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tion of the State of Indiana, for a copy of his elaborate annual report; and it is most encouraging to see how, in spite of war, the cause of public education flourishes in the vigorous States of the great West. Of about 600,000 children, between the ages of six and twenty-one, over 452,000 are reported in school. The State employs 5,330 male and 4,163 female teachers. The average compensation of male school teachers, of all grades, is $49.30 per month ; of females, $29.76. The State has 8,231 school-houses, and 265,388 volumes in township libraries; and, finally, the Superintendent is able to report “ a healthy and encouraging growth in the system.”
From Louisville, Ky., we have received the first number of a neatly printed sheet, entitled “ The School and Fireside ; a journal for Schools and Families;” which, as we learn from its prospectus, is the only paper of the kind published south of the Ohio River. May all success attend this pioneer in a good cause ! We shall be happy to exchange with it.
“ FIDELIS IN MINIMO."
Upon Life's narrow stage,
May all our powers engage.
Unknowing wealth or fame,
If honoring his name.
Or leave us quite alone;
If God our work shall own.
Thus says the Master to His servant true,
And crowns the humble brow,-
Be thou a ruler now."
A. R. W.
EQUATION OF PAYMENTS. Equation of payments, one of the most useful operations in Arithmetic, is oftentimes tedious in its practical application. I submit the following, as being a slight improvement on even the six per cent method, though embracing precisely the same principles. I select the following from Eaton's Arithmetic, p. 155:
A has bought of B several bills of goods, on different terms of credit, as follows :
April 15, 1857, on three months' credit, a bill of $200 ; May 1, 1857, on four months' credit, a bill of $600.
B has also bought of A as follows:
May 15, 1857, on three months' credit, a bill of $300 ; June 14, 1857, on four months' credit, a bill of $900.
When shall B pay to A the balance of his debt ?
As the interest on a sum of money at 6 per cent for 60 days, is found by, removing the separatrix two places to the left, so the interest would be the same for 30 days at 12 per cent. Finding the interest on A's bill at 12 per cent, reckoning from the last day of the month preceding the earliest date, gives the following: Interest for 3 months on $200 . . . . . $6 00 " 15 days " " . . . . . . 100
4 months “ 600 . . . . . . 24 00 6 1 " " " . . . . . . 6 00 • 1 day " " . . . . . . 20
Amount of bill, $800 Amount of interest, $27 20 Interest on bill for 30 days is $8.00, and it would require 4.65 mos. for $800 to gain $37.20 : reckoning 4.65 mos. = 4 mos. 20 days nearly, from the last day of March, gives Aug. 20, the equated time for A to pay his bill.
As, by finding the interest at 12 per cent the dividend is doubled, there is no need of finding the interest on the bill for 60 days as in the 6 per cent method, and then take balf of it for one month; but divide the amount of interest by the interest of the bill for 30 days, and the result gives the number of months to be counted from the last day of the month preceding the earliest date in the question, as the equated time for A to pay bis bill.
To find the time when B shall pay the balance of his debt, find the interest as before on A's bill, also on B's, and divide the difference between the interests
the sides by the interest for 30 days at 12 per cent on the difference between
bills, and the result gives the number of months to be reckoned from the last day of March. The work would be as follows:Interest for 3 months on $200 . . . . . . $6 00
16 " 15 days " " . . . . . . 1 00
. . . . . 6 00
Interest on $400 for 30 days, at 12 per cent is $4.00, and it would require 8.62 mos. for $400 to gain $34.50 : reckoning 8.62 mos. = 8 mos. 18 days nearly, from the last day of March, gives Dec. 18 the equated time. It will be noticed that by this method, the interest can, in almost every instance, be calculated in the head as fast as the figures can be set down. The cents in the face of the bill can be disregarded altogether, as they will not affect the result.
COMPLEX FRACTIONS. To reduce a complex to a simple fraction, multiply both terms by the least common multiple of their denominators. Example : —81X15=125
-=1} 53X15= 78
Let the scholars cipher out the proper numbers to fill the blanks in the following paragraph :
The land and water surfaces of the United States are equal to 3,256,000 square miles ; land 3,010,370, water about 240,000 square miles. The States embrace 1,804,351 square miles of landed surface, and the Territories, 1,206,019 miles, as exhibited by the census of 1860. The number of inhabitants in the United States in 1860 was 31,433,321 ; in the States, 31,148,046, and 295,275 in the Territories, thus showing an average of inhabitants to each square mile in the States, while in the Territories there are
square miles to each inhabitant, and the territorial area would represent
miles to each inhabitant.
In 1860, Massachusetts had 156, Rhode Island 133, New York 82, and Pennsylvania 62 inhabitants to the square mile, which rate applied to the United States would give in Massachusetts,
in Rhode Island, in New York, and
in Pennsylvania. Belgium, England and Wales, and France, in 1855, had 397,307, and 176 inhabitants to the square mile respectively. If the United States were as densely populated as France, our population would number
; or, if populated as densely as England and Wales
; and, if according to Belgium's density of population (397 to the square mile), the United States would contain which is 110,080,000 more than the entire population of the world in 1866.
In Birmingham, the great seat of the steel-pen manufacture, 98000 gross are made per week. Supposing the average length of a steel pen to be 14 inch, how far would they extend, if placed end to end? - how far would the product of a year?
They are produced at a cost of from 1š pence to 1 shilling per gross. Suppose the average cost of a gross to be sixpence what is the cost of a week's product ?- of a year's ?
To square any number less than 100, for instance, 67. Add such a number as shall cause it to end in a 0. Subtract the same number. Multiply the results, and add the square of the number added at first. 67+3=70; 67—3=64, 64 X 70=4480; 3: =9; 4480 +9=4489. This is undoubtedly the simplest rule in use; certainly it is superior to those published in the January number.
To" Call the Roll." Let each scholar receive at the commencement of the term his number. At the opening of each session, the teacher says “ Numbers.' Scholar number 1 says “1;” number 2, “ 2;” scholar number 3 is absent; the teacher says " 3,” noting the absence. Immediately scholar No. 4 says “4," and the other scholars follow in turn, until the number of an absent one is reached, which the teacher calls; and so on ad finitum.
The Massachusetts Cotton Mills, during the year ending May 11, 1865, manufactured 167,665,365 yards of cotton cloth. How many miles is that? How many square miles ?
BOOK NOTICES. The Nation. We ask our readers' attention to the advertisement of this excellent weekly. It is the best attempt yet made to establish a paper of high tone, where topics of permanent importance, political, moral or literary may be discussed by thoughtful men in a calm and dispassionate spirit. A paper of such a character has special claims on the attention of teachers. The History Of A MOUTHFUL OF BREAD, AND ITS EFFECT ON THE
ORGANIZATION OF MEN AND ANIMALS. By Jean Macé. Translated from the eighth French edition, by Mrs. Alfred Gatty. New York: American News Co. 12ino, pp. 398.
We want to commend this admirable little book, which we have long been acquainted with in the French original, to the attention of all Primary and Grammar School teachers, as an excellent model of simple, familiar instruction on the subject of Physiology and Natural History. “ The letters,” says Mrs. Gatty,– who, by the way, is the editor of that nice English juvenile, Aunt Judy's Magazine, — " are addressed to a child, in the original even to a little girl, and, most undoubtedly, as the book stands, it is fit for any child's perusal who can find amusement in its pages; while to the rather older readers, of whom, I trust, there will be a great many, I will venture to say that the advantage they will gain in the subject having been so treated as to be brought within the comprehension, and adapted to the tastes of a child, is pretty nearly incalculable. The quaintness and drollery of the illustrations, with which difficult scientific facts are set forth, will provoke many a smile, no doubt, and in some young people perhaps a tendency to feel themselves treated babyishly; but, if in the course of the babyish treatment they find themselves almost unexpectedly becoming masters of an amount of valuable information on very difficult subjects, they will have nothing to complain of. Let such young readers refer to even a popular encyclopædia for an insight into any of the subjects of the twenty-eight chapters of this volume, — The Heart, The Lungs,' • The Stomach,' • Atmospheric Pressure, no matter which, --- and see how much they can understand of it without an amount of preliminary instruction which would require half a year's study; and they will then thoroughly appreciate the quite marvellous ingenuity and beautiful skill with which M. Macé has brought the great leading anatomical and physical facts out of the depths of scientific learning, and made them literally comprehensible to a child.”
The first part treats of man, and contains a complete little treatise on human physiology; the second of animals, and gives in successive chapters an outline of the classification of the animal kingdom.
The book is a real addition to the very short list of good elementary works on physical science, and, as such we warmly recommend it to all our readers. READING WITHOUT TEARS. By the author of “ Peep of Day," etc. Part 2d,
New York: Harpers. Square 16mo, pp. 292. AMERICAN LEAVES : FAMILIAR Notes Of Thought and LIFE. By Sam
uel Osgood. New York: Harpers. 12mo, pp. 380.
The day has pretty well gone by for clergymen to be treated with any particular respect as clergymen. The parson is no longer, as in the days of our grandfathers, the autocrat, or even the litile Pope, of the parish. Men, and women too, nowadays, think for themselves, with small respect for assumed clerical authority to constrain their consciences, or regulate their beliefs. And this is as it should be. Not only is it every man's right, – and every woman's quite as much, - to form his own faith, and to look up directly to God, with no fear, and no need of human intervention ; but it is more than a right,-it is a solemn duty. How can we be individuals without having our own individual opinions ? Not that we should not be thankful for all the guidance which the wisdom of others, whether in the present or in the past, can give; but that, just as there are no two of all the millions of leaves on the trees exactly alike, just as no two human faces so resemble each other that there is no trait of difference, so, as long as human minds and characters are in the same manner infinitely diverse, there are strictly speaking, just as many creeds in the world as there are independent thinking human beings : for, whatever may be our outward conformity, our creeds make themselves, and are the results of all the acts and all the experiences of our lives.
And so it comes to pass, and it is what has led us into this train of thought, that the clergyman who would have influence nowadays must have it by virtue of being a man, and not by virtue of being a clergyman. The search for a perfect creed, like the search for the philosopher's stone, is well nigh given up; the claims of Protestant churches to infallibility are looked upon much in the same light as those of Roinish. Every where the right and duty of free thought are more and more recognized, and he who can help us in that is more and more heartily welcomed. The religious problems of the day are practical problems; the dry theologic choppings of old scholastic divines have lost their interest. True religion shows itself, not in long prayers and solemn