathy and confidence of all. This done, and you are prepared to manage your school. If would bave everything move on pleasantly and successfully, in the school room, you must have the confidence and co-operation of your employers as well as of your pupils. Secure these, then, first of all. And remember another thing, your duty to yourself and your profession, demands that all your interest, time, and strength, be given to your school, whatever be your compensation.
FIRST ORGAN.—The first organ ever heard in public worship in this country was sent from London to the King's Chapel in 1714. The organist came out from Eng. land with the instrument, as no person in the colony was to be found able to assume its charge. The first organ ever built in this country was made by Edward Bronfield, who died August 18, '56.
EDITORIAL MISCELLANY. New Subscribers.--A goodly number have availed themselves of our liberal offer to Female Teachers, and have already ordered copies of the Vermont School Journal. We here renew the offer. To any Female Common School Teacher, in the state, we will send A copy of the School Journal, (Vol. III) for fifty cents, or a copy of the School Journal, and a copy of " Gleanings from School Life Experience," for seventy-five cents. To any Teacher who will, after this date, send us five new subscribers, with advance pay, we will return a receipt in full for her own subscription for an additional year, or two copies of the Gleanings.
Teachers’ Institutes.- We would call the attention of teachers to Secretary Adams' notice of Institutes, to be holden during the month of June. No teacher, in the counties in which they are to be held, should fail to be present. All need the suggestions and inspiration, which these gatherings are calculated to impart.
VASSAR FEMALE COLLEGE.—By a munificent donation, of $408.000, MATTHEW Vassar, Esq., of Poughkeepsie, N. Y., has established and endowed a College for Young Ladies, which is to go into operation, as soon as the plan of the donor can be perfected. 'The grounds appropriated for college purposes, consist of 200 acres, and lie to the east of Poughkeepsie, about one mile distant from the city limits. Mr. Vassar, on committing the trust to his Board of Trustees, made the following remarks, explanatory of his motives and views in devoting this fortune to so noble a purpose.
“It occurred to me, that woman, having received from her Creator the same intellectual constitution as man, has the same right to intellectual culture and development.
I considered that the MOTHERS of a country mould the character of its citizens, determine its institutions, and shape its destiny.
Next to the influence of the mother, is that of the FEMALE TEACHER, who is employed to train young children at a period when impressions are most vivid and lasting.
It also seemed to me, that if woman were properly educated, some new avenues to useful and honorable employment, in entire harmony with the gentleness and modesty of her sex, might be opened to her.
It further appeared, there is not in our country—there is not in the world, so far as is known- a single fully-endowed institution for the education of women.
It was also in evidence, that for the last thiety years, the stand.