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1. The area of a right angled triangle is 720 feet, and the perpendicular is 90 per cent. of the base. Required the hypothenuse.
Ans. 53.814 + feet. 2. Call the product of the perpendicular and base of the above triangle dollars, and expend it for sugar at 24 cents a pound, reserving nine and one-eleventh per cent. of the purchase money as commission. Required the number of pounds bought.
Ans. 5500. 3 Call the above number of pounds dimes, and invest the same in flour at 16% per cent. less than its real worth, and sell it for ten-elevenths of its real worth, and give · the gain per cent.
Ans. Nine and one-eleventh. . 4. Get that part of the number of sq. ft. in the triangle as is expressed by the last answer, multiply the result by 22, call the product pounds, and state what per cent. it is of the answer to the second example.
Ans. Twenty-six and two-elevenths. 5. Expend the same number of dollars as denotes the real worth of the flour (No. 3) in cloth at $1.65 per yard, and sell it for 25 per cent. less than the asking price but for 10 per cent. more than cost. Required the asking price.
Ans. $968.00 6. Sell three-fourths as many yards of cloth as were purchased in the last example, at $2,00 per yard, and invest the sum in coffee at 15 cents a pound. Get the coffee roasted at an expense of it cents per pound, and allow three-fifths of an ounce to each pound for waste. For how much per pound must it be sold to make a profit of 12 per cent. ?
Ans. Nineteen and two-sevenths cents. 7. The answer to the fourth example is what per cent. of the answer to the third ?
Ans. 288. 8. Add 20 per cent. of the sum received for the coffee to itself, subtract the amount from the answer to the fifth example, add $13.00 to the remainder, and state how long it will take the last sum to amount to $120.00 at six per cent. simple interest.
Ans. 5 years, 6 months, 20 days. 9. Invest the principal of the last example in dry goods which you may sell at an advance of 63 per cent. What would have been the gain per cent. had they been sold for $105.00 ?
Ans. 163. 10. Multiply the answer to the seventh example by that of the ninth, divide the product by the answer to the third, call the quotient dollars and get the interest on it for the time expressed in the answer to the eighth example, and find at what rate per cent. that interest must be let to amount to $1.958 in 1 year, 6 months.
[Questions from the Progressive Intellec:ual Arithmetic, by Horatio N. Robinson, A. M., Ivison & Phinney, publishers, New York. 1859.]
1. Dayid caught a trout 17 inches long; the tail was two-fifths as long as the body, and the head was 3 inches long; how long was the tail ?
2. From the ground to the top of a church steeple is 146 feet; of the height of the steeple above the church, plus 6 feet, is equal to the height of the church; what is the height of the steeple above the church?
3. A purse and contents are valued at 46 shillings ; & of the value of the purse is equal to two-fifths of the value of what is in it; what is the purse worth?
4. The number of miles that the distance from Charleston to Columbia exceeds 100 miles equals 11 times the distance it lacks of being 150 miles; how far is it from Charleston to Columbia ?
5. A, being askeủ his age, replied, “15 times what I lack of being a hundred years old is 9 years more than if what my age exceeds 64.” What was his age ?
6. A rope was cut into 3 pieces; the first piece was 5 feet long, the second was as long as the first plus f of the third, and the third was as long as the other two; what was the length of the rope ?
7. A farmer took money for stock, as follows: $18 for swine, $6 more than $ of the whole for sheep, and for cattle $7 jess than $ as much as for sheep and swine; how many dollars did he receive ?
8. Henry earned 20 dollars in the spring; in the fall he earned as much as in the spring and } as much as in the summer, and in the summer as much as in the spring and fall ; how much did he earn in all ?
9. Jason bought a watch, and had $20 remaining; he then gave 2 times the cost of the watch for a rifle, and had one-seventh of his money left; what did the rifle cost?
10. A drover paid $76 for calves and sheep, paying $3 apiece for calves and $2 for sheep; he sold # of his calves and two-fifths of his sheep for $23, and in so doing lost 8 per cent. on their cost; how many of each did he purchase ?
DONATIONS TO OUR COLLEGES. During the last two years—a period of war-dur. ing which our enemies here and in Europe confidently predicted our national ruin, a most wonderful liberality has beeň developed toward our institutions of learning. The following are some of the marvelous figures :
Bowdoin College, Me., has received $72,000, of which $50,000 were in one donation.
Dartmouth College, N. H., has received $47,000.
Amherst College has received more than $100,000, in sums of $60,000, $30,000 and $20,000 each. Harvard has received a bequest of $44,000.
Andover Theological Seminary has received $50,000, of which $30,000 were from one firm.
Trinity College, Hartford, Ct., has received nearly $100,000.
Yale College has received (including $135,000 from the United States Government for its agricultural school) the magnificent sum of $450,000; to which, perhaps, $100,000 will probably soon be added. Of the portion already paid, the following sums have been given by individuals in single donations, viz. : $85,000, $50,000, $30,000, $27,000, $25,000, $20,000, $12,000. New York University has received $60,000. Hamilton College over $100,000. Rutgers' College, N. J., has received $100,000. Princeton College, N. J., $130,000; of which $30,000 is in a single donation.
Washington University, St. Louis, $50,000 in two donations of $25,000 eachone from New York, the other from Boston.
Chicago Theological Seminary has received $80,000.
Lane Theological Seminary, Walnut Hills, Cincinnati, Ohio, has just received a donation from a friend amounting to $10,000, to be applied to enlarging the library of the Seminary.
Within the past two years the aggregate donations to the various colleges amount to $2,500,000.
THE ELEVENTH ANNUAL REPORT OF THE COMMISSIONER OF COMMON SCHOOLS FOR Ohio has been received, from which we take the following statistics :
"Number of school-houses in the State, 11,262. Value of all school-houses in the State, including grounds, $6,168,736. Number of schools, each graded school with its different departments being counted as one school, 11,994. Number of high schools, 149. Number of white youth in the State, between five and twentyone years of age, as enumerated in September, 1863, 922,367. Number of colored youth between five and twenty-one years of age, 16,605. Whole number of youth enumerated-male, 474,061 ; female, 464,911; total, 938,972; increase for the year, 19,098. Number of scholars enrolled in the schools during the year-male, 353,541 ; female, 341,379 ; total, 694,920. Average number of scholars in daily attendance, 396,256 ; average per cent of scholars enrolled in daily attendance, 57. Number of different persons employed in schools, during the year, as teachers—male, 7,832; female, 12,826; total, 20,658.
“Average wages of teachers per month (4 school weeks): In common schools— male teachers, $28.25.; female teachers, $17.95. In high schools-male teachers $62.87 ; female teachers, $34.81. Amount of school moneys expended during the year, $2,738,124.88."
" When I went Buarding 'Round." There are 632 towns in Ohio in which the teachers board around.
THERE are one hundred and four churches and halls opened in Boston every Sunday for religious worship, and the average attendance, as stated by sextons and pastors, amounts to 68,475, in a population of 175,000.
THERE exists in the whole world nearly 7,000,000 of Jews, of whom one-half are in Europe, especially in Russia, where there are 1,220,000. The number in Austria is 853,000; in Prussia, 284,500; in the rest of Germany, 492,000. At Frankforton-the-Main there is one Jew to sixteen Christians. In Sweden and Norway, only one in six hundred. France contains 80,000 ; England, 42,000; and Switzerland, 3,200. A remarkable fact is, that in the countries where the Jews are completely emancipated, that is in France, Belgium and England, their number is diminishing, while elsewhere it is increasing.
Rev. B. F. MILLARD, the agent of the American Bible Society in Brooklyn, reports that during the past six months he has sold 2,748 volumes of the Scriptures, and given away 6,676.
The Catalogue of Beloit College shows seniors 7, juniors 20, sophomores 17, freshmen 24. There are 12 in the army from these classes.
In Pennsylvania there are 13,000 public schools, with 16,000 teachers, and 709,000 pupils.
The Boston Public Library numbers 116,934 volumes and 31,800 pamphlets.
SUPERINTENDENT'S QUARTERLY REPORT.
OFFICE OF THE SUPERINTENDENT, PROVIDENCE, Feb. 10, 1864. To the School Committee of the City of Providence :
GENTLEMEN : Our schools have suffered the past term more from absence and irregular attendance than in any previous term of which there is any record. Much of this absence has been caused by sickness, which has been unusually prevalent in every part of the city. In some schools the attendance has not been sixty-five per cent. of the whole number belonging. With such obstacles, the usual satisfactory results ought not to be expected. In most of our teachers there has been no lack of interest or of earnest and faithful effort to improve and elevate their schools. In the High School, in particular, and in the Grammar schools, the instruction has never been more thorough and of a higher order. I regret to add that we still have schools that might and ought to be improved. While the Committee should be extremely careful that no injustice be done to any teacher, they should also not fail to protect the rights of children in providing for them that thorough instruction which is justly their due.
There are but few duties more delicate or difficult to perform than that of deciding upon the true character and condition of a school, and awarding both to teachers and pupils that praise or censure which they most truly deserve. Different examiners have different standards of excellence, by which they judge of a school, and these are sometimes of an opposite character, so that the same school may be by one standard considered excellent, and by another almost worthless. Many judge of a school by its appearance, at the examination at the close of the term, without making any inquiry how such results have been obtained. If the school is orderly, the recitations prompt and accurately recited, and most of the questions answered cor
rectly, they decide without hesitation that the school must be a good one, and that teachers and pupils are deserving of high commendation. But at such an examination, or rather exhibition, it does not appear how long the scholars have been preparing to exhibit themselves in this creditable manner. None but those most interested know how many times the 'same questions have been asked and repeated during the term. Many teachers feel that the reputation and character of their schools depend upon the show they can make at these quarterly exhibitions. So long as this is the case, their main efforts will be to secure, some way or other, the approbation of the committee on these occasions; and they will have before them continually a temptation too powerful for most to resist—to review previous studies unnecessarily—to make but slow progress, and to keep back their brightest scholars that they may make a brilliant show.
Some make good order and discipline the criterion of excellence in a school. If the pupils sit erect and motionless like little statues, fearing to turn either to the right or left lest they should break some petty or unnecessary rule, and are watched by the teacher with an eagle eye, and with the rattan ready to inflict a blow for the slightest movement, whether it be involuntary or otherwise, they are too ready to decide that such a school must be in a most excellent condition, and teachers are often misled by the approbation they receive from visitors for such kind of rigid discipline. There is also great liability to err in forming a correct judgment of a school by comparing one with another of the same grade, without making due allowance for the superior advantages and the greater facilities one has over another. In some the attendance is much more regular and constant than in others. The percentage of absence in our schools varies from two per cent. to forty. Many teachers receive very important aid from the coöperation of parents. This can be fully appreciated by those only who have to conduct their schools without it. Truancy, with its train of evils, which never have been and never can be adequately portrayed, casts a blighting influence unequally in different parts of the city. Some teachers have to struggle and contend continually against it, while others have much less annoyance from this source..
The standard of scholarship in each grade is not always the same. There is frequently a great difference in this respect. This must of necessity be the case where the population is fluctuating. When the lower grade of a school is crowded, the scholars in the next higher must be advanced to make room, even if they are not fully prepared for promotion, so that a comparison with other schools would be not only unfavorable, but also unjust to teacher and scholars. In forming a correct opinion of a school, or in judging of the character and efficiency of a teacher, we should, in the first place ascertain how much has been accomplished in a given time, and whether this is advance or review. This is absolutely essential to a correct decision. We should then carefully examine how perfectly and thoroughly the work has been done, and what have been the facilities the teacher has enjoyed, and what obstacles and hindrances he has had to encounter. These should have their full weight and influence in making up our judgment of a teacher or a school. There are other considerations also which should be taken into the account.
The methods of teaching and kind of discipline are by no means to be overlooked. A teacher may be successful in securing obedience to his authority, he may know how to adapt his explanations exactly to the capacity and comprehension of each pupil, and the recitations in all the studies may be prompt and nearly perfect, and yet he may be far from being a teacher of the highest order. His discipline may be