Another plan which we adopt, is in practice almost every day; but it is better adapted to what is called the class-room: we have the alphabet printed in large letters, both in Roman and Italic characters, on one sheet of paper: this paper is pasted on a board, or on pasteboard, and placed against the wall; the whole class then stand around it, but instead of one of the monitors pointing to the letters, the master or mistress does it; so that the children not only obtain instruction from each other, but every child has a lesson from the master or mistress twice every day.

Before they go to the reading lessons, they have the sounds of all the words in spelling: thus the sound of a—ball, call, fall, wall; then the reading-lesson is full of words of the same sound. In like manner they proceed with other letters, as i—the sound of which they learn from such words as five, drive, strive, until, by a series of lessons, they become acquainted with all the sounds; and are able to read any common book.

I have observed in some instances the most deplorable laxity in this particular. Cases have occurred in which children have been for two years at school, and yet scarcely knew the whole alphabet; and I have known others to be four years in an infant school, without being able to read. I hesitate not to say that the fault rests exclusively with the teachers, who, finding this department of their work more troublesome than others which are attractive to visitors, have sometimes neglected it, and even thrown it entirely aside, affirming that reading is not a part of the infant system at all! Such a declaration is, however, only to be accounted for from the most lamentable ignorance, preverseness, or both. Had it been true, we should not have had a single infant school in Scotland, and throughout that country the children read delightfully.

The great importance of full instruction in reading will be apparent from the following considerations.

1. If the parents do not find the children learn to read, they will discontinue sending them. This they consider essential, and nothing else will be deemed by them an adequate substitute.

2. Children cannot make desirable progress in other schools which they may enter, unless they obtain an ability to read at least simple lessons.

3. Neglect in this respect impedes the progress of the infant system. Such an obstacle ought not to exist, and should at once be removed.

4. In manufacturing districts children go to work very soon; and if they are not able to read before, there is reason to fear they will not afterwards acquire the power; but if they have this, Sunday schools may supply other deficiencies.

5. Want of ability to read prevents, of course, a knowledge of the Word of God.

To prevent this evil, I have arranged a series, denominated "Developing Lessons," the great object of which is to induce children to think and reflect on what they see. They are thus formed: at the top is a coloured picture, or series of coloured pictures of insects, quadrupeds, and general objects. For instance, there is one containing the poplar, hawk-moth, and wasp. The lesson is as follows: "The wasp can sting, and fly as well as the moth, which does not sting. I hope no wasp will sting me; he is small, but the hawk-moth is large. The moth eats leaves, but the wasp loves sweet things, and makes a round nest. If boys take the nest they may be stung: the fish like the wasp-grubs." On this, questions are proposed: Which stings? Which is small and which large? Which eats leaves? Which makes a round nest? &c. &c.

To take another instance. There is a figure of an Italian, to which is appended the following: "The Italian has got a flask of oil and a fish in his hand, and something else in his hand which the little child who reads this must find out. Any child can tell who makes use of the sense of seeing. In Italy they make a good deal of wine; big grapes grow there that they make it with. Italians can sing very well, and so can little children when they are taught." Questions are likewise proposed on this, as before.

Of these lessons, however, there is a great variety. All schools should possess them: they will effectually prevent the evil alluded to, by checking the apathy of children in learning to read, and calling the teacher's powers into full exercise. They are equally adapted to spelling and reading.

I will give several specimens of reading lessons in natural history, each of which has a large, well-engraved and coloured plate at the top, copied from nature.

THE EAGLE.

How glad some poor children would be if they could read about the eagle. He is a big strong bird, and has such great wings, and such long sharp claws, that he can dig them into the lamb, hare, rabbit, and other animals, and thus fly away with them to feed his young ones, and to eat them himself. Eagles make such a large nest on the side of some high rock, where nobody can get at it. There used to be eagles in Wales, and there are some now in Scotland, but very few in England, for they do not like to be where there are many people. The Almighty gave man dominion over the birds of the air, as well as over the other animals, and as he gave man power to think, if the eagles become troublesome, men catch them, though they can fly so high; and as the eagle knows this, he likes to keep out of our way, and go into parts of the world where there are not so many people. There are many sorts of eagles: the black eagle, the sea eagle, the bald eagle, and others. They have all strong bills bent down in front, and strong claws. This bird is mentioned in the Bible.

Questions are proposed after this is read, and thus the examination proceeds:—Q. What is that? A. An eagle. Q. What sort of a bird is he? A. He is big and strong. Q. What are those? A. His feathers. Q. What else are they called? A. His plumage. Q. Is the eagle a small bird? A. No, very large. Q. Are his claws long and sharp? A. Yes. Q. What animals could he carry away? A. A lamb, a hare, a rabbit, or other small animals. Q. What does he do with those? A. Feed his young ones. Q. Where does the eagle make his nest? A. On the side of some rock. Q. Why does he make it there? A. That no one may get at it. Q. Used there to be eagles in Wales? A. Yes. Q. Where are there a few still? A. In England, Scotland, and Ireland. Q. Why are they not as plentiful as they were? A. Because they do not like to be where many men live. Q. Did the Almighty give man dominion over the birds of the air? A. Yes. Q. What other power did he give man? A. Power to think. Q. As men can think, when the eagles became troublesome, what did they do? A. They caught them. Q. And what did the eagles that were not caught do? A. They went to places where men were not so plenty. Q. Are, there many different kinds of eagles? A. Yes. Q. Name some. A. The black eagle, the bald eagle, the sea eagle, and others.

THE VULTURE.

The vulture is like the eagle in size, and some of its habits; but it is so very different from it in many ways, that there is little danger of confusing the two together: the greatest distinction between them is, that the head of the vulture is either quite naked, or covered only with a short down, while the eagle's is well feathered. This is the chief difference in appearance, but in their habits there is a much greater. Instead of flying over hills and valleys in pursuit of living game, the vultures only search for dead carcasses, which they prefer, although they may have been a long time dead, and therefore very bad, and smelling very offensively. They generally live in very warm countries, and are useful in clearing away those dead carcasses which, but for them, would cause many dreadful diseases. In some countries, indeed, on account of this, the inhabitants will not allow any one to injure them, and they are called for this reason scavengers, which means that they do the business for which scavengers are employed. Vultures are very greedy and ravenous; they will often eat so much that they are not able to move or fly, but sit quite stupidly and insensible. One of them will often, at a single meal, devour the entire body of an albatross (bones and all), which is a bird nearly as large as the vulture itself. They will smell a dead carcass at a very great distance, and will soon surround and devour it.

Vultures lay two eggs at a time and only once a year: they build their nests on the same kind of places as eagles do, so that it is very hard to find them.

What does the vulture resemble the eagle in? A. In size and in some of its habits. Q. In what does it differ from the eagle? A. In having a neck and head either naked or covered with short down. Q. What is the difference in the manner in which they feed? A. The eagle seeks its food over hill and valley, and lives entirely on prey which he takes alive, while the vulture seeks out dead and putrid carcasses. Q. For what reason do you suppose is the vulture's neck not covered with feathers as the eagle's is? A. If they had feathers on their necks, like eagles and hawks, they would soon become clotted with blood. Q. Why would this happen? A. Because they are continually plunging their necks into decayed flesh and bloody carcasses. Q. How do vultures sit? A. In a dull, mopeing manner. Q. Where do they generally sit? A. On tall dead trees. Q. Do they continue thus long? A. Yes, for several hours. Q. What is the cause of their thus sitting so dull and inactive? A. The great quantity of food they have eaten. Q. Is there any description of vulture forming an exception to the general character of those birds? A. Yes, that particular kind called the snake eater. Q. Where is this bird a native of? A. Of Africa. Q. Why is it called the snake eater? A. On account of its singular manner of destroying serpents, on which it feeds. Q. Describe the manner in which this bird kills its prey. A. He waits until the serpent raises its head, and then strikes him with his wing, and repeats the blow until the serpent is killed. Q. What do the natives of Asia and Africa call the vulture? A. The scavenger. Q. Why? A. Because they are so useful in eating dead carcasses. Q. How is this useful? A. It clears the ground of them; otherwise, in those warm places, they would be the cause of much disease. Q. What does this shew us? A. That the good God has created nothing without its use. Q. What is the largest bird of the vulture kind? A. The great condor of South America. Q. What does its wing often measure from tip to tip? A. Twelve feet when spread out. Q. How do the natives of South America often catch the vulture? A. The dead carcass of a cow or horse is set for a bait, on which they feed so ravenously that they become stupid, and are easily taken.

THE CROCODILE.

I hope you will not put your dirty hands on this picture of the crocodile. The live ones have hard scales on their backs, and such a many teeth, that they could bite a man's leg off; but there are none in our land, only young ones that sailors bring home with them. The crocodile can run fast; those are best off who are out of his way. He lives by the water; he goes much in it; and he can swim well. Young ones come out of eggs, which the old ones lay in the sand. Some beasts eat the eggs, or else there would be too many crocodiles. The crocodile can run fast if he runs straight, and those who wish to get out of his way run zigzag, and he takes some time to turn; the poor black men know this, and can get out of his way; but some of them can fight and kill him on the land or in the water. I think the crocodile is mentioned in Scripture. Ask your teacher what Scripture means. When you learn geography you will know where many of the places are that are mentioned in the Bible, and you will see where the river Nile is. There are such a many crocodiles on the banks of that river that the people are afraid to go alone. What a many wonderful animals our great Creator has made! How humble and thankful we should be to see so many great wonders!

Q. What have crocodiles on their backs? A. Hard scales. Q. Have they many teeth? A. Yes, a great many. Q. Could they bite off a man's leg? A. They could. Q. Are there any in our country? A. None wild, but a few that sailors bring in ships. Q. Can the crocodile run fast? A. Yes. Q. Where does he live? A. In the water. Q. What do their young ones come out of? A. Out of eggs, which the old one lays in the sand. Q. How do people run that wish to get out of the crocodile's way? A. Zigzag, like the waved line in our lesson. Q. What do some men do? A. Fight and kill them in the water. Q. Where do most of those animals live? A. In the river Nile. Q. Where is this river? A. In Egypt.

The spelling lessons contain words capable of explanation, such as white, black, round, square; others are classed as fleet, ship, brig, sloop, &c.; and others are in contrast, as hot, cold, dark, light, wet, dry, &c.

In this department we use the tablet placed beneath the arithmeticon, the invention and improvement of which are described in the volume entitled "Early Discipline Illustrated, or the Infant System Successful and Progressing." A clear idea of the whole apparatus is given by the wood-cut on the next page, and it ought certainly to be found in every infant school. The sense of sight is then brought into full action to aid the mind, and that with results which would not easily be conceived. We shall take another opportunity of explaining the use of the upper part of the apparatus, the lower demanding our present attention.



To use the tablet, let the followings things be observed. It is supposed the children know well there are twenty-six letters in the alphabet; that twenty are called consonants, and that six are vowels. We take first one perpendicular row of letters in the figure. Now point to D, and say, What is that'? and the answer will be, D. Ask, Is it a vowel or consonant, and they will reply, A consonant; but ask, Why do you know it is D, and the answer will probably be, It is so because it is. Hide the circular part of the letter, and ask, What is the position of the other part, and they will say, having previously learnt the elements of form which will shortly be explained, A perpendicular line; hide that, and ask them what the other part is, telling them to bend one of their fore-fingers in the same form, and they will say, A curved line. If they are then asked how they may know it is D, they will say, Because it is made of a perpendicular line and has a curved line behind. Further information may then be given. Turn the D letter up thus , and say, I want to teach you the difference between concave and convex: the under part of the curve is concave and the upper part of it is convex. Then say, I shall now take the letter away, and wish you to shew me concave and convex on one of your fingers; when they will bend the forefinger and point them both out on it. Go on with the other letters in the same way: shew them the vowels after the consonants and analyze each one. For example, A is formed of two inclined lines and a horizontal line to join them in the centre; and the top of that letter is an acute angle, and were a line placed at the bottom it would be a triangle. A brass letter may be moreover shewn to be a substance: its properties may be described as hard, smooth, bright, &c., and its coming from the mineral kingdom may be noticed, and thus the instruction may be indefinitely varied.

The power of letters may then be pointed out. Ask them to spell M R, and they will give you the sound of R, or something like it, and so in reference to other letters. But place the A against the M as it appears in the figure, and you may teach them to say A, M, AM; and thus all the way down the left side of the row of consonants. If then you carry the vowel down on the other side of them, you will change the lesson, and by such means go on almost ad infinitum. Double rows of consonants may be placed with a vowel between them, and when well practiced in this, they will ask for the vowel to be omitted that they may supply it, which they will do very readily and with great pleasure, while there is a tasking of the mind which cannot but prove beneficial.

Again, turn the frame with the balls round, so that the wires are perpendicular instead of horizontal, raise a ball gently, and say, To ascend, ascending, ascended; let it fall gently, saying, to descend, descending, descended; with a little explanation these words will then be understood, and others may be taught in the same way. To fall, falling, fallen; to rise, rising, risen; to go, going, gone, will readily occur, and others will easily be supplied by the ingenuity of the instructor. The frame may also be applied to grammar.

It is to be used as follows:—Move one of the balls to a part of the frame distinct from the rest. The children will then repeat, "There it is, there it is." Apply your finger to the ball, and set it running round. The children will immediately change from saying, "There it is," to "There it goes, there it goes."

When they have repeated "There it goes" long enough to impress it on their memory, stop the ball; the children will probably say, "Now it stops, now it stops." When that is the case, move another ball to it, and then explain to the children the difference between singular and plural, desiring them to call out, "There they are, there they are;" and when they have done that as long as may be proper, set both balls moving, and it is likely they will call out, "There they go, there they go." I do not particularize further, because I know that good teachers will at once see the principle aimed at, and supply the other requisite lessons: the object of this book being rather to shew the principle of the thing, than to go into detail.



CHAPTER XII.

ARITHMETIC.

The arithmeticon—How applied—Numeration—Addition—Subtraction— Multiplication—Division—Fraction—Arithmetical tables—Arithmetical Songs—Observations.

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"In arithmetic, as in every other branch of education, the principal object should be to preserve the understanding from implicit belief, to invigorate its powers, and to induce the laudable ambition of progressive improvement."—Edgeworth

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The advantage of a knowledge of arithmetic has never been disputed. Its universal application to the business of life renders it an important acquisition to all ranks and conditions of men. The practicability of imparting the rudiments of arithmetic to very young children has been satisfactorily shewn by the Infant-school System; and it has been found, likewise, that it is the readiest and surest way of developing the thinking faculties of the infant mind. Since the most complicated and difficult questions of arithmetic, as well as the most simple, are all solvable by the same rules, and on the same principles, it is of the utmost importance to give children a clear insight into the primary principles of number. For this purpose we take care to shew them, by visible objects, that all numbers are combinations of unity; and that all changes of number must arise either from adding to or taking from a certain stated number. After this, or rather, perhaps I should say, in conjunction with this instruction, we exhibit to the children the signs of number, and make them acquainted with their various combinations; and lastly, we bring them to the abstract consideration of number; or what may be termed mental arithmetic. If you reverse this, which has generally been the system of instruction pursued—if you set a child to learn its multiplication, pence, and other tables, before you have shewn it by realities, the combinations of unity which these tables express in words—you are rendering the whole abstruse, difficult, and uninteresting; and, in short, are giving it knowledge which it is unable to apply.

As far as regards the general principles of numerical tuition, it may be sufficient to state, that we should begin with unity, and proceed very gradually, by slow and sure steps, through the simplest forms of combinations to the more comprehensive. Trace and retrace your first steps—the children can never be too thoroughly familiar with the first principles or facts of number.

We have various ways of teaching arithmetic, in use in the schools; I shall speak of them all, beginning with a description of the arithmeticon, which is of great utility.



I have thought it necessary in this edition to give the original woodcut of the arithmeticon, which it will be seen contains twelve wires, with one ball on the first wire, two on the second, and so progressing up to twelve. The improvement is, that each wire should contain twelve balls, so that the whole of the multiplication table may be done by it, up to 12 times 12 are 144. The next step was having the balls painted black and white alternately, to assist the sense of seeing, it being certain that an uneducated eye cannot distinguish the combinations of colour, any more than an uneducated ear can distinguish the combinations of sounds. So far the thing succeeded with respect to the sense of seeing; but there was yet another thing to be legislated for, and that was to prevent the children's attention being drawn off from the objects to which it was to be directed, viz. the smaller number of balls as separated from the greater. This object could only be attained by inventing a board to slide in and hide the greater number from their view, and so far we succeeded in gaining their undivided attention to the balls we thought necessary to move out. Time and experience only could shew that there was another thing wanting, and that was a tablet, as represented in the second woodcut, which had a tendency to teach the children the difference between real numbers and representative characters, therefore the necessity of brass figures, as represented on the tablet; hence the children would call figure seven No. 1, it being but one object, and each figure they would only count as one, thus making 937, which are the representative characters, only three, which is the real fact, there being only three objects. It was therefore found necessary to teach the children that the figure seven would represent 7 ones, 7 tens, 7 hundreds, 7 thousands, or 7 millions, according to where it might be placed in connection with the other figures; and as this has already been described, I feel it unnecessary to enlarge upon the subject.



THE ARITHMETICON.

It will be seen that on the twelve parallel wires there are 144 balls, alternately black and white. By these the elements of arithmetic may be taught as follows:—

Numeration.—Take one ball from the lowest wire, and say units, one, two from the next, and say tens, two; three from the third, and say hundreds, three; four from the fourth, and say thousands, four; five from the fifth, and say tens of thousands, five; six from the sixth, and say hundreds of thousands, six; seven from the seventh, and say millions, seven; eight from the eighth, and say tens of millions, eight; nine from the ninth, and say hundreds of millions, nine; ten from the tenth, and say thousands of millions, ten; eleven from the eleventh, and say tens of thousands of millions, eleven; twelve from the twelfth, and say hundreds of thousands of millions, twelve.

The tablet beneath the balls has six spaces for the insertion of brass letters and figures, a box of which accompanies the frame. Suppose then the only figure inserted is the 7 in the second space from the top: now were the children asked what it was, they would all say, without instruction, "It is one." If, however, you tell them that an object of such a form stands instead of seven ones, and place seven balls together on a wire, they will at once see the use and power of the number. Place a 3 next the seven, merely ask what it is, and they will reply, "We don't know;" but if you put out three balls on a wire, they will say instantly, "O it is three ones, or three;" and that they may have the proper name they may be told that they have before them figure 7 and figure 3. Put a 9 to these figures, and their attention will be arrested: say, Do you think you can tell me what this is? and, while you are speaking, move the balls gently out, and, as soon as they see them, they will immediately cry out "Nine;" and in this way they may acquire a knowledge of all the figures separately. Then you may proceed thus: Units 7, tens 3; place three balls on the top wire and seven on the second, and say, Thirty-seven, as you point to the figures, and thirty-seven as you point to the balls. Then go on, units 7, tens, 3, hundreds 9, place nine balls on the top wire, three on the second, and seven on the third, and say, pointing to each, Nine hundred and thirty-seven. And so onwards.

To assist the understanding and exercise the judgment, slide a figure in the frame, and say, Figure 8. Q. What is this? A. No. 8. Q. If No. 1 be put on the left side of the 8, what will it be? A. 81. Q. If the 1 be put on the right side, then what will it be? A. 18. Q. If the figure 4 be put before the 1, then what will the number be? A. 418. Q. Shift the figure 4, and put it on the left side of the 8, then ask the children to tell the number, the answer is 184. The teacher can keep adding and shifting as he pleases, according to the capacity of his pupils, taking care to explain as he goes on, and to satisfy himself that his little flock perfectly understand him. Suppose figures 5476953821 are in the frame; then let the children begin at the left hand, saying, units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, thousands of millions. After which, begin at the right side, and they will say, Five thousand four hundred and seventy-six million, nine hundred and fifty-three thousand, eight hundred and twenty-one. If the children are practised in this way, they will soon learn numeration.

The frame was employed for this purpose long before its application to others was perceived; but at length I found we might proceed to

Addition.—We proceed as follows:—1 and 2 are 3, and 3 are 6, and 4 are 10, and 5 are 15, and 6 are 21, and 7 are 28, and 8 are 36, and 9 are 45, and 10 are 55, and 11 are 66, and 12 are 78.

Then the master may exercise them backwards, saying, 12 and 11 are 23, and 10 are 33, and 9 are 42, and 8 are 50, and 7 are 57, and 6 are 63, and 5 are 68, and 4 are 72, and 3 are 75, and 2 are 77, and 1 is 78, and so on in great variety.

Again: place seven balls on one wire, and two on the next, and ask them how many 7 and 2 are; to this they will soon answer, Nine: then put the brass figure 9 on the tablet beneath, and they will see how the amount is marked: then take eight balls and three, when they will see that eight and three are eleven. Explain to them that they cannot put underneath two figure ones which mean 11, but they must put 1 under the 8, and carry 1 to the 4, when you must place one ball under the four, and, asking them what that makes, they will say, Five. Proceed by saying, How much are five and nine? put out the proper number of balls, and they will say, Five and nine are fourteen. Put a four underneath, and tell them, as there is no figure to put the 1 under, it must be placed next to it: hence they see that 937 added to 482, make a total of 1419.

Subtraction may be taught in as many ways by this instrument. Thus: take 1 from 1, nothing remains; moving the first ball at the same time to the other end of the frame. Then remove one from the second wire, and say, take one from 2, the children will instantly perceive that only 1 remains; then 1 from 3, and 2 remain; 1 from 4, 3 remain; 1 from 5, 4 remain; 1 from 6, 5 remain; 1 from 7, 6 remain; 1 from 8, 7 remain; 1 from 9, 8 remain; 1 from 10, 9 remain; 1 from 11, 10 remain; 1 from 12, 11 remain.

Then the balls may be worked backwards, beginning at the wire containing 12 balls, saying, take 2 from 12, 10 remain; 2 from 11, 9 remain; 2 from 10, 8 remain; 2 from 9, 7 remain; 2 from 8, 6 remain; 2 from 7, 5 remain; 2 from 6, 4 remain; 2 from 5, 3 remain; 2 from 4, 2 remain; 2 from 3, 1 remains.

The brass figure should be used for the remainder in each case. Say, then, can you take 8 from 3 as you point to the figures, and they will say "Yes;" but skew them 3 balls on a wire and ask them to deduct 8 from them, when they will perceive their error. Explain that in such a case they must borrow one; then say take 8 from 13, placing 12 balls on the top wire, borrow one from the second, and take away eight and they will see the remainder is five; and so on through the sum, and others of the same kind.

In Multiplication, the lessons are performed as follows. The teacher moves the first ball, and immediately after the two balls on the second wire, placing them underneath the first, saying at the same time, twice one are two, which the children will readily perceive. We next remove the two balls on the second wire for a multiplier, and then remove two balls from the third wire, placing them exactly under the first two, which forms a square, and then say twice two are four, which every child will discern for himself, as he plainly perceives there are no more. We then move three on the third wire, and place three from the fourth wire underneath them saying, twice three are six. Remove the four on the fourth wire, and four on the fifth, place them as before and say, twice four are eight. Remove five from the fifth wire, and five from the sixth wire underneath them, saying twice five are ten. Remove six from the sixth wire, and six from the seventh wire underneath them and say, twice six are twelve. Remove seven from the seventh wire, and seven from the eighth wire underneath them, saying, twice seven are fourteen. Remove eight from the eighth wire, and eight from the ninth, saying, twice eight are sixteen. Remove nine on the ninth wire, and nine on the tenth wire, saying twice nine are eighteen. Remove ten on the tenth wire, and ten on the eleventh underneath them, saying, twice ten are twenty. Remove eleven on the eleventh wire, and eleven on the twelfth, saying, twice eleven are twenty-two. Remove one from the tenth wire to add to the eleven on the eleventh wire, afterwards the remaining ball on the twelfth wire, saying, twice twelve are twenty-four.

Next proceed backwards, saying, 12 times 2 are 24, 11 times 2 are 22, 10 times 2 are 20, &c.

For Division, suppose you take from the 144 balls gathered together at one end, one from each row, and place the 12 at the other end, thus making a perpendicular row of ones: then make four perpendicular rows of three each and the children will see there are 4 3's in 12. Divide the 12 into six parcels, and they will see there are. 6 2's in 12. Leave only two out, and they will see, at your direction, that 2 is the sixth part of 12. Take away one of these and they will see one is the twelfth part of 12, and that 12 1's are twelve.

To explain the state of the frame as it appears in the cut, we must first suppose that the twenty-four balls which appear in four lots, are gathered together at the figured side: when the children will see there are three perpendicular 8's, and as easily that there are 8 horizontal 3's. If then the teacher wishes them to tell how many 6's there are in twenty-four, he moves them out as they appear in the cut, and they see there are four; and the same principle is acted on throughout.

The only remaining branch of numerical knowledge, which consists in an ability to comprehend the powers of numbers, without either visible objects or signs—is imparted as follows:

Addition.

One of the children is placed before the gallery, and repeats aloud, in a kind of chaunt, the whole of the school repeating after him; One and one are two; two and one are three; three and one are four, &c. up to twelve.

Two and two are four; four and two are six; six and two are eight, &c. to twenty-four.

Three and three are six; six and three are nine; nine and three are twelve, &c. to thirty-six.

Subtraction.

One from twelve leaves eleven; one from eleven leaves ten, &c.

Two from twenty-four leave twenty-two; two from twenty-two leave twenty, &c.

Multiplication.

Twice one are two; twice two are four, &c. &c. Three times three are nine, three times four are twelve, &c. &c.

Twelve times two are twenty-four; eleven times two are twenty-two, &c. &c.

Twelve times three are thirty-six; eleven times three are thirty-three, &c. &c. until the whole of the multiplication table is gone through.

Division.

There are twelve twos in twenty-four.—There are eleven twos in twenty-two, &c. &c. There are twelve threes in thirty-six, &c. There are twelve fours in forty-eight, &c. &c.

Fractions.

Two are the half (1/2) of four. " " " third (1/3) of six. " " " fourth (1/2) of eight. " " " fifth (1/5) of ten. " " " sixth (1/6) of twelve. " " " seventh (1/7) of fourteen. " " " twelfth (1/12) of twenty-four; two are the eleventh (1/11) of twenty-two, &c. &c.

Three are the half (1/2) of six. " " " third (1/3) of nine. " " " fourth (1/4) of twelve.

Three are the twelfth (1/12) of thirty-six; three are the eleventh (1/11) of thirty-three, &c. &c.

Four are the half (1/2) of eight, &c.

In twenty-three are four times five, and three-fifths (3/5) of five; in thirty-five are four times eight, and three-eighths (3/8) of eight.

In twenty-two are seven times three, and one-third (1/3) of three.

In thirty-four are four times eight, and one-fourth (1/4) of eight.

The tables subjoined are repeated by the same method, each section being a distinct lesson. To give an idea to the reader, the boy in the rostrum says ten shillings the half (1/2) of a pound; six shillings and eightpence one-third (1/3) of a pound, &c.

Sixpence the half (1/2) of a shilling, &c. Always remembering, that whatever the boy says in the rostrum, the other children must repeat after him, but not till the monitor has ended his sentence; and before the monitor delivers the second sentence, he waits till the children have concluded the first, they waiting for him, and he for them; this prevents confusion, and is the means of enabling persons to understand perfectly what is going on in the school.

In a book lately published, which is a compilation by two London masters, it is stated, in the preface, that they were at a loss for proper lessons: had they used those in existence I cannot help thinking they were enough for the capacity of children under six years of age.

254 ARITHMETICAL TABLES.

Numeration, Addition, Subtraction, Multiplication, Division, and Pence Tables.

- ADDITION AND SUBTRACTION TABLE 1 & 2 & 3 & 4 & 5 & 6 & 1 are 2 1 are 3 1 are 4 1 are 5 1 are 6 1 are 7 2 3 2 4 2 5 2 6 2 7 2 8 3 4 3 5 3 6 3 7 3 8 3 9 4 5 4 6 4 7 4 8 4 9 4 10 5 6 5 7 5 8 5 9 5 10 5 11 6 7 6 8 6 9 6 10 6 11 6 12 7 8 7 9 7 l0 7 11 7 12 7 13 8 9 8 10 8 11 8 12 8 13 8 14 9 10 9 11 9 12 9 13 9 14 9 15 10 11 10 12 10 13 10 14 10 15 10 16 11 l2 11 13 11 14 11 15 11 16 11 17 l2 13 12 14 12 14 12 16 12 17 l2 18 - 7 & 8 & 9 & 10 & 11 & 12 & 1 are 8 1 are 9 1 are 10 1 are 11 1 are 12 1 are 13 2 9 2 10 2 11 2 12 2 13 2 14 3 10 3 11 3 12 3 13 3 14 3 15 4 11 4 12 4 13 4 14 4 15 4 16 5 12 5 13 5 14 5 15 5 16 5 17 6 13 6 14 6 15 6 16 6 17 6 18 7 14 7 15 7 16 7 17 7 18 7 19 8 15 8 16 8 17 8 18 8 19 8 20 9 16 9 17 9 18 9 19 9 20 9 21 10 17 10 18 10 19 10 20 10 21 10 22 11 l8 11 19 11 20 11 21 11 22 11 23 12 19 12 20 11 21 l2 22 12 23 12 24 =================================================================== MULTIPLICATION AND DIVISION TABLE. NUMERATION TABLE. - 2 2 are 4 4 5 are 20 6 12 are 72 1 Units. 3 6 6 24 7 7 49 21 Tens. 4 8 7 28 8 56 321 Hundreds 5 10 8 32 9 63 4,321 Thousands. 6 12 9 36 10 70 54,321 X of Thousands. 7 14 10 40 11 77 654,321 C of Thousands. 8 16 11 44 12 84 7,654,321 Millions. 9 18 12 48 8 8 64 87,654,321 X of Millions. 10 20 5 5 25 9 72 987,654,321 C of Millions. 11 22 6 30 10 80 =========================== 12 24 7 35 11 88 3 3 9 8 40 12 96 PENCE TABLE 4 12 9 45 9 9 81 5 15 10 50 10 90 - 6 18 11 55 11 99 d. s. d. d. s. d. 7 21 12 60 12 108 20 is 1 8 90 is 7 6 8 24 6 6 36 10 10 100 30 2 6 100 8 4 9 27 7 42 11 110 40 3 4 110 9 2 10 30 8 48 12 120 50 4 2 120 10 0 11 33 9 54 11 11 121 60 5 0 130 10 10 12 36 10 60 12 132 70 5 10 140 11 8 4 4 16 11 66 12 12 144 80 6 8 144 12 0 -

Tables of Weights and Measures.

Shilling Tables

s. l. s. 20 are 1 0 30 —— 1 10 40 —— 2 0 50 —— 2 10 60 —— 3 0 70 —— 3 10 80 —— 4 0 90 —— 4 10 100 are 5 0 110 —- 5 10 120 —- 6 0 130 —- 6 10 140 —- 7 0 150 —- 7 10 160 —- 8 0 170 —- 8 10

* * * * *

Practice Tables.

* * * * *

Of a Pound.

s. d. 10 0 are half 6 8 —- third 5 0 —- fourth 4 0 —- fifth 3 4 —- sixth 2 6 —- eighth 1 8 —- twelfth 1 0 —- twentieth

Of a shilling.

6d. are half 4 —- third 3 —- fourth 2 —- sixth 1 —- twelfth

* * * * *

Time.

60 seconds 1 minute 60 minutes 1 hour 24 hours 1 day 7 days 1 week 4 weeks 1 lunar month 12 cal. mon. 1 year 13 lunar months, 1 day, 6 hours, or 365 days, 6 hours, 1 year.

Thirty days hath September, April, June, and November; All the rest have thirty-one, Save February, which alone Hath twenty-eigth, except Leap year, And twenty-nine is then its share.

* * * * *

Troy Weight.

24 grains 1 pennywt. 20 pennywhts. 1 ounce 12 ounces 1 pound

* * * * *

Avoirdupoise Weight.

16 drams 1 ounce 16 ounces 1 pound 28 pounds 1 quarter 4 quarters 1 hund. wt. 20 hund. wt. 1 ton

* * * * *

Apothecaries Weight.

20 grains 1 scruple 3 scruples 1 dram 8 drams 1 ounce 12 ounces 1 pound

* * * * *

Wool Weight.

7 pounds 1 clove 2 cloves 1 stone 2 stones 1 tod 61/2 tods 1 wey 2 weys 1 sack 12 sacks 1 last

* * * * *

Wine Measure.

2 pints 1 quart 4 quarts 1 gallon 10 gallons 1 ank. brandy 42 gallons 1 tierce 63 gallons 1 hogshead 84 gallons 1 puncheon 2 hogsheads 1 pipe 2 pipes 1 ton

* * * * *

Ale and Beer Measure. 2 pints 1 quart 4 quarts 1 gallon 8 gallons 1 firkin of ale 9 gallons 1 firk. of beer 2 firkins 1 kilderkin 2 kilderkins 1 barrel 14 barrel 1 hogshead 2 barrels 1 puncheon 3 barrels 1 butt

* * * * *

Coal Measure.

4 pecks 1 bushel 9 bushels 1 vat or strike 3 bushels 1 sack 12 sacks 1 chaldron 91 chaldron 1 score

* * * * *

Dry Measure.

2 pints 1 quart 2 quarts 1 pottle 2 pottles 1 gallon 2 gallons 1 peck 4 pecks 1 bushel 2 bushels 1 strike 5 bushels 1 sack flour 8 bushels 1 quarter 5 quarters 1 wey or load 5 pecks 1 bushl. water measure 4 bushels 1 coom 10 cooms 1 wey 2 weys 1 last corn

* * * * *

Solid or Cubic Measure.

1728 inches 1 foot 27 feet 1 yard or load

* * * * *

Long Measure.

3 barleycorns 1 inch 12 inches 1 foot 3 feet 1 yard 6 feet 1 fathom 51/2 yards 1 pole or rod 40 poles 1 furlong 8 furlongs 1 mile 3 miles 1 league 20 leagues 1 degree

* * * * *

Cloth Measure.

24 inches 1 nail 4 nails 1 quarter 4 quarters 1 yard 5 quarters 1 English ell 3 quarters 1 Flemish ell 6 quarters 1 French ell

* * * * *

Land or Square Measure.

144 inches 1 foot 9 feet 1 yard 303/4 yards 1 pole 40 poles 1 rood 4 roods 1 acre 640 acres 1 mile

This includes length and breadth.

* * * * *

Hay.

36 pounds 1 truss of straw 56 pounds 1 do. of old hay 60 pounds 1 do. of new hey 36 trusses 1 load

MONEY.

Two farthings one halfpenny make, A penny four of such will take; And to allow I am most willing That twelve pence always make a shilling; And that five shillings make a crown, Twenty a sovereign, the same as pound. Some have no cash, some have to spare— Some who have wealth for none will care. Some through misfortune's hand brought low, Their money gone, are filled with woe, But I know better than to grieve; If I have none I will not thieve; I'll be content whate'er's my lot, Nor for misfortunes care a groat. There is a Providence whose care And sovereign love I crave to share; His love is gold without alloy; Those who possess't have endless joy.

TIME OR CHRONOLOGY.

Sixty seconds make a minute; Time enough to tie my shoe Sixty minutes make an hour; Shall it pass and nought to do?

Twenty-four hours will make a day Too much time to spend in sleep, Too much time to spend in play, For seven days will end the week,

Fifty and two such weeks will put Near an end to every year; Days three hundred sixty-five Are the whole that it can share.

Saving leap year, when one day Added is to gain lost time; May it not be spent in play, Nor in any evil crime.

Time is short, we often say; Let us, then, improve it well; That eternally we may Live where happy angels dwell.

AVOIRDUPOISE WEIGHT.

Sixteen drachms are just an ounce, As you'll find at any shop; Sixteen ounces make a pound, Should you want a mutton chop.

Twenty-eight pounds are the fourth Of an hundred weight call'd gross; Four such quarters are the whole Of an hundred weight at most.

Oh! how delightful, Oh! how delightful, Oh! how delightful, To sing this rule.

Twenty hundreds make a ton; By this rule all things are sold That have any waste or dross And are bought so, too, I'm told.

When we buy and when we sell, May we always use just weight; May we justice love so well To do always what is right.

Oh! how delightful, &c., &c., &c.

APOTHECARIES' WEIGHT.

Twenty grains make a scruple,—some scruple to take; Though at times it is needful, just for our health's sake; Three scruples one drachm, eight drachms make one ounce, Twelve ounces one pound, for the pestle to pounce.

By this rule is all medicine mix'd, though I'm told By Avoirdupoise weight 'tis bought and 'tis sold. But the best of all physic, if I may advise, Is temperate living and good exercise.

DRY MEASURE.

Two pints will make one quart Of barley, oats, or rye; Two quarts one pottle are, of wheat Or any thing that's dry.

Two pottles do one gallon make, Two gallons one peck fair, Four pecks one bushel, heap or brim, Eight bushels one quarter are.

If, when you sell, you give Good measure shaken down, Through motives good, you will receive An everlasting crown.

ALE AND BEER MEASURE.

Two pints will make one quart, Four quarts one gallon, strong:— Some drink but little, some too much,— To drink too much is wrong.

Eight gallons one firkin make, Of liquor that's call'd ale Nine gallons one firkin of beer, Whether 'tis mild or stale.

With gallons fifty-four A hogshead I can fill: But hope I never shall drink much, Drink much whoever will.

WINE, OIL, AND SPIRIT MEASURE.

Two pints will make one quart Of any wine, I'm told: Four quarts one gallon are of port Or claret, new or old.

Forty-two gallons will A tierce fill to the bung: And sixty-three's a hogshead full Of brandy, oil, or rum.

Eighty-four gallons make One puncheon fill'd to brim, Two hogsheads make one pipe or butt, Two pipes will make one tun.

A little wine within Oft cheers the mind that's sad; But too much brandy, rum, or gin, No doubt is very bad.

From all excess beware, Which sorrow must attend; Drunkards a life of woe must share,— When time with them shall end.

The arithmeticon, I would just remark, may be applied to geometry. Round, square, oblong, &c. &c., may be easily taught. It may also be used in teaching geography. The shape of the earth may be shewn by a ball, the surface by the outside, its revolution on its axis by turning it round, and the idea of day and night may be given by a ball and a candle in a dark-room.

As the construction and application of this instrument is the result of personal, long-continued, and anxious effort, and as I have rarely seen a pirated one made properly or understood, I may express a hope that whenever it is wanted either for schools or nurseries, application will be made for it to my depot.

I have only to add, that a board is placed at the back to keep the children from seeing the balls, except as they are put out; and that the brass figures at the side are intended to assist the master when he is called away, so that he may see, on returning to the frame, where he left off.

The slightest glance at the wood-cut will shew how unjust the observations of the writer of "Schools for the Industrious Classes, or the Present State of Education amongst the Working People of England," published under the superintendance of the Central Society of Education, are, where he says, "We are willing to assume that Mr. Wilderspin has originated some improvements in the system of Infant School education; but Mr. Wilderspin claims so much that many persons have been led to refuse him that degree of credit to which he is fairly entitled. For example, he claims a beneficial interest in an instrument called the Arithmeticon, of which he says he was the inventor. This instrument was described in a work on arithmetic, published by Mr. Friend forty years ago. The instrument is, however, of much older date; it is the same in principle as the Abacus of the Romans, and in its form resembles as nearly as possible the Swanpan of the Chinese, of which there is a drawing in the Encyclopaedia Brittanica. Mr. Wilderspin merely invented the name." Now, I defy the writer of this to prove that the Arithmeticon existed before I invented it. I claim no more than what is my due. The Abacus of the Romans is entirely different; still more so is the Chinese Swanpan; if any person will take the trouble to look into the Encyclopaedia Britannica, they will see the difference at once, although I never heard of either until they were mentioned in the pamphlet referred to. There are 144 balls on mine, and it is properly simplified for infants with the addition of the tablet, which explains the representative characters as well as the real ones, which are the balls.

I have not yet heard what the Central Society have invented; probably we shall soon hear of the mighty wonders performed by them, from one end of the three kingdoms to the other. Their whole account of the origin of the Infant System is as partial and unjust as it possibly can be. Mr. Simpson, whom they quote, can tell them so, as can also some of the committee of management, whose names I see at the commencement of the work. The Central Society seem to wish to pull me down, as also does the other society to whom reference is made is the same page of which I complain; and I distinctly charge both societies with doing me great injustice; the society complains of my plans without knowing them, the other adopts them without acknowledgment, and both have sprung up fungus-like, after the Infant System had been in existence many years, and I had served three apprenticeships to extend and promote it, without receiving subscriptions or any public aid whatever. It is hard, after a man has expended the essence of his constitution, and spent his children's property for the public good, in inducing people to establish schools in the principal towns in the three kingdoms,—struck at the root of domestic happiness, by personally visiting each town, doing the thing instead of writing about it—that societies of his own countrymen should be so anxious to give the credit to foreigners. Verily it is most true that a Prophet has no honour in his own country. The first public honour I ever received was at Inverness, in the Highlands of Scotland, the last was by the Jews in London, and I think there was a space of about twenty years between each.



CHAPTER XIII.

FORM, POSITION, AND SIZE.

Method of instruction, geometrical song—Anecdotes—Size—Song measure—Observations.

* * * * *

"Geometry is eminently serviceable to improve and strengthen the intellectual faculties."—Jones.

* * * * *

Among the novel features of the Infant School System, that of geometrical lessons is the most peculiar. How it happened that a mode of instruction so evidently calculated for the infant mind was so long overlooked, I cannot imagine; and it is still more surprising that, having been once thought of, there should be any doubt as to its utility. Certain it is that the various forms of bodies is one of the first items of natural education, and we cannot err when treading in the steps of Nature. It is undeniable that geometrical knowledge is of great service in many of the mechanic arts, and, therefore, proper to be taught children who are likely to be employed in some of those arts; but, independently of this, we cannot adopt a better method of exciting and strengthening their powers of observation. I have seen a thousand instances, moreover, in the conduct of the children, which have assured me, that it is a very pleasing as well as useful branch of instruction. The children, being taught the first elements of form, and the terms used to express the various figures of bodies, find in its application to objects around them an inexhaustible source of amusement. Streets, houses, rooms, fields, ponds, plates, dishes, tables; in short, every thing they see calls for observation, and affords an opportunity for the application of their geometrical knowledge. Let it not, then, be said that it is beyond their capacity, for it is the simplest and most comprehensible to them of all knowledge;—let it not be said that it is useless, since its application to the useful arts is great and indisputable; nor is it to be asserted that it is unpleasing to them, since it has been shewn to add greatly to their happiness.

It is essential in this, as in every other branch of education, to begin with the first principles, and proceed slowly to their application, and the complicated forms arising therefrom. The next thing is to promote that application of which we have before spoken, to the various objects around them. It is this, and this alone, which forms the distinction between a school lesson and practical knowledge; and so far will the children be found from being averse from this exertion, that it makes the acquirement of knowledge a pleasure instead of a task. With these prefatory remarks I shall introduce a description of the method I have pursued, and a few examples of geometrical lessons.

We will suppose that the whole of the children are seated in the gallery, and that the teacher (provided with a brass instrument formed for the purpose, which is merely a series of joints like those to a counting-house candlestick, from which I borrowed the idea,[A] and which may be altered as required, in a moment,) points to a straight line, asking, What is this? A. A straight line. Q. Why did you not call it a crooked line? A. Because it is not crooked, but straight. Q. What are these? A. Curved lines. Q. What do curved lines mean? A. When they are bent or crooked. Q. What are these? A. Parallel straight lines. Q. What does parallel mean? A. Parallel means when they are equally distant from each other in every part. Q. If any of you children were reading a book. that gave an account of some town which had twelve streets, and it is said that the streets were parallel, would you understand what it meant? A. Yes; it would mean that the streets were all the same way, side by side, like the lines which we now see. Q. What are those? A. Diverging or converging straight lines. Q. What is the difference between diverging and converging lines and parallel lines? A. Diverging or converging lines are not at an equal distance from each other, in every part, but parallel lines are. Q. What does diverge mean? A. Diverge means when they go from each other, and they diverge at one end and converge at the other.[B] Q. What does converge mean? A. Converge means when they come towards each other. Q. Suppose the lines were longer, what would be the consequence? A. Please, sir, if they were longer, they would meet together at the end they converge. Q. What would they form by meeting together? A. By meeting together they would form an angle. Q. What kind of an angle? A. An acute angle? Q. Would they form an angle at the other end? A. No; they would go further from each other. Q. What is this? A. A perpendicular line. Q. What does perpendicular mean? A. A line up straight, like the stem of some trees. Q. If you look, you will see that one end of the line comes on the middle of another line; what does it form? A. The one which we now see forms two right angles. Q. I will make a straight line, and one end of it shall lean on another straight line, but instead of being upright like the perpendicular line, you see that it is sloping. What does it form? A. One side of it is an acute angle, and the other side is an obtuse angle. Q. Which side is the obtuse angle? A. That which is the most open. Q. And which is the acute angle? A. That which is the least open. Q. What does acute mean? A. When the angle is sharp. Q. What does obtuse mean? A. When the angle is less sharp than the right angle. Q. If I were to call any one of you an acute child, would you know what I meant? A. Yes, sir; one that looks out sharp, and tries to think, and pays attention to what is said to him; and then you would say he was an acute child.

[Footnote b: Mr. Chambers has been good enough to call the instrument referred to, a gonograph; to that name I have no objection.]

[Footnote B: Desire the children to hold up two fingers, keeping them apart, and they will perceive they diverge at top and converge at bottom.]

Equi-lateral Triangle.

Q. What is this? A. An equi-lateral triangle. Q. Why is it called equi-lateral? A. Because its sides are all equal. Q. How many sides has it? A. Three sides. Q. How many angles has it? A. Three angles. Q. What do you mean by angles? A. The space between two right lines, drawn gradually nearer to each other, till they meet in a point. Q. And what do you call the point where the two lines meet? A. The angular point. Q. Tell me why you call it a tri-angle. A. We call it a tri-angle because it has three angles. Q. What do you mean by equal? A. When the three sides are of the same length. Q. Have you any thing else to observe upon this? A. Yes, all its angles are acute.

Isoceles Triangle.

Q. What is this? A. An acute-angled isoceles triangle. Q. What does acute mean? A. When the angles are sharp. Q. Why is it called an isoceles triangle? A. Because only two of its sides are equal. Q. How many sides has it? A. Three, the same as the other. Q. Are there any other kind of isoceles triangles? A. Yes, there are right-angled and obtuse-angled.

[Here the other triangles are to be shewn, and the master must explain to the children the meaning of right-angled and obtuse-angled.]

Scalene Triangle.

Q. What is this? A. An acute-angled scalene triangle. Q. Why is it called an acute-angled scalene triangle? A. Because all its angles are acute, and its sides are not equal. Q. Why is it called scalene? A. Because it has all its sides unequal. Q. Are there any other kind of scalene triangles? A. Yes, there is a right-angled scalene triangle, which has one right angle. Q. What else? A. An obtuse-angled scalene triangle, which has one obtuse angle. Q. Can an acute triangle be an equi-lateral triangle? A. Yes, it may be equilateral, isoceles, or scalene. Q. Can a right-angled triangle, or an obtuse-angled triangle, be an equilateral? A. No; it must be either an isoceles or a scalene triangle.

Square.

Q. What is this? A. A square. Q. Why is it called a square? A. Because all its angles are right angles, and its sides are equal. Q. How many angles has it? A. Four angles. Q. What would it make if we draw a line from one angle to the opposite one? A. Two right-angled isoceles triangles. Q. What would you call the line that we drew from one angle to the other? A. A diagonal. Q. Suppose we draw another line from the other two angles. A. Then it would make four triangles.

Pent-agon.

Q. What is this? A. A regular pentagon. Q. Why is it called a pentagon? A. Because it has five sides and five angles. Q. Why is it called regular? A. Because its sides and angles are equal. Q. What does pentagon mean? A. A five-sided figure. Q. Are there any other kinds of pentagons? A. Yes, irregular pentagons? Q. What does irregular mean? A. When the sides and angles are not equal.

Hex-agon.

Q. What is this? A. A hexagon. Q. Why is it called a hexagon? A. Because it has six sides and six angles. Q. What does hexagon mean? A. A six-sided figure. Q. Are there more than one sort of hexagons? A. Yes, there are regular and irregular. Q. What is a regular hexagon? A. When the sides and angles are all equal. Q. What is an irregular hexagon? A. When the sides and angles are not equal.

Hept-agon.

Q. What is this? A. A regular heptagon. Q. Why is it called a heptagon? A. Because it has seven sides and seven angles. Q. Why is it called a regular heptagon? A. Because its sides and angles are equal. Q. What does a heptagon mean? A. A seven-sided figure. Q. What is an irregular heptagon? A. A seven-sided figure, whose sides are not equal.

Oct-agon.

Q. What is this? A. A regular octagon. Q. Why is it called a regular octagon? A. Because it has eight sides and eight angles, and they are all equal. Q. What does an octagon mean? A. An eight-sided figure. Q. What is an irregular octagon? A. An eight-sided figure, whose sides and angles are not all equal. Q. What does an octave mean? A. Eight notes in music.

Non-agon.

Q. What is this? A. A nonagon. Q. Why is it called a nonagon? A. Because it has nine sides and nine angles. Q. What does a nonagon mean? A. A nine-sided figure. Q. What is an irregular nonagon? A. A nine-sided figure whose sides and angles are not equal.

Dec-agon.

Q. What is this? A. A regular decagon. Q. What does a decagon mean? A. A ten-sided figure. Q. Why is it called a decagon? A. Because it has ten sides and ten angles, and there are both regular and irregular decagons.

Rect-angle or Oblong.

Q. What is this? A. A rectangle or oblong. Q. How many sides and angles has it? A. Four, the same as a square. Q. What is the difference between a rectangle and a square? A. A rectangle has two long sides, and the other two are much shorter, but a square has its sides equal.

Rhomb.

Q. What is this? A. A rhomb. Q. What is the difference between a rhomb and a rectangle? A. The sides of the rhomb are equal, but the sides of the rectangle are not all equal. Q. Is there any other difference? A. Yes, the angles of the rectangle are equal, but the rhomb has only its opposite angles equal.

Rhomboid.

Q. What is this? A. A rhomboid. Q. What is the difference between a rhomb and a rhomboid? A. The sides of the rhomboid are not equal, nor yet its angles, but the sides of the rhomb are equal.

Trapezoid.

Q. What is this. A. A trapezoid. Q. How many sides has it? A. Four sides and four angles, it has only two of its angles equal, which are opposite to each other.

Tetragon.

Q. What do we call these figures that have four sides. A. Tetragons, tetra meaning four. Q. Are they called by another name? A. Yes, they are called quadrilaterals, or quadrangles. Q. How many regular tetragons are among those we have mentioned? A. One, that is the square, all the others are irregular tetragons, because their sides and angles are not all equal. Q. By what name would you call the whole of the figures on this board? A. Polygons; those that have their sides and angles equal we would call regular polygons. Q. What would you call those angles whose sides were not equal? A. Irregular polygons, and the smallest number of sides a polygon can have is three, and the number of corners are always equal to the number of sides.

Ellipse or Oval.

Q. What is this? A. An ellipse or an oval. Q. What shape is the top or crown of my bat? A. Circular. Q. What shape is that part which comes on my forehead and the back part of my head? A. Oval.

The other polygons are taught the children in rotation, in the same simple manner, all tending to please and edify them.

The following is sung:—

Horizontal, perpendicular, Horizontal, perpendicular, Parallel, parallel, Parallel, lines, Diverging, converging, diverging lines, Diverging, converging, diverging lines.

Spreading wider, or expansion, Drawing nearer, or contraction, Falling, rising, Slanting, crossing, Convex, concave, curved lines, Convex, concave, curved lines.

Here's a wave line, there's an angle, Here's a wave line, there's an angle; An ellipsis, Or an oval, A semicircle half way round, Then a circle wheeling round.

Some amusing circumstances have occured from the knowledge of form thus acquired.

"D'ye ken, Mr. Wilderspin," said a child at Glasgow one day, "that we have an oblong table: it's made o' deal; four sides, four corners, twa lang sides, and twa short anes; corners mean angles, and angles mean corners. My brother ga'ed himsel sic a clink o' the eye against ane at hame; but ye ken there was nane that could tell the shape o' the thing that did it!"

A little boy was watching his mother making pan-cakes and wishing they were all done; when, after various observations as to their comparative goodness with and without sugar, he exclaimed, "I wonder which are best, elliptical pan-cakes or circular ones!" As this was Greek to the mother she turned round with "What d'ye say?" When the child repeated the observation. "Bless the child!" said the astonished parent, "what odd things ye are always saying; what can you mean by liptical pancakes? Why, you little fool, don't you know they are made of flour and eggs, and did you not see me put the milk into the large pan and stir all up together?" "Yes," said the little fellow, "I know what they are made of, and I know what bread is made of, but that is'nt the shape; indeed, indeed, mother, they are elliptical pan-cakes, because they are made in an elliptical frying-pan." An old soldier who lodged in the house, was now called down by the mother, and he decided that the child was right, and far from being what, in her surprize and alarm, she took him to be.

On another occasion a little girl had been taken to market by her mother, where she was struck by the sight of the carcasses of six sheep recently killed, and said, "Mother, what are these?" The reply was, "Dead sheep, dead sheep, don't bother." "They are suspended, perpendicular, and parallels," rejoined the child. "What? What?" was then the question. "Why, mother," was the child's answer, "don't you see they hang up, that's suspended; they are straight up, that's perpendicular; and they are at equal distances, that's parallel."

On another occasion a child came crying to school, at having been beaten for contradicting his father, and begged of me to go to his father and explain; which I did. The man received me kindly, and told me that he had beaten the child for insisting that the table which he pointed out was not round, which he repeated was against all evidence of the senses; that the child told him that if it was round, nothing would stand upon it, which so enraged him, that he thrashed him, as he deserved, and sent him off to school, adding, to be thus contradicted by a child so young, was too bad. The poor little fellow stood between us looking the picture of innocence combined with oppression, which his countenance fully developed, but said not a word. Under the said table there happened to be a ball left by a younger child. I took it up and kindly asked the man the shape of it? he instantly replied, "Round." "Then," said I, "is that table the same shape as the ball?" The man thought for a minute, and then said, "It is round-flat." I then explained the difference to him between the one and the other, more accurately, of course, than the infant could; and told him, as he himself saw a distinction, it was evident they were not both alike, and told him that the table was circular. "Ah!" said be, "that is just what the little one said! but I did not understand what circular meant; but now I see he is right." The little fellow was so pleased, that he ran to his father directly with delight. The other could not resist the parental impulse, but seized the boy and kissed him heartily.

The idea of size is necessary to a correct apprehension of objects. To talk of yards, feet, or inches, to a child, unless they are shown, is just as intelligible as miles, leagues, or degrees. Let there then be two five-feet rods, a black foot and a white foot alternately, the bottom foot marked in inches, and let there be a horizontal piece to slide up and down to make various heights. Thus, when the height of a lion, or elephant, &c. &c., is mentioned, it may be shown by the rod; while the girth may be exhibited by a piece of cord, which should always be ready. Long measure is taught as follows:

Take barley-corns of mod'rate length, And three you'll find will make an inch; Twelve inches make a foot;—if strength Permit; I'll leap it and not flinch. Three feet's a yard, as understood By those possess'd with sense and soul; Five feet and half will make a rood, And also make a perch or pole. Oh how pretty, wond'rously pretty, Every rule We learn at school Is wondrously pretty.

Forty such poles a furlong make, And eight such furlongs make a mile, O'er hedge, or ditch, or seas, or lake; O'er railing, fence, or gate, or stile. Three miles a league, by sea or land, And twenty leagues are one degree; Just four times ninety degrees a band Will make to girt the earth and sea. Oh how pretty, &c.

But what's the girth of hell or heaven? (No natural thought or eye can see,) To neither girth or length is given; 'Tis without space—Immensity. Still shall the good and truly wise, The seat of heaven with safety find; Because 'tis seen with inward eyes, The first resides within their mind. Oh how pretty, &c.

Whatever can be shewn by the rod should be, and I entreat teachers not to neglect this part of their duty. If the tables be merely learnt, the children will be no wiser than before.

Another anecdote may be added here, to shew that children even under punishment may think of their position with advantage. Doctor J., of Manchester, sent two of his children to an infant school, for the upper classes, and one of his little daughters had broken some rule in conjunction with two other little ladies in the same school; two of the little folks were placed, one in each corner of the room, and Miss J. was placed in the centre, when the child came home in the evening, Doctor J. enquired, "Well, Mary, how have you got on at school to day?" the reply was "Oh, papa, little Miss —— and Fanny ——, and I, were put out, they were put in the corners and I in the middle of the room, and there we all stood, papa, a complete triangle of dunces." The worthy doctor took great pleasure in mentioning this anecdote in company, as shewing the effect of a judicious cultivation of the thinking faculties.

In my peregrinations by sea and land, with infants, we have had some odd and amusing scenes. I sometimes have had infants at sea for several days and nights to the great amusement of the sailors: I have seen some of these fine fellows at times in fits of laughter at the odd words, as they called them, which the children used; at other times I have seen some of them in tears, at the want of knowledge, they saw in themselves; and when they heard the infants sing on deck, and explain the odd words by things in the ship, the sailors were delighted to have the youngsters in their berths, and no nurse could take better care of them than these noble fellows did.

I could relate anecdote after anecdote to prove the utility of this part of our system, but as it is now more generally in the training juvenile schools, and becoming better known, it may not be necessary, especially as the prejudice against it is giving way, and the public mind is better informed than it was on the subject, and moreover it must be given more in detail in the larger work on Juvenile Training or National Education.



CHAPTER XIV.

GEOGRAPHY.

Its attraction for children—Sacred Geography-Geographical song—and lesson on geography.

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"From sea to sea, from realm to realm I rove."—Tickell.

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Geography is to children a delightful study. We give some idea of it at an early period in infant schools, by singing, "London is the capital, the capital, the capital, London is the capital, the capital of England," and other capitals in the same way; and also by pictures of the costumes of the various people of the world. To teach the four quarters of the globe, we tell children the different points of the play-ground, and then send them to the eastern, western, northern, or southern quarters, as we please. A weathercock should also be placed at the top of the school, and every favourable day opportunities should be seized by the teachers to give practical instructions upon it.[A]

[Footnote A: If the lesson is on objects it will shew how children are taught the points of the compass, with which we find they are very much delighted, the best proof that can be given that it is not injurious to the faculties.]

Sacred geography is of great importance, and children are much pleased at finding out the spots visited by our Saviour, or the route of the apostle Paul.

THE EARTH.

The earth, on which we all now live, Is called a globe—its shape I'll give; If in your pocket you've a ball, You have it's shape,—but that's not all; For land and water it contains, And presently I'll give their names. The quarters are called, Africa, Europe, Asia, and America; These contain straits, oceans, seas, Continents, promontories, Islands, rivers, gulfs, or bays, Isthmusses, peninsulas,— Each divides or separates Nations, kingdoms, cities, states,— Mountains, forests, hills, and dales, Dreary deserts, rocks, and vales.

In forests, deserts, bills, and plains, Where feet have never trod, There still in mighty power, He reigns, An ever-present God.

THE CARDINAL POINTS.

The east is where the sun does rise Each morning, in the glorious skies; Full west he sets, or hides his head, And points to us the time for bed; He's in the south at dinner time; The north is facing to a line.

The above can be given as a gallery lesson, and it will at once be seen that it requires explanation: the explanation is given by the teacher in the same way as we have hinted at in former lessons, though for the sake of those teachers who may not be competent to do it, we subjoin the following:

Q. Little children what have we been singing about? A. The earth on which we live. Q. What is the earth called? A. A globe. Q. What is the shape of a globe? A. Round, like an orange. Q. Is the earth round, like an orange? A. Yes. Q. Does it always stand still? A. No, it goes round the sun. Q. How often does it go round the sun in a year? A. Once. Q. Does it go round anything else but the sun? A. Yes, round its own axis, in the same way as you turn the balls round on the wires of the arithmeticon. Q. What are these motions called? A. Its motion round the sun is called its annual or yearly motion. Q. What is its other motion called? A. Its diurnal or daily motion. Q. What is caused by its motion round the sun? A. The succession of summer, winter, spring, and autumn, which are called the four seasons, is caused by this. Q. What is caused by its daily motion round its own axis? A. Day and night. Q. Into what two principal things is this earth on which we live divided? A. Into land and water. Q. Into how many great parts is the globe divided? A. Into five. Q. Which are they? A. Europe, Asia, Africa, America, and Australia. Q. Which part do you live in? A. In Europe. Q. We sung that those great parts contained

Straits, oceans, seas, Continents, promontories, Islands, rivers, gulfs, or bays, Isthmusses, peninsulas.

Q. What is a strait? A. A narrow part of the sea joining one great sea to another. Q. What is an ocean? A. A very large sea. Q. What is a gulf or bay? A. A part of the sea running a long way into the land. Q. What is a continent? A. A very large tract of land. Q. What does a continent contain? A. Nations and kingdoms, such as England. Q. What more? A. Many cities and towns. Q. What more? A. Mountains. Q What are mountains? A. Very high steep places. Q. What more does a continent contain? A. Forests, hills, deserts, and valleys. Q. What is a forest? A. Many large trees growing over a great deal of the land is a forest. Q. What are hills? A. Parts of the ground which rise higher than the rest. Q. What is a desert? A. A part of the earth where nothing will grow, and which is covered with hot sand. Q. What is a valley? A. A part of the earth which is lower than the rest, with hills at each side. Q. Who made all that we have been speaking of? A. Almighty God.

I can remember the time when no national school in England possessed a map. It was thought dangerous to teach geography, as in fact anything but cramming the memory, and reading and writing. With regard to the reading I will say nothing as to how much was understood, explaining then, was out of the question. What a change have I lived to see!



CHAPTER XV.

PICTURES AND CONVERSATION.

Pictures—Religious instruction—Specimens of picture lessons on Scripture and natural history—other means of religious instruction—Effects of religious instruction—observation.

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"The parents of Dr. Doddridge brought him up in the early knowledge of religion. Before he could read, his mother taught him the histories of the Old and New Testament, by the assistance of some Dutch tiles in the chimney of the room where they usually sat; and accompanied her instructions with such wise and pious reflections, as make strong and lasting impressions upon his heart"—See his Life.[A]

[Footnote A: This gave me the idea of introducing Scripture pictures for the infants; and that they are successful can be vouched for by hundreds of teachers besides myself.]

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To give the children general information, it has been found advisable to have recourse to pictures of natural history, such as of birds, beasts, fishes, flowers, insects, &c., all of which tend to shew the glory of God; and as colours attract the attention of children as soon as any thing, they eagerly inquire what such a thing is, and this gives the teacher an opportunity of instructing them to great advantage; for when a child of his own free will eagerly desires to be informed, he is sure to profit by the information then imparted.

We use also pictures of public buildings, and of the different trades; by the former, the children acquire much information, from the explanations which are given to them of the use of buildings, in what year they were built, &c.; whilst by the latter, we are enabled to find out the bias of a child's inclination. Some would like to be shoemakers, others builders, others weavers, others brewers, &c.; in short it is both pleasing and edifying to hear the children give answers to the different questions. I remember one little boy, who said he should like to be a doctor; and when asked why he made choice of that profession in preference to any other, his answer was, "Because he should like to cure all the sick people." If parents did but study the inclinations of their children a little more, I humbly conceive, that there would be more eminent men in every profession than there are. It is great imprudence to determine what business children shall be of before their tempers and inclinations are well known. Every one is best in his own profession—and this should not be determined on rashly and carelessly.

But as it is possible that a person may be very clever in his business or profession, and yet not be a Christian, it has been thought necessary to direct the children's attention particularly to the Scriptures. Many difficulties lie in our way; the principal one arises not from their inability to read the Bible, nor from their inability to comprehend it, but from the apathy of the heart to its divine principles and precepts. Some parents, indeed, are quite delighted if their children can read a chapter or two in the Bible, and think that when they can do this, they have arrived at the summit of knowledge, without once considering whether they understand a single sentence of what they read, or whether, if they understand it, they feel its truth and importance. And how can it be expected that they should do either, when no ground-work has been laid at the time when they received their first impressions and imbibed their first ideas? Every one comes into the world without ideas, yet with a capacity to receive knowledge of every kind, and is therefore capable, to a certain extent, of becoming intelligent and wise. An infant would take hold of the most poisonous reptile, that might sting him to death in an instant; or attempt to stroke the lion with as little fear as he would the lamb; in short, he is incapable of distinguishing a friend from a foe. And yet so wonderfully is man formed by his adorable Creator, that he is capable of increasing his knowledge, and advancing towards perfection to all eternity, without ever being able to arrive at the summit.

I am the ardent friend of religious education, but what I thus denominate I must proceed to explain; because of the errors that abound on this subject. Much that bears the name is altogether unworthy of it. Moral and religious sentiments may be written as copies; summaries of truth, admirable in themselves, may be deposited in the memory; chapter after chapter too may be repeated by rote, and yet, after all, the slightest salutary influence may not be exerted on the mind or the heart. These may resemble "the way-side" in the parable, on which the fowls of the air devoured the corn as soon as it was sown; and hence those plans should be devised and pursued from which we may anticipate a harvest of real good. On these, however, my limits will only allow a few hints.

As soon as possible, I would have a distinction made between the form and power of religion; between the grimaces and long-facedness so injurious to multitudes, and that principle of supreme love to God which he alone can implant in the heart. I would exhibit too that "good will to man" which the gospel urges and inspires, which regards the human race apart from all the circumstances of clime, colour, or grade; and which has a special reference to those who are most necessitous. And how can this be done more hopefully than by inculcating, in dependence on the divine blessing, the history, sermons, and parables of our Lord Jesus Christ; and by the simple, affectionate, and faithful illustration and enforcement of other parts of holy writ? The infant system, therefore, includes a considerable number of Scripture lessons, of which the following are specimens:

JOSEPH AND HIS BRETHREN.

The following method is adopted:—The picture being suspended against the wall, and one class of the children standing opposite to it, the master repeats the following passages: "And Joseph dreamed a dream, and he told it to his brethren; and they hated him yet the more. And he said unto them, Hear, I pray you, the dream which I have dreamed; for behold, we were binding sheaves in the field, and lo! my sheaf arose and also stood upright; and behold, your sheaves stood round abort, and made obeisance to my sheaf."

The teacher being provided with a pointer will point to the picture, and put the following questions, or such as he may think better, to the children:

Q. What is this? A. Joseph's first dream. Q. What is a dream? A. When you dream, you see things during the time of sleep. Q. Did any of you ever dream any thing?

Here the children will repeat what they have dreamed; perhaps something like the following:—Please, sir, once I dreamed I was in a garden. Q. What did you see? A. I saw flowers and such nice apples. Q. How do you know it was a dream? A. Because, when I awoke, I found I was in bed.

During this recital the children will listen very attentively, for they are highly pleased to hear each other's relations. The master having satisfied himself that the children, in some measure, understand the nature of a dream, he may proceed as follows:—

Q. What did Joseph dream about first? A. He dreamed that his brother's sheaves made obeisance to his sheaf. Q. What is a sheaf? A. A bundle of corn. Q. What do you understand by making obeisance? A. To bend your body, which we call making a bow. Q. What is binding sheaves? A. To bind them, which they do with a band of twisted straw. Q. How many brothers had Joseph? A. Eleven. Q. What was Joseph's father's name? A. Jacob, he is also sometimes called Israel.

Master.—And it is further written concerning Joseph, that he dreamed yet another dream, and told it to his brethren, and said, Behold, I have dreamed a dream more; and behold the sun and moon and eleven stars made obeisance to me.

Q. What do you understand by the sun? A. The sun is that bright object in the sky which shines in the day-time, and which gives us heat and light. Q. Who made the sun? A. Almighty God. Q. For what purpose did God make the sun? A. To warm and nourish the earth and every thing upon it. Q. What do you mean by the earth? A. The ground on which we walk, and on which the corn, trees, and flowers grow. Q. What is it that makes them grow? A. The heat and light of the sun. Q. Does it require any thing else to make them grow? A. Yes; rain, and the assistance of Almighty God. Q. What is the moon? A. That object which is placed in the sky, and shines in the night, and appears larger than the stars. Q. What do you mean by the stars? A. Those bright objects that appear in the sky at night. Q. What are they? A. Some of them are worlds, and others are suns to give them light. Q. Who placed them there? A. Almighty God. Q. Should we fear and love him for his goodness? A. Yes; and for his mercy towards us. Q. Do you think it wonderful that God should make all these things? A. Yes. Q. Are there any more things that are wonderful to you? A. Yes;—

Where'er we turn our wondering eyes, His power and skill we see; Wonders on wonders grandly rise, And speak the Deity.

Q. Who is the Deity? A. Almighty God.

Nothing can be a greater error than to allow the children to use the name of God on every trifling occasion. Whenever it is necessary, it should, in my opinion, be commenced with Almighty, first, both by teacher and scholars. I am convinced, from what I have seen in many places, that the frequent repetition of his holy name has a very injurious effect.