higher class, is his being able to write a lesson and form a a Key to the same. 6. See an example in Simple Addition. 14 Apples. The boy writes as follows: “ I be21 gin at the 5 and say, 5 and 4 are 9, 34 and 1 is 10 and 4 are 14; set down 15 4 and carry 1, because there is one time ten in 14." 84 * “ Then I say, 1 that I carried and 1 makes 2, and 3 are 5, and 2 are 7, and 1 is eight; I set 8 on the left side of 4, which makes 84; the amount of the apples; or sum total of the apples.” 7. When a scholar can do this or something similar without assistance, he may be advanced to another class. 8. The usual method of teaching on the Lancaster plan, is to have a card of lessons suspended before the scholars in plain view; then each one writes and copies the card according to the directions of the monitor. EXAMPLE. 1, one: 2, two: 3, three: 4, four: 5, five: 6, six: 7, seven, &c. till arising to a hundred or more. 9. When writing these numbers, the pupils must be taught how to read them, thus : 12; begin at the 2 and say, “ units, tens; twelve.” Again, 76; begin at the 6 and say, “ units, tens; seventy-six.” 101; begin at the 1 on the right hand and say, “ units, tens, hundreds; one hundred and one. 1815; begin at the 5 and say " units, tens, hundreds, thousands; one thousand eight hundred and fifteen.” 10. The principal Teacher or some one of the expert monitors, will lecture noviciates in this manner, till they can read four figures correctly: Then have the Numeration Table suspended to view, and let some little ambitious gentleman place half a dozen or more of his comrades in a semicircle, near the card hanging, by the wall, and, with a long pointer or wand, teach them the numbers, and how to read the same, 11. This can be done in the way of pastime, for it will rest their weary limbs by changing their posture of sitting on a bench, to that of standing erect. 12. When learners become advanced to those cards which have a key, they will copy a lesson from the card as the monitor directs; and the monitor will see that the figures are correctly arranged on their slates. 13. Then the monitor will begin to read the key, and the class will work by his reading, having the card to look at as a guide ; he will also have an eye to their performances, and see that each scholar attends to every para ticular part thereof with exactness. 14. The cards may be cut out and hung up by the wa or in any convenient place before a class; but if the owner chuse, he may take copies occasionally and let the book remain entire. 15. It is also expected that teachers will form many more lessons than are herein printed ; and those new lessons, ought to be composed according according to the capacity of the learners for which they are designed. 16. A few examples in combination of figures are inserted as a specimen: First suspend one or two cards before the class in such position, that every one may view the figures with ease; then the monitor writes on his slate and shows the whole class how they must proceed. EXAMPLE. 4 and 2 are 6; 3 and 2 are 5; 6 and 1 is 7; 5 and 2 are 7; 8 and 1 is 9. After this simple mode of working with easy tasks, introduce something in a small degree more difficult ; as 2 and 4 are 6 and 1 is 7, and 2 are 9, and 3 are 12, and i is 13, and 3 are 16, and 2 are 18, and 1 is 19, and 2 are 21, &c. till the little tender minds become capable of reflecting and calculating independently. 17. Then proceed with larger numbers, but always have due regard to the capableness of learners : For instance; when a class have written some considerable time on one particular series, suppose it to be clause 16, or a whole card similar thereto, give them a task which will require a more strict attention ; such as, 4 and 3 are 7, and 3 are 10, and 4 are 14, and 3 are 17, and 4 are 21, and 5 are 26, and 4 are 30, and 6 are 36, and 3 are 39, and 4 are 43, &c. 18. But when we are about to make these advances, it will be proper to examine the class, one by one, as follows: Order them to clean slates; this may be done with a piece of moist cloth, a piece of hat, or a sponge; then turn the blank side of the card to view, and begin with No. 1, or head of the class, and from the key, or from one of the cards, form questions thus ; “ 4 and 2, how many? 3 and 2, how many ? how many are 5 and 2, and 1?"* Examine their slates and see who is right, and who has erred. Let there be no partiality in forming these questions when they are independent of the card or key, and let the scholars go up and down as in spelling classes. This operation will enable the principal Teacher to know how far he may increase the magnitude of the figures in his next lesson. And he will also be able to determine, how many scholars may be moved to a higher class. FIGURES TAUGHT WITHOUT A BOOK. 19. There is a mode of teaching children in arithmetic without a book; this mode I will endeavour to describe. Take a smooth board of about two feet in breadth and three feet in length, suspend it on a nail by the wall, and place a dozen spare slates by the board : then let the Teacher, or some of the capable monitors, with a piece of chalk, write a lesson in figures on the board, suitable for the scholars who are to be called before it for exercise. 20. When this is done, name such a class as you think proper; suppose it will be No. 3. No. 3, to the sideboard calculation.” When they become noisy by incautious steps, stop them without delay—they ought to come from their seats in order as they there sat: each one with his pencil, expeditiously, but cautiously, without noise, approaches the sideboard, takes a slate, and the whole See Card No. 16. form in a semicircle. The monitor then begins after the manner described in clause 21. But in order to make the business plain to every capacity, let us have a lesson in view. We will take a lesson, or task, or sum, as you please to call it, in Simple Addition, which suppose stands marked on the sideboard thus : 3 4 2 2 5 3 2 5 1 5 3 2 4 Here we chuse figures of small numbers to encourage the pupils. The mode of teaching every branch of science, ought to be such as will make it pleasing to the learner, so far as the nature of things will admit. 21. Now we will describe the duty of the monitor: He stands behind the class with a wand, or long handsome stiek for a pointer, and directs No. 1, or head of the class, to add the first right hand column of figures. No. 1 proceeds as follows: 64 and 2 are 6, and 3 are 9, and 2 are 11, and 4 are 15, and 1 is 16, and 5 are 21 ; set down 1 and carry 2 to the next column, because there are twice 10 in 21." Then the Teacher will begin a lecture thus : “ As the second column is ten times greater than the first, and the third is ten times greater than the second, and the fourth is ten times greater than the third, so whatever is carried forward from column to column, must be called ten or tens. When we have 14, we set down 4 and carry one time ten, because the 4 is four above ten, and there is one time ten in 14. If we have 35, set down 5 and carry 3, because |