relations to his parents, and friends, and playfellows; but there is not actually any thing within the reach of the child's attention, whether it belong to nature, or to the employments and arts of life, that might not be made the object of a lesson by which some useful knowledge might be imparted, and, which is still more important, by which the child might be familiarized with the habit of thinking on what he sees, and speaking after he has thought. The mode of doing this, is not by any means to talk much to a child, but to enter into conversation with a child."

LORD KAIMES ON GRAMMAR TASKS.

"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 knowledge they acquire of a language, are not indebted to dry rules, but to practice and observation. this day I never think without shuddering of Disputer's Grammar, which was my daily persecution during the most important period of my life. Curiosity, when I was farther advanced in years, prompted me to look at a book that had given me so much trouble. At this time I understood the rules per

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fectly, and was astonished that formerly they had been to me words without meaning, which I had been taught to apply mechanically, without knowing how or why. 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 ?"

VALUABLE PUBLICATION.

I rejoice to inform my readers, that while the foregoing pages were in the press, I learnt from the newspapers the fact, that an Etymological Spelling Book had been published, which, it struck me, would probably form the best possible companion to this little work. I obtained a copy from London, and found it to be precisely what I wished to find it. The author, Mr. Henry Butter, has arranged the book in the most admirable manner, and has furnished complete lists of all those words, (with their derivations, from the Latin and Greek,) the variations of which, in our language, afford such scope for amusement in reading. I have no hesitation in saying that a careful attention to the " Key to Reading," together with the use of Butter's Spelling Book, will enable any person to conduct reading exercises with pleasure and advantage, either in public or private teaching. The Spelling Book may be had of Simpkin and Marshall, London, and E. and J. Smith, Liverpool; price, Is. 6d.

MENTAL ARITHMETIC.

I SHALL not attempt, under this head, to do much more than to put into print a few of the particulars to which I refer in that part of my lectures which treats of the great opportunities teachers and pupils may have of devoting a portion of their attention to mental arithmetic, if the time now wasted in the drudgery attendant on the old mode of teaching were saved, as it may certainly be, by the use of our arithmetical invention. We have proved from actual experiment, publicly made, that the time saved by means of our arithmetical scales for the elementary rules, is equal to five-sixths of the whole time consumed in practising those rules on the ordinary systems.

It is not possible that every student can become a "wonderful calculator;" but every student may be made early acquainted with the principles and the practice of something like ready reckoning.

Generally, arithmetic is regarded by youth as the dullest of all the dull things taught at schools; and no wonder. It is seldom that the teachers and pupils, whose time is so much occupied with the mere working and correcting of routine sums, can have leisure for discussing the mentality of the

science, or even for enjoying its amusing peculiarities. Let a little amusement be resorted to, as soon as a knowledge of the value of figures has been obtained, and the learner will not find arithmetic so destitute of interest as he imagined; and when he has become expert in the elementary rules, he will be easily led to attempt the very useful practice of mental arithmetic.

One of the first points, perhaps, to present to the mind of a child, is the peculiarity of the number 9, which is the product of the "magical number," 3, multiplied into itself. However many nines be added together, or by whatever number or numbers it may be multiplied, the line of figures forming the sum or product may be added together, and it will consist of an amount equal to one or more nines. For instance, twice 9 are 18; the 1 and the 8 are 9. Three times 9 are 27; the 2 and the 7 are 9. Four times 9 are 36; the 3 and the 6 are 9. A learner finds some amusement in increasing the amount, as if he expected a variation might be found; but when he gets to 11 times 9, he finds the product is only 99; two nines. And, at the next step higher, namely, 12 times 9, he obtains only 108, or one nine.

Then he may be shown the fact that the nine digits, 1 2 3 4 5 6 7 8 9, added together, amount to a number of nines, namely, 5 nines, or 45; and he may be taught, that if, instead of adding the line up, he will multiply the middle figure by the last figure, he will find the value of the whole most

readily; and this is upon a principle of taking averages, which he will have occasion to resort to in higher departments of the science.

He may then be directed to notice the effect of adding together two lines formed of the nine digits, but in reversed order.

For instance,

123456789

987654321

111111110

There is something striking to the eye in such a product, for the wonderful number recurs again, in nine ones; and it may serve to induce thinking. Or let the one line be subtracted from the other, in: this way:

987654321
123456789

864197532

In this result the odd and even numbers become curiously arranged; the whole of the nine digits are there as in the upper lines, but there is no surplus or repetition; and of course they amount to five nines !

Would the pupil wish to see a sum in multiplication, the product of which should contain several figures, but all alike? Tell him to set down all the digits except the 8, and if he would like the product to be all ones, let the line be multiplied by one 9.

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12345679

9