1 Square Yard.

1 Square Yard.

2 Square Yards.

2 Square Yards.

When the dimensions of the mason work of a house are required, the different parts of the building, which require separate calculations, as the side-walls, the end-walls, the gables, the chimney-stalks, &c. should be separately delineated; and if such delineations are not found in the books where the questions are stated, the pupil, before proceeding to his calculations, should be desired to sketch a plan of the several dimensions which require his attention, in order that he may have a clear conception of the operations before him. Such questions as the following should likewise be illustrated by diagrams. "Glasgow is 44 miles west from Edinburgh; Peebles is exactly south from Edinburgh, and 49 miles in a straight line from Glasgow. What is the distance between Edinburgh and Peebles?" This question is taken from "Hamilton's Arithmetic,” and is inserted as one of the exercises connected with the extraction of the Square Root; but no figure or explanation is given, excepting the following foot-note. "The square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of the other two sides." It should be represented as under.

GLASGOW

44 Miles.

EDINBURGH

49 Miles.

PEEBLES

By this figure, the pupil will see that his calculations must have a respect to two right-angled triangles, of which he has two sides of each given to find the other sides, the sum of which will be the breadth of the street. The nature of fractions may be illustrated in a similar manner. As fractions are parts of a unit, the denominator of any fraction may be considered as the number of parts into which the unit is supposed to be divided. The follow ing fractions,,,, may therefore be represented by a deline. ation, as follows:

By such delineations, the nature of a fraction, and the value of it, may be rendered obvious to the eye of a pupil.-A great many other questions and processes in arithmetic might, in this way, be rendered clear and interesting to the young practitioner in numbers; and where such sensible representations have a tendency to elucidate any process, they ought never to be omitted. In elementary books on arithmetic, such delineations and illustrations should frequently be given; and, where they are omitted, the pupil should be induced to exert his own judgment and imagination, in order to delineate whatever process is susceptible of such tangible representations.

I shall only remark further, on this head, that the questions given as exercises in the several rules of arithmetic, should be all of a practical nature, or such as will generally occur in the actual business of life-that the suppositions stated in any question should all be consistent with real facts and occurrences—that facts in relation to commerce, geography, astronomy, natural philosophy, statistics, and other sciences, should be selected as exercises in the different rules, so that the pupil, while engaged in numeri

cal calculations, may at the same time be increasing his stock of general knowledge—and that questions of a trivial nature, which are only intended to puzzle and perplex, without having any practical tendency, be altogether discarded. In many of our arithmetical books for the use of schools, questions and exercises, instead of being expressed in clear and definite terms, are frequently stated in such vague and indefinite language, that their object and meaning can scarcely be appreciated by the teacher, and far less by his pupils and exercises are given which have a tendency only to puzzle and confound the learner, without being capable of being applied to any one useful object or operation. Such questions as the following may be reckoned among this class. "Suppose £2 and of of a pound sterling will buy three yards and of of a yard of cloth, how much will of 4 of a yard cost?" "The number of scholars in a school was 80; there were one-half more in the second form than in the first; the number in the third was of that in the second; and in the fourth, of the third. How many were there in each form?"

In some late publication, such as "Butler's Arithmetical Exercises," and "Chalmers' Introduction to Arithmetic," a considerable variety of biographical, historical, scientific, and miscellaneous information is interspersed and connected with the different questions and exercises. If the facts and processes alluded to in such publications, were sometimes represented by accurate pictures and delineations, it would tend to give the young an interest in the subject of their calculations, and to convey to their minds clear ideas of objects and operations, which cannot be so easily imparted by mere verbal descriptions; and consequently, would be adding to their store of genial information. The expense of books constructed on this plan, ought to be no obstacle in the way of their publication, when we consider the vast importance of conveying well-defined conceptions to juvenile minds, and of rendering every scholastic exercise in which they engage interesting and delightful.

SECTION V.-Grammar.

Grammar, considered in its most extensive sense, being a branch of the philosophy of mind, the study of it requires a considerable degree of mental exertion; and is, therefore, in its more abstract and minute details, beyond the comprehension of mere children. Few things are more absurd and preposterous than the practice, so generally prevalent, of attempting to teach grammar to children of five or six years of age, by making them commit to memory its definitions and technical rules, which to them

are nothing else than a collection of unmeaning sounds. In most instances they might as well be employed in repeating the names of the Greek characters, the jingles of the nursery, or a portion of the Turkish Alcoran. The following is the opinion of Lord Kaimes on this point:- -“In teaching a language, it is the universal practice to begin with grammar, and to do every thing by rules. I affirm this to be a most preposterous method. Grammar is contrived for men, not for children. Its natural place is between language and logic: it ought to close lectures on the former, and to be the first lectures on the latter. It is a gross deception that a language cannot be taught without rules. A boy who is flogged into grammar rules, makes a shift to apply them; but he applies them by rote like a parrot. Boys, for the know-ledge they acquire of a language, are not indebted to dry rules, but to practice and observation. To this day, I never think without shuddering, of Disputer's Grammar, which was my daily persecution during the most important period of my life. Deplorable it is that young creatures should be so punished, without being guilty of any fault, more than sufficient to produce a disgust at learning, instead of promoting it. Whence then this absurdity of persecuting boys with grammar rules?"

In most of our plans of education, instead of smoothing the path to knowledge, we have been careful to throw numerous difficulties and obstacles in the way. Not many years ago, we had two characters for the letter s, one of them so like the letter f, that, in many cases, the difference could not be perceived. We had likewise compound letters, such as ct, fl, fh, &c. joined together in such an awkward manner, that the young could not distinguish them as the same letters they had previously recognised in their separate state; so that, in addition to the ungracious task of learning the letters of the alphabet in their insulated state, under the terror of the lash, they had to acquire the names and figures of a new set of characters, before they could peruse the simplest lessons in their primers. Such characters, it is to be hoped, are now for ever discarded. We have still, however, an absurd practice in our dictionaries and books of reference, which tends to perplex not only our tyros, but even our advanced students, when turning up such works-I mean the practice of confounding the letters I and J, and the letters U and V, which are as distinct from each other as a vowel is from a consonant; so that all the words beginning with J must be sought for under the letter I, and the words beginning with V, under the letter U, causing to every one a certain degree of trouble and perplexity, when searching for words beginning with any of these letters. Most of our schoo