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oats and corn in earth, sand and water. (b) Observation of germination and growth.

8. Determination of parts of plant-root, stem, leaf, bud, flower.

9. Learning to know common flowers.

b. Animal life.

1. Insects-transformation of, collection of

cocoons.

2. Lessons on cat, dog, horse, cow, squirrel, robin, blackbird, woodpecker and chicken. Observe, compare and describe their covering, parts, food, care of young. Illustrate their habits by stories.

c. Physiology.

Learn to name and locate the parts of the body-head, neck, trunk, arms (right, left), hands, feet. Study movement, use and care of each part; show what can be done by each part; how adapted to use; right uses; kindness, how shown by hands, feet, lips; simple lessons on eating, drinking, breathing, sleeping, with special reference to hygiene and right habits; self-control; temperance in eating and drinking.

d. Geography.

1. General position-direction and distance; observation and placing of objects; description by use of prepositions and adjectives.

2. Particular position-direction; out-door observations of the cardinal and semicardinal directions.

3. Forms of water-cloud, fog, mist, rain, dew, frost, snow, ice; observation of the forms as they occur and where they occur, to recognize each and to find the more obvious qualities and uses of each. 4. Winds-temperature, to recognize by feeling the degrees hot, warm, cold; velocity, to recognize and distinguish by their effects the calm, breeze and gale.

e. Weather Study.

The following questions suggest what kind of weather observations may be made by pupils in primary grades:

1. Was there dew this morning?

2. Was there frost?

3. Was there fog?

4. Is it cloudy or clear? (It may be partly cloudy.)

5. What is the direction of the wind this morning?

6. What kind of a night was last night? (It was cold, or warm, or pleasant. It was

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1. Autumn fruits-apple, pear, plum, grape, etc. (a) Collections of. (b) Study typical forms. (c) Drawings. (d) Descriptions both oral and written.

2. Autumn leaves-(a) Collections of. (b)
Study typical forms. (c) Drawings.
(d) Descriptions both oral and written.
3. Autumn flowers gentian, golden-rod, as-
ter, etc. (a) Collections of. (b) Study
typical forms. (c) Drawings. (d) De-
scriptions both oral and written.

4. Autumn seeds-(a) Collections of. (b)
Study of typical forms. (c) Drawings.
(d) Descriptions both oral and written.
5. Preparations for winter-as shown by
changes in leaves, buds and bark.
6. Effects of frost-on leaves, buds, stems
and flowers.

7. Preparations for spring-(a) Germination of
seeds planted in a school-room. Keep
record of frequent observations of grow-
ing plants. (b) Germination and growth
of self-sown seeds, maple, acorns, etc.
(c) Flow of sap, growth of stems, leaves
and flowers.

8. Study of flowers for forms and colors. b. Animal life.

1. Insects-ant, bee, beetle, grasshopper, etc.
(a) Collections. (b) Study typical forms.
(c) Drawings and descriptions. (d)
Habits. (e) Transformation.

2. Covering of animals for the seasons.
3. Habits of hibernation.

4. Prehension of food.

(a) Organs of. (b) Method of by different animals.

5. Reappearance of birds-notice the instincts shown in migration, nesting and care of young.

6. Study of tadpole and frog.

c. Physiology.

1. Simple lessons on the senses and what we learn through them; the skin, use, care and cleanliness; care of teeth, nails and hair. In all lessons endeavor to teach self-control in relation to voluntary actions of the body.

2. The bony frame of the body-(a) Its uses, to give shape, to give support, to give protection. (b) How bones may grow out of shape. (c) Effects of clothing, as high heeled boots and shoes. (d) Effects of unhealthy position of the body upon the bones. (e) How tobacco and alcohol affect the growth of the bones. 3. Breathing-(a) Organs of. (b) Processes of. (c) Purposes. (d) Position of body in. (e) Bad effects of-improper position of the body, breathing impure air, improper breathing.

d. Geography.

Continue work of first year.

Study of forms of solids, as cube, pyramid, sphere, etc. From the study of the sphere, develop the shape of the earth. From conversations based upon readings from Seven Little Sisters, and similar books, develop as far as practicable at this stage an idea of the earth as a whole.

e. Weather study.

Observation and morning notes-(a) Dew, frost or neither. (b) Rain or snow (within twenty-four hours). (c) Direction of wind at 8 o'clock A. M. (d) Clear, cloudy, partly cloudy, rain or snowing at 8 A. M.

See direction for work in first grade.

OBSTACLES TO CHINESE PROGRESS.

From the Chinese standpoint Tsi An is liberal and progressive, but she is so igorant and secluded that it is difficult for any foreign ideas to reach her. When she sees something good she wants it, but she has no conception of the condition of China compared with that of other countries, and, of course, cannot apply the remedies that are needed. She does not lack intelligence, but knowledge, and has surrounded herself with advisers who have never been outside of China and are even more unenlightened as to modern affairs. Contrary to the popular impression, Li Hung Chang has not been restored to power. He doubtless retains the friendly relations he has always enjoyed with the Empress Dowager since he suppressed the Taiping rebellion, but his name does not appear on the list of the new ministry.-Amercan Monthly Review of Reviews for December.

MATHEMATICS.

EDITED BY

ROBERT J. ALEY, Ph. D., Bloomington, Ind.

HISTORY OF ARITHMETIC.

VII.-OPERATION SYMBOLS.

In the oldest mathematical treatise known, the work of the Egyptian priest, Ahmes, addition is indicated by a pair of legs walking forward, substraction by a pair of legs walking backward, and equality by the sign L. The nations contemporaneous with the Egyptians, and later nations down to the latter part of the fifteenth century, had few or no symbols of operations. The Hindus and Greeks indicated addition by mere juxtaposition. A trace of this notation is still retained in our method of writing mixed numbers; e. g., 33 means 3+. The common practice was to write out in words the operation desired. The Italian algebraists when they finally gave up writing everything in words, used P or p to indicate addition.

John Widmann in 1489 printed an arithmetic in Leipzig, in which the signs + and - first occur. They were called signum additorum and signum subtractorum, respectively. Their use in this book seems to have been to denote excess and deficiency. It is very probable that these signs originated among the merchants, and were used to denote excess or deficiency in packages. The signs also occur in the first German algebra, by Christopher Rudolph, 1525. Michael Stifel, a German, in 1544 (possibly not till 1553), uses the symbols in the sense in which we now use them. The origin of the form of the symbols is not known. The symbol + has been supposed to be a corruption of P, and also of et. It is now generally accepted that they were at first mercantile signs, that the — is the older, and that the + was made by drawing the vertical line through the -. By 1630 the signs were in general use.

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William Oughtred in 1631 introduced the sign of multiplication (X). He was an eminent English mathematician, the author of Clavis Mathematicae, the "Key of Mathematics." Harriott in 1631 used the dot (.) to indicate multiplication. He was a companion of Sir Walter Raleigh, and made the first survey of Virginia and North Carolina. He was the author of the first really good text-book on algebra in England. Nothing is known as to the reason for using these particular symbols.

Division was indicated in the Arabian way, writing the quantities in the form of a fraction in any of the forms 6-3, or f. Oughtred in 1630

used a dot (.) to donote both division and ratio. Johann Heinrich Rahn used to denote division in 1659 at Zurich. John Pell, a friend of Sir Isaac Newton, used the same symbol in London in 1668. By some authors Pell is regarded as the inventor of the symbol. The use of the colon (:) to denote a ratio or division is probably due to Clairault in 1760.

The symbol for equally ( = ) was introduced by Robert Recorde in 1557. In 1540 Recorde published an arithmetic called the Grounde of Artes, in which he used + and —; “+ whyche betokeneth too muche, as this line —, plaine without a cross line, betokeneth too little." He uses two equal parallel lines with their opposite ends joined diagonally to denote equality. In his Whetstone of Witte, 1557, he uses the sign (=) because "noe 2 thynges can be moare equalle." In 1575 Xylander denoted equality by (). From 1600 to 1680 equality was usually designated by ∞ or x, either of which is a contraction for the first two letters of the word æqualis. The useless symbol ( :: ) to denote equality of ratios, was introduced by Oughtred in 1631, and brought into general use by Wallis in 1686.

Rudolph in his algebra of 1553 remarks that "the radix quadrata is, for brevity, designated in his algorithm with the character √, as √. In a German manuscript of the fifteenth century the square root was denoted by placing a dot (.) before the quantity. Stifel, the great German algebraist, brought the symbol into general use. It is thought that the symbol is a modification of the letter r, the initial of radix.

These important symbols were slow in development. Hallam says: "It is very singular that discoveries of the greatest convenience, and, apparently, not above the ingenuity of a village schoolmaster, should have been overlooked by men of extraordinary acuteness, like Tartaglia, Cardan, and Ferrari; and hardly less so that, by dint of that acuteness, they dispensed with the aid of these contrivances in which we suppose that so much of the utility of algebraic expression consists."

THE STUDY OF MATHEMATICS.

The Open Court Publishing Company of Chicago deserves the thanks of all lovers of mathematics for republishing DeMorgan's Study and Difficulties of Mathematics. Few Englishmen have done so much as De Morgan in making mathematics attractive. He wrote many excellent text-books, and was constantly before the public in the magazines and current cyclopedias of his day. In the

book before us we have his best thought upon the elementary principles of arithmetic, algebra and geometry.

A favorite saying with a great German mathematican is, "Nothing in mathematics is so abstruse that it can not be made perfectly clear." Any one who reads this book of De Morgan will agree that the statement is true in elementary mathematics. The explanations of fractions, decimals, fundamental laws of algebra, the negative sign and proportion are so clear and simple, that the reader is fascinated, and wonders why he ever considered these subjects difficult.

The chapter on the "Study of Algebra" has much in it to help the private student and also many valuable suggestions to the teacher. The teacher who reads Chapter XIII, "On the Definitions of Geometry," will certainly not continue the mistake of allowing loose and meaningless definitions to pass current in his class.

The book is worthy of a place in every teacher's and student's library. It is full of sound pedagogy. The value of the book is greatly increased by the references to modern mathematical works inserted by the editor, Mr. T. J. McCormick. The book can be had from the publishers for $1.25.

NOTES.

The meeting of the Mathematical Section at the recent State Teachers' Association was unusually interesting, A fine paper on arithmetic in the Grades read by Superintendent Haines of Noblesville will be printed in the March issue of the EDUCATOR.

President McClellan of the Ontario Normal School will write an article for this department which will appear in an early issue. He will treat some phase of the psychology of number.

Professor S. C. Davisson of Indiana University who has been studying at Harvard, sailed for Germany January 28th. He will spend a year and a half in some German university, most probably at Tübigen.

Professor Stevens of Purdue gave a most interesting paper before the Indiana Academy of Sciences upon "Mathematical Definitions." We hope to be able at some future time to give the paper in full in these columns.

Dr. Whitaker of the Central Manual Training School of Philadelphia has written an excellent elementary trigonometry. The discussion of homogeneity and approximate calculation in the introductory chapter is to be commended. The trigonometric functions are fully treated, the graphic representation of the functions being an

interesting feature. A large number of concrete problems is given. In the chapter on "Properties of Triangles" quite a number of the more interesting results of modern geometry are worked out. The frequent use of geometrical diagrams to elucidate the text makes the book interesting.

THE TOWNSHIP PRINCIPAL IN WABASH COUNTY.

In Wabash county the principal of the township high school is, by common consent, designated as the township principal. By virtue of this unofficial position he has several duties and privileges, that, in most counties, are prerogatives of the county superintendent and township trustee. These duties have been placed upon the township paincipal by the county board of education for several reasons. First, it brings the schools of each township in closer contact with the superintendent, enabling closer supervision. Second, it tends to equalize, systematize and harmonize the school work of the county. Third, it lessens the work of that over-burdened officer, the county superintendent. Fourth, the township trustee is relieved of certain educational duties that always should have been in the hands of men actively engaged in educational work.

The township principal has charge of the township institute in about the same sense that teacher has charge of a school. He appoints a committee of the best teachers on program, and sees that the institute adheres strictly to the regular order of business. When not present, the trustee and superintendent communicate with the teachers of the township through him. He is to be shown the examination manuscripts, and consulted by the teacher with regard to the promotion of pupils above the third grade.

A quotation from the county course of study will partly explain the township principal's new and peculiar duties: "The plan adopted by the county board of education two years ago for promotion and graduation, is as follows: The township principals with the county superintendent are to constitute the examination board. The board prepares the questions and grades, the papers of those who take the examinations in the common school subjects and also the high school subjects. There are two examinations each year,one in the spring near the close of school, and one in the fall before the school opens. By this arrangement those who are conditioned in any subject at the spring examination may make up the work and pass on the conditioned subjects at the fall examination."

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That is, the township principal is given at least one common school subject and one high school subject by the county superintendent upon which to prepare questions for the examination for graduation in the common school course and for credits upon the township high school course. He holds the examination and grades the manuscripts of the pupils of the entire county in those subjects upon which he prepared the questions.

These duties add many days work to the labor of the township principal. Many of the trustees pay for this extra time at the regular per diem, while others pay only in part. This should be remedied, as the grading of manuscripts is especially laborious work and should be well paid for. Otherwise it should be done by the county superintendent. This plan, so far as known to the writer, was worked out by the present county superintendent, John N. Myers, and has brought about many admirable results.

Thus the township principal in this county is a township superintendent in an embryonic stage of development. I sincerely hope that the present legislature will make him a superintendent with the necessary authority and power closely to supervise the schools. The township would then enjoy the benefits of a close supervision of schools just as the town now does. Are not the children of our farms and country villages just as deserving as those of the towns? Is it not their right to have the best teachers and right methods in the schools they attend? By what means can this better be attained than by having a superintendent of township schools?

LAKETON, IND.

CHARLES I. KERR.

IS THIS PROSPERITY?

The story of the foreign commerce of 1898 is now complete. Its exports are the largest in our history, its imports the smallest since 1885, although the consuming population is now 33 per cent. greater than at that time. And as if to emphasize the great work of this greatest year the month of December made for itself the highest record of exports ever made by any month in our history. The total exports of December were $137,847,448 and of the full calendar year $1,254,925,169. Only two earlier calendar years crossed the billion dollar line, that of 1897 having been $1,099,709,045 and 1896 $1,005,857,241. The largest record of any month prior to that just entered was that of November, 1898, which was $129,780,014, while only sixteen months in our history ever crossed the one hundred million dollar line in exports.

THE TOWNSHIP INSTITUTE. SEVENTH MEETING.

SOCIAL ELEMENTS.

I. HARMONY WITH THE PRESENT ORDER.

1. Illustrate the meaning and the need of social order
and harmony of conduct. Why should we have
rules and laws? The absurdity of anarchy.
2. The purpose of order in society.

In what sense is order "Heaven's first law"? Is it natural or artificial? Explain the extent to which man is a social being. Is this a denial of individualism?

3. Explain the meaning of orderly institutions and

customs.

4. Various ideas and kinds of law.

a. Common law.

b. Civil law.

c. Statute law.

d. International law.

e. Ethical law.

f. Law of habits and conventions, and society. 5. Moral principles the basis of law. Enlarge on this Do the masses of the people understand the evils of public bribery-the underlying wrong and certain consequence of it? Or, of mob law and its effects? Note carefully p. 359. Explain:

"If the so-called more enlightened members of the community accept public gifts from the man who buys up the council, and the so-called less enlightened members accept individual gifts from the man who sells out the council, we surely must take our punishment together."

6. Modes and organs of social control. Pp. 360-366. 7. Devices and processes of control.

II. SOCIAL PROGRESS.

1. Kead carefully the extract from Mazzini's address, pp. 370-372. Who was Mazzini? Define the spirit which he voices.

2. Make a summary of what you think are involved in the idea of social progress. Specify the particulars in which you can see marked progress in recent years. Are there signs of retrogression? Is war a means of progress?

3. Explain how inventions are a great cause of pro-
gress. Do " progress and poverty" go together?
Do men decay as wealth accumulates? Has moral
and spiritual progress kept pace with the material
progress resulting from invention?

4. Means of preserving and increasing inventions.
5. Is there a law of human progress?

III. THE PROSPECT AND THE DUTY BEFORE US.

Let us consider how we shall make the public school a greater agency in the progress of our people and our beloved country. Let us believe, with the village schoolmaster in Bonnie Brier Bush, that if we have the heart to spend our thought and money on a lad of parts, like "Geordie Hoo," we shall have two rewards which no man can take from us. One will be "the honest gratitude of a laddie whose desire for knowledge we have satisfied, and the second will be this-another scholar in the land"; and we may well think, "with auld John Knox, that every scholar is something added to the riches of the commonwealth."

ORDERLY PROGRESS.

In this closing study we have come to consider the general movement of an advancing community.

Not all communities and peoples are progressive. Some are stationary or even retrogressive. People who live in the realm called Christendom have become accustomed to think that progress is necessary and universal. But stagnation and decay are actually the conditions of a vast majority of the human race. The earth does not bring forth wheat and choice fruits without planting and tillage, although it may produce weeds and serpents without human cultivation.

In Social Elements we have a discussion of Order and Progress. There are advantages of combining these in the title "Orderly Progress," and this idea is illustrated in the text. It may properly be urged that the social student should strive to gain a clear conception of what is meant by "a moving equilibrium.” The illustration of the bicycle, which remains upright only as it is propelled forward, is apt and instructive. But in the vital activities of growing youth we have a higher type of harmony in development. Health ineans life and movement of many organs and members, each in its place and all coordinated in one body.

Progress, in the strict sense of the word, must be carefully distinguished from the diffusion of goods, material and spiritual. In a very important sense we may admit that it is proper to speak of social progress when known truths and inventions are given publicity and wide introduction. But the points of absolutely new gifts to the race are moments of discovery and invention. man, whether of genius, talent or ordinary wit, is usually the origin of novelties. Sometimes the inventions are minute improvements in a tool or machine, made by mechanics who watch the work with almost microscopic vision.

One

In one great factory in Ohio the intelligent company offer prizes to the work people for suggestions of improvement. In some establishments it is the custom to pay something to the laborers whose inventions are patented. To the shame of their class it must be confessed that sometimes the capitalist managers simply steal the invention without either credit or pay to the workmen, and take to themselves the honor and the wealth which flow from the new idea. This base and selfish conduct is anti-social and tends to rob society of the advantages of an eager curiosity and alertness which would come from a just and fair reward to laborers for their hints.

In these days of democratic tendencies to leveling we must not forget the laboratory workers who toil long and patiently in the universities.

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