work hard now so that if it is hot by-and-bye we can then play." With this encouragement all are ready.

"The first group may let their pencils draw the answer to this example." "My little helpers in the second group may do their Busy Work." (At this point the trainer, or assistant, walks quietly up and down the aisles distributing small units of design -colored pieces of paper in the form of triangles, squares, rectangles, and circles.) "The third group may come to me." Twenty eager children crowd about her, tug at her dress, put their chubby lips up to be kissed, or lean upon her for a fond caress. The teacher is all kindness and each token of their love is returned with corresponding affection. Turning to the blackboard she deftly begins to sketch a house. Hardly has the second stroke of the crayon been made ere the active minds about her begin to work. One speculative Yankee blurts out, "I guess it is going to be a cart"; another, almost under her elbow, queries "A barn"; another, "A box." At length the last window is cut and the last door hung. The teacher stands back and inquires, "What have I made, children ?" "A house," is the quick response, for all, even, to the dullest, now recognize the familiar picture. "Who will tell me a nice story about the house?" Up comes a score of hands and stories are plentiful. "I see a picture of a house." "I think it is a school-house." "You have drawn a house on the black board," among the rest. "Has any one ever seen a house?" "Why yes'm, yes'm," are the rapid replies. "What kind?" The hands flutter once more, the interest is intense, for all are eager to impart their little stock of information. "A wooden house, brick house, school-house, hen-house, dog-house, wood house, court house, meeting-house, boarding house, stone house, freight-house, station-house, snow house," are the baker's dozen of houses they have observed. As fast as each is given, a little "story" is told about it which the teacher rapidly, but with beautiful penmanship, places upon the board. Thirteen sentences of the children's own creation are now to be read. "Shut your eyes tight, tight," is the teacher's admonition, while she quietly points to a sentence. "Look quick!" In a flash every eve is riveted upon the sentence indı

cated by the pointer and every hand is waving high in air. One by one the sentences are read till the excitement is at a high pitch, when the query comes from the teacher, "How many have seen a dog-house?" "I," and "I," and "I,”—yes, all have seen one. "Then let your pencils draw a pretty picture of one for me, and tell a little story about it. Let me see how many can

And all scamper to their

have a Daisy Slate! Good bye." seats, for a Quincy teacher never says coldly, one, face; two, file; but always a cheery "Good bye."

Let us consider what a lesson like this involves. There is, first of all, originality and stimulation of thought and its expres sion; then the creation of interest and enthusiasm, sight reading, drawing, writing, spelling, neatness, and a laudable desire to excel. Surely a combination lesson par excellence, and how dif ferent from the antiquated method of teaching the common branches separately. We never use them isolated. Why then

teach them so?

Nowhere have we ever seen a more faithful practice of the advice "Read naturally," than at Quincy. This naturalness of expression is much increased by the practice, as soon as the children are old enough to grasp the thought fully, of raising their eyes from the book and looking at the teacher, or whoever may be present. The following incident, related to us by the teacher in whose presence it occurred, is the best possible proof that Quincy children read naturally. The scene was in a Primary room. John Quincy Adams was present on a tour of in

spection. A little girl read, "What is your coat made of?" Somewhat disconcerted and wondering why the child cared to know the quality of his dress, he hesitated before answering. Another question quickly followed the first, "Is it made of wool?" "Y-e-s, I guess so; at least it ought to be," answered the innocent Mr. Adams. Here the teacher thought it best to interfere, and explained that the child was not addressing him, but was only reading from the book. Mr. Adams made a hasty departure, convinced of the naturalness of the Quincy methods.

PERCENTAGE.

BY N. NEWBY.

THE following treatment of percentage is submitted in the hope that whatever of good there is in it, may be utilized by those who need it.

1. THE TERMS USED.-The base, the rate per cent., and percentage are but new names, to the pupil, for multiplicand, multiplier and product, respectively. Percentage is thus related to multiplication in the signification of its terms. For working purposes the rate per cent. is a number of hundredths.

2. THE CASE.-I. Given the base and the rate per cent. to find the percentage.

Solution. Since the percentage is the product of the base by the rate per cent., the percentage is found by multiplying the base by the rate.

II. Given the base and the percentage to find the rate per

cent.

Solution. Since the percentage is the product of the base by the rate per cent., the rate per cent. is found by dividing the percentage by the base, expressing the quotient as hundredths. III. Given the percentage and the rate per cent. to find the base.

Solution. Since the percentage is the product of the base by the rate per cent., the base is found by dividing the percentage by the rate per cent.

In the first case we have given two factors to find their product, while in the second and third cases we have given the product of two factors, and one of them to find the other.

On the basis of processes employed; the cases of percentage are but two; but since in the second case the quotient is limited to hundredths order (by virtue of its office as rate per cent.) and because there are three essential terms employed in percentage, it is convenient to make three cases.

In many of the text books, the terms amount and difference are used. Each of these is, however, a number of times one hundredth of the base, and is thus included under the definition of the percentage.

The entire matter of percentage as required in the common schools is outlined in the foregoing scheme.

3.

THE APPLICATIONS.-The various applications of percentage may be grouped into two classes. 1. Those problems in which the percentage is the product of two factors, viz: the base and the rate per cent. 2. Those problems in which the percentage is the product of three factors, viz: the base, the rate per cent. and the number representing the time in years involved in the transaction under consideration. Profit and loss, commission, stocks, insurance, taxes, etc., are examples of applications of the first class-while interest, discount, exchange, etc., are examples of applications of the second class.

Upon beginning the study of any of the "applications" the terms which correspond to the base, the rate per cent., and the percentage, should be clearly fixed in the mind. The pupil then readily translates any particular problem in profit and loss, commission, etc., into a problem of percentage and solves it under some one of the three general cases. For example: 1. The number on which gain or loss is estimated is the base. The cost price is usually the base. 2. The gain, the loss, or the selling price is the percentage. 3. The rate of gain, rate of loss, or rate of selling is the rate per cent.

EXAMPLE I. A man paid $110 for a horse and sold it at a profit of 20 per cent.; required the gain.

Translation. We have given the cost, $110, which is base, and the rate of gain, .20, which is rate per cent., to find the gain which is the percentage.

Solution. Since the percentage is the product of the base by the rate per cent., the percentage, in this example, is found by multiplying $110 by .20; the product $22, is the percentage, which is the required gain. Therefore he gained $22.

EXAMPLE II. A hat costing $8, was sold for $9. the rate of gain?

Preliminary Step. $9 minus $8 $1 = the gain.

What was

Translation. We now have given the cost, $8, which is base, and the gain, $1, which is the percentage, to find the rate of gain, which is rate per cent.

Solution. Since the percentage is the product of the base by the rate per cent., the rate per cent., in this example, is found by dividing $1 by $8, expressing the quotient as hundredths. The quotient, .12%, is the rate per cent., which is the required rate of gain. Therefore, etc.

These examples briefly indicate the character of thinking that the pupils should do under all the applications of percentage in order to receive that culture which the subject can be made to yield.

It is granted that there are analytic solutions by which the answer to such exercises is more quickly obtained than by the method here suggested; but an analytic solution is always determined by the conditions of each individual problem. Such solutions do indeed give a very desirable kind of culture, but they do not tend to broad generalizations.. They do not tend to unify different parts of the subject, and hence are not important factors of the subject as science.

The method of treating percentage which I have herein presented, I have called the deductive method-since each individual problem under whatsoever "application" it may occur, is immediately referred by means of corresponding terms to one of the general cases of percentage for solution. The teacher who will faithfully and persistently use this method will assuredly give to his pupils a broad and an abiding knowledge of the "applica tions" in their organic relation to the principles of percentage.

A similar treatment of all parts of arithmetic will make of this branch a most potent means of mental culture instead of a machine for "doing sums."

TERRE HAUTE, IND.

THE SYLLOGISM IN ARITHMETIC.

GEORGE C. HUBBARD.

"THE study, par excellence, for the culture of deductive reasoning, is mathematics." "Reasoning is the process of deriving one judgment from two other judgments." "All reasoning can be, and naturally is expressed in the form of the syllogism." "The two propositions from which the third is derived is called