time told that is governs the nominative case. The usual reason given to pupils, that the act passes over to the object, as John strikes James, is absurd, when he sees in most cases there is no action at all upon the object, except in some metaphysical sense. Therefore, as a matter of fact, if case is to be retained, we would teach, that prepositions and some verbs govern nouns in case only, and others, like is, are, etc., govern in case and number. But why not discard case altogether, have only the subject, predicate, and complement (something to complete the idea of the predicate)?

Again, how is it possible for the young pupil to understand why the article and adjective are so called? This huge obstacle to the child's progress we have by tradition; no necessity in the complete and thorough understanding of the language exists for it. He sees readily great propriety in the name of adverb (added to the verb), why may we not make the word adnoun be as useful to him as adverb? He sees the adverb is thrown at or to the verb, as much as the adjective is to the noun. Why not have adnouns as well as adverbs the article and adjective, adnouns, until at least the higher course of language is reached, called English Literature. We believe a grammar of twenty-five or thirty pages might be made, comprising all the young pupil need learn of grammar as a science and art; and the time now worse than thrown away in the study of the history and philosophy of the language called grammar, be profitably spent in acquiring the use of language. If onehalf of the time now spent on English grammar were employed in committing, in the most perfect manner, specimens of the best English gems in thought and style, and one-fourth of it in imitating those specimens in composition and talk, and the remaining fourth in the study of words and sentences, their relations and dependencies, we firmly believe the pupil would not only be more generally educated, but would acquire such habits of excellent speech and composition as can be obtained in no other way. Is there not an opportunity to improve our borrowed analysis and nomenclature in grammar, and is it not very desirable? E. H.

ARITHMETIC.

"TIME is money," says the old adage. With the teacher it is more than money, and more in proportion as the mental is higher than the material. Arithmetic, though so important, has absorbed too much time and strength. The enthusiastic teacher desires to gain more time for reading, for the study of language, for making his pupils acquainted with the beautiful in literature and art, for object-lessons and vocal culture. He can gain a portion of this time by throwing aside the text-book in Arithmetic as far as it enslaves him, and teaching topically.

We suggest the following order of topics as more philosophical than the arrangement in many text-books.

Numeration of whole numbers and decimals. It is as easy for scholars to enumerate on the right of the decimal point as on the left. Addition and subtraction of whole numbers and decimals as far as millions and millionths. Multiplication and division of both whole numbers and decimals. Federal Money, Common Fractions, and Compound Numbers. Percentage without regard to time, viz: Percentage proper, Commission, Brokerage, Insurance, Stocks, Taxes, Custom House Business and Simple Discount. Percentage with regard to time, viz: Interest, True and Bank Discount, Proportion, Profit and Loss, Equation of Payments, etc.

An experience of several years in the school-room has convinced the writer that it is a waste of time to teach beginners in Written Arithmetic the definition of arithmetic.

Nor is there any need of requiring fine or text-book definitions of each of the fundamental rules before the scholar has used them in practice. If a definition be required at all, let it be simple and child-comprehensible.

Reduction should first be taught with simple numbers. Let the scholars frequently reduce such examples as eight hundreds, four tens and seven units to units, and back again.

In addition, the scholar should never be allowed to write down at one side the carrying number, but taught to add it as the first figure of the next column. Allowing scholars to add by using their

fingers, also lessens the discipline which is so desirable in first operations,

Subtraction should be taught but one way when the lower figure is larger than the upper, and that is to call the next column figure of the minuend one less rather than to add one to the figure in the subtrahiend.

It is well to require scholars to write out the names of the terms used even in simple work, for it shows a thorough understanding of every part of the operation. And this writing the names of the different results and factors should be continued throughout the study.

Scholars should be familiar with such examples as product and one factor given to find the other factor. Dividing by the factors of a composite number being never used after it is learned, it should not be taught till the scholar is perfect in all other parts of the arithmetic.

In common fractions, group under one rule all examples in addition, subtraction and division, by reducing to a common denominator and then adding, subtracting or dividing the numerator or numerators, as the case may require. In this way twelve rules are reduced to one.

After the scholar has become perfectly familiar with this method let him learn any of the shorter ways.

In division of simple fractions let him learn to divide by inverting the divisor; but in no case should this be explained, except to classes higher than the grammar grade. In all cases let the whole or mixed numbers, if any, be reduced to improper fractions; so that always one fraction is to be divided by another.

A few mental examples, perhaps made by the scholars, should be daily given. Let them involve the principle under discussion.

Quickness and correctness of work are of more practical value than explanations or definitions, and of infinitely more value than ability to solve puzzle or catch examples. A few minutes a day spent upon the fundamental rules will insure immediate improvement in this respect.

A well-known teacher and practical mathematician recently informed the writer, that he once directed the assistants in his Grammar School to spend half the time each day devoted to arithmetic, for six months, in this mechanical work. At the end of that time the average per cent of correct answers in the whole school, increased from about twenty per cent to over eighty per cent; and twice as many scholars from the first class entered the High School, as entered before the plan was adopted, when the whole year was principally spent upon principles, definitions and explanations.

If these views are true, committees and superintendents should judge of a teacher's ability by the correctness and rapidity of the answers her scholars give, rather than by their natural power to solve arithmetical puzzles.

In no study do scholars need so frequent reviews as in arithmetic. These can be given in the shape of review combination examples for home lessons, to be brought in neatly performed on slate or paper the next morning.

Written explanations for upper classes are very beneficial.

Many of the rules in arithmetic can be readily condensed for easier committal and remembrance; as, for instance, the Merchant's Rule in Partial Payments. It may be thus given: From the amount of the principal, or face of the note, subtract the added amounts of the indorsements. C. F. K.

"ONE IDEA."

PERHAPS the reason for the continuous flow of new school-books is that a perfect one has not yet made its appearance. Probably no man ever built himself a house that satisfied him. Something might have been different, and he is uneasy till he has tried again; but perfection eludes all his endeavors.

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The same fortune attends the making of school-books. thor starts off with one idea, which he conceives other authors have overlooked. He models his book to that one idea, overriding, it may be, forms which have been in use for ages, and are

as well understood as anything in the language, and have as firm authority as anything else in the dictionary. Absorbed with his hobby, the author runs into other faults, perhaps far more serious than those he assumes to correct.

I am led into these reflections, by the examination of several books of recent appearance. In one,* an advocate for the use of infinitives in the treatment of geometry assumes a sphere to be a regular polyædron of an infinite number of faces, whose aggregate multiplied by of radius will give the volume. From this it would appear that the regular icosiædron is no longer regular polyædrons, in regard to the number of faces. The same author considers a frustum of a pyramid or cone composed of layers of equal planes having no thickness.

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There is another book † of more recent date, which deals in infinitives of a different kind. We must not use the significant and well authorized word, "times," in multiplication and division. Thus, "At 37 cents a yard 8 yards will cost eight 37's of cents; eight 7's of units are 56 units, eight 3's of tens are 24 tens, etc."

The extraordinary use of the apostrophe, here and elsewhere, unfortunately is left unexplained. Again: "As many shad at 32 cents apiece, can be bought for 175 cents, as there are 32's in 175. There are five 32's in 175, etc."

And what is more singular still, we are told that the hitherto well-established principle, "In any proportion the product of the means is equal to the product of the extremes, is not true when the terms are denominate numbers; thus in the proportion 4pk.: 5pk.= = $12: $15, dollars multiplied by pecks would be neither dollars nor pecks, nor anything else; but $15. multiplied by the number of units in the first term, 4, would be $60, etc." If this illustration shows anything, it shows that in all operations upon numbers, the numbers are used as abstract numbers. We no more multiply $15 by 4 than we do by 4 pecks. The truth is, we do neither; money can. not be produced in this easy way.

*Brooks' Geometry.

† Walton's Illustrative Practical Arithmetic.