But more particularly will a teacher interest his school in this department by making observations of this kind and comparisons, &c., among the birds they are in the habit of seeing, such as the cuckoo, swallow, tom-tit, skylark, woodpecker, jay, or ducks and geese.

In this way they become observers of the external world with which they are in contact; it adds both to their happiness and to their usefulness, inasmuch as all these things have a practical bearing on social life.*

In teaching English History, the Outlines by the Society for promoting Christian Knowledge have been used here, being the only book on this subject which, on account of price, is attainable by the generality of children in a school like this; when reading, instruction of the following kind, in a conversational way, is given to them-on the different people who have invaded us at different periods of our history -Roman, Saxon, Dane, Norman-the Roman and other remains in this neighbourhood-the Roman road between Winton and Sarum, running through part of the parish, and anything of this kind of a local nature-how a people invading another, and remaining among them, is likely to affect their language, manners, &c.-traces of this is shown in our language; the manners and customs of particular periodshow people were housed, and clothed, and fed-the little intercourse there could be between people living even in different counties, for want of internal communication afforded by roads, &c.-there might even be famine in one county and abundance in the adjoining one ;-how such evils are remedied by roads, canals, &c. ;-the different inventions in science, &c., and dwelling upon the more remarkable ones, bringing with them great social improvements-paper, printing-the Reformation, impulse given to it by this;-nations contending for the honour of the invention-how this enables one generation to start from the point where another leaves "These are thy glorious works, Parent of goodAlmighty! Thine this universal frame,

Thus wondrous fair: Thyself how wondrous then,
Unspeakable! who sit'st above the heavens-
To us invisible, or dimly seen

In these thy lowest works; yet these declare
Thy goodness beyond thought, and power divine."

MILTON.

off-how rapid the progress of colonies from the mother country in consequence; the improvements attending the introduction of turnpike-roads-post-office ;-application of wind, water, steam, &c., as the moving power in machinery. How the introduction of the manufacture of cotton among a people, to anything like the extent of it in this country, must alter the mode of dress-the domestic employments of families, doing away with spinning, carding, knitting, &c., as home occupations; comparing the employments of a family in agricultural life at the present day with what they were at different periods. Again, the time which it took at no very distant period to travel between London and the provinces,* and how done;-the great men that have risen up at intervals in science, literature, &c., and in other ways;-the number and extent of our colonies, giving them such popular explanation of the nature of the constitution, one part of the legislature being hereditary, another elective, &c., as is within the comprehension of children ;+-the comforts and conveniences within the reach of every class in society compared with those of earlier periods; and thus, instead of making it a dry detail of the chronological order of reigns, which in itself would not be instructive, endeavouring to give an interest to it, by speaking of those things in past ages which bore upon their daily occupations, and showing how they may improve the future by reflecting on the past.

ARITHMETIC.

Arithmetic should be made an exercise of the mind, and not merely an application of rules got by heart; in fact, it *The following is the copy of a card which used to be, and perhaps is still preserved at York, in the bar of the inn to which it refers :

"York Four Days' Coach, begins the 18th of April, 1703. All that are desirous to pass from London to York, or from York to London, or any other place on that road, let them repair to the Black Swan in Holbourne, in London; and to the Black Swan in Coney-street, York, at each which places they may be received in a stage-coach, every Monday, Wednesday, and Friday-which performs the whole journey in four days-if God permit."

The same distance is now travelled by railroad in eight or nine hours. † Dr. Johnson observes in the Rambler: "That not a washerwoman sits down to breakfast without tea from the East Indies, and sugar from the West."

ought to be taught on a sort of common-sense principle, beginning with very simple things, and leading the children on, step by step. It is difficult to fix on their minds ideas of abstract numbers, and therefore, at first, the numerals 1, 2, 3, &c., should be connected with visible objects; such as books, boys, girls, &c., and thus they should be made to understand that a number, when applied to things or objects, means a collection of units of that thing or object, but that the same kind of unit must run throughout; that, in a class of children each child is an unit, and that, when we speak of a hundred children in a school, we speak of a hundred units, each of which is a child; but that we must have units of the same kind, or we could not class them all together; that we might say a hundred children when half are boys and half are girls, because the word child means either boy or girl, and in that sense either of them is an unit; but we could not say one hundred boys or one hundred girls when there are fifty of each sort; the unit, of boys or girls, not running through the school, but only half way: we might say a hundred head of cattle, when half were sheep and half were cows, but we could not say one hundred sheep or one hundred cows. In the same way the sportsman says a hundred head of game, meaning by that hares, rabbits, &c., but in all a hundred separate heads of animals.

It will help very much to facilitate the future steps if the teacher can get the children to form correct ideas as to the local value of each figure, and this may be done by altering the position of the same figures, so as to make them represent different numbers; as 56, that is five tens and six units; 65 would be six tens and five units; 678 is six hundreds, seven tens, and eight units,-but 876, &c.: that 0 has no value in itself, but being placed on the right hand of a figure makes its value ten times as great as it was, because it shifts the first figure from the units to the tens place, and so on; as 6 by placing 0 on the right hand becomes 60, and so on, and from this to infer that by placing a 0 on the right-hand side of any number, you multiply it by ten. This is to be a sort of induction or conclusion they are to arrive at, as a general rule drawn from testing it by particular instances.

In the same way he would point out that any other figure placed on the right hand of a number multiplies that number

by ten, inasmuch as it advances each figure one place to the left, and at the same time increases the number by the number of digits it contains; two figures by 100, &c.; thus 95, placing 6 on the right hand, becomes 956, or 900 + 50+6; placing 65 becomes 9565, or 9000 + 500 +60 + 5. That 5, 6, &c. are always so many units, but the unit of value rises in a tenfold proportion every place the figure is advanced to the left.

When they know a little of numeration, the teacher should write on the black board, and make them thoroughly understand, writing down numbers in the following way: 69 or 609; 756 or 700 + 50+6; 1050 or 1000 + 0 hundreds, + 50 + 0, making them say seven hundreds, five tens, six units; one thousand, no hundreds, five tens, no units : this they ought to be exercised in until they know what they are about.

In exercising them as a class by the repeated addition or subtraction of the same number, it may be made more of a mental exercise by checking them every now and then, testing what has been done; for instance, adding by sevens, and they have come up to 63; stop there, and ask the boy whose turn is next, whether they are correct as far as they have gone;

perhaps he says yes. Why? because

63

7

9, or seven added

nine times to itself gives 63, and the probability is they are right, and one would generally let them conclude so; but here the teacher will point out to them-there may be an error of seven, or any multiple of seven, and in that case the result would still be divisible by seven, and at the same time wrong; tell them to reckon the boys, and if nine, the proof is complete. Again, supposing them to have gone on adding by sevens until the sum is 77: ask, right or wrong; the boy will answer right, because 11; then go on a little further, and a boy says, for instance, 99: divide, there is a remainder of one; it was right at 77 when the eleventh boy answered, therefore the error must be with the last three boys. They should also be practised in asking such questions as, How many divisors has the number 12 above unity-how many 15? thus 12 = 2 × 3 × 2, or 5 × 3 splitting the num

77

7

ber into its factors: that all even numbers are divisible by 2, and that no odd number is. This seems simple, but if constantly repeated has a good effect.*

3 may be written 1 + 1 + 1 or 3

2+2

1 + 1 + 1 + 1 + 1 or 5
2+2+2 or 3 + 3

9 may be written in separate units, or 3 + 3 + 3; that a class of nine children may be made to stand out as units, but they cannot be made to stand out in twos without a remainder in sets of three but not of four.

Thus showing them that up to 20, a class containing an even number of children may be made into more sets without a remainder, than a class containing an odd number; it is well to illustrate this practically either by parcelling out a class, or a number of small pieces of wood, thus carrying conviction both to the eye and to the mind. There is no exercise which has a better practical effect than pointing out all the factors into which numbers up to a hundred, for instance, can be broken, such as 24= 2 × 12, or 3 × 8,3 × 2 × 4, or 3 x 2 x 2 x 2.

This subject of the number of divisors without a remainder, would lead the teacher to speak of the subdivisions of a

* If the teacher is acquainted with a little Algebra, he would do well to apply it to a few of the common properties of numbers. Thus in this case: Every even number may be represented by the form (2n)

Every odd number by

(2n+1) giving to n in each of these forms its successive values, 0, 1, 2, 3. (2n) becomes 0, 2, 4, 6, &c. all the even numbers. (2n+1)

Now it is clear

1, 3, 5, 7, &c. all the odd numbers.

2n

1) giving the quotient (n) that all even numbers are

(2n + 1) =

divisible by 2 without a remainder,

|=n+ therefore the odd ones are not.

" 2

Therefore the square of every even number is divisible by 4 without a remainder.

The square of an odd number is not.