intelligence is excited and cultivated, and this combined with the power of correct and ready expression. 'Language,' Pestalozzi observes, is the reflex of all the impressions which Nature's entire domain has made on the human race. Therefore I make use of it, and endeavour, by the guidance of its uttered sounds, to reproduce in the child the selfsame impressions which, in the human race, have occasioned and formed these sounds. Great is the gift of language! It gives to the child in one moment what Nature required thousands of years to give to man.' Compare these observations with the statement of Pestalozzi's opinions in p. 227, and mark how, in dealing with the relations of words and things, this profound but irresolute thinker fluctuated between the two great schools of thought which have divided the world since the days of Plato and Aristotle.

Secondly, with respect to Form. Pestalozzi invented a few of those simple mechanical appliances by which the eye and touch of babies are taught to distinguish between round and square, a process which we find thus magniloquently described: 'He learns the data of the science from the examination of geometrical solids.' Under the head of form he included writing, drawing, and geometry, holding that the basis of each of these requirements was the perception of shape and dimension. Drawing ought to be an universal accomplishment, because it leads the child from vague perceptions to clear ideas. The art of measuring must, however, precede that of drawing. 'If a child,' says he, 'is called upon to imitate objects before he has acquired a distinct notion of their proportions, his instructions in the art of drawing will fail to produce on his mental development the beneficial influence which alone makes it worth learning.' Then, again, writing, he contended, should be taught, not before, but after drawing, 'for writing is, in fact, a kind of linear drawing, and that of fixed forms, from which no arbitrary or fanciful deviations are permissible.'*

As to

are

the method of imparting the last of the three Pestalozzian 'elements,' namely, Number, he thus writes himself: The rudiments of number should always be taught by submitting to the eye of the child certain objects representing the units. A child can conceive the idea of "two balls," "two roses," "two books," but it cannot conceive the idea of "two" in the abstract.' To this Dr. Mayo adds: 'When the child has been thus exercised in distinguishing and naming "one," "two," "three," the number of the different objects presented, he will soon have an intuitive perception that the terms "one," "two," "three " always the same, while the objects, to which they are applied, vary; he will thus be prepared to separate the idea of number from that of the thing, and so ascend to the abstract idea. When he has a correct idea of the numbers up to ten, he is ready to carry on different combinations of these numbers. By practical examples, he learns to form rules for himself-he works his own way, acquiring power, vigour, and readiness at each advance; he is not led hoodwinked through the intricacies of arithmetic, but understands what he is about, first becoming acquainted with elements, and then enjoying the pleasure of finding the results of their various combinations. The whole is a reasonable

The principles of Pestalozzi's system of Geometrical instruction have been successfully and beautifully applied in The Lessons on Form' of Mr. Reiner, late of the Home and Colonial Training College.

exercise.' To conclude with a few words on the Pestalozzian method of teaching the elements of Latin, for which this seems to be the proper place. Dr. Mayo thus writes in one of the letters from which extracts were made in the last number: 'He does not begin with definitions, because children never comprehend them; but first, calling up the idea in the child's mind by conversing with him, he gives him the simple sentence "leo est animal." Here the words leo and animal, being, one almost the same, the other quite the same as those which express the same ideas in English, they readily enter the child's mind. From this he proceeds to an ape is what?""an animal." "Simia est-what?" "animal," the child using the word he had learned just before. Proceeding in this manner he stocks the child's mind with words, before he enters on the inflexions of those words, always endeavouring to link what the child has to learn with what he has already acquired. In the declensions he does not propose to the child "musa, a Muse, musæ, of a Muse "-words which cannot interest the child, because they represent only parts of ideas-but he involves the important word in sentences, thus: "rosa est flos amænissimus horti," 66 rose odor est suavis," etc., through all the cases The child having learned the inflexion of rosa has a similar word proposed to him, also enveloped in little sentences, but he is now required to find the termination. The advantages of this method are briefly these: you do not disgust the child with his first intellectual exertions, you exercise other faculties besides memory, you enrich his mind with a great number of ideas, and you furnish him with a copia verborum before you set him down to translate a classical author or to express his own ideas in a connected chain in the language.' He thus contrasts the above with the ordinary method of teaching language: 'In spite of every indication that the youthful mind spontaneously gives, that it is led from the perception of particulars to the conception of universal propositions-that it must first see embodied in realities and clothed with circumstances, the ideas which it is afterwards to recognise in their pure, abstract, intellectual form-the prevailing practice is forcibly to drive a child of tender years through the generalities of grammar, unintelligible and uninteresting to him, till at last in the course of their practical application, the true order of thought is established in his mind, and he understands and appreciates his grammar, through the knowledge which he derives. from studying the language itself.'

The ideas thus enunciated were developed with well-known success in Dr. Mayo's own Pestalozzian school at Cheam. They lie at the bottom of the 'Hamiltonian' method, and of the 'Mastery System' of Mr. Prendergast, which is daily commending itself more and more to the minds of educationalists, as the true, rational, and scientific method; and, backed by his able and persevering advocacy, bids fair to revolu tionize in the coming generation, the whole English system of teaching languages living and dead.

The foregoing is a very fragmentary and imperfect sketch of a subject on which volumes might be, and indeed have been, written-the methods of Pestalozzi. In the next and last article on his system, an attempt will be made to state and explain his principles.

(To be continued.)

PUBLIC curiosity was greatly excited on the occasion of the removal from my workshop to the school of the apparatus here illustrated. Two solemnlooking boys carried the large frame, tied to a pole borne on their shoulders, while two others walked by their side with the ropes, pulleys, screw, etc., round their necks. I brought up the rear. We all preserved the utmost gravity, while the giddy crowd of onlookers indulged in frivolous remarks. It is part of a bedstead,' said one; a profane vulgarity that caused me at once to adopt the Polyphemic stride peculiar to an elementary teacher when in deep thought. model of a sort of gallows for hanging Fenians,' said another; at which the small boy with the ropes about his neck looked all the innocent anguish of a man on his way to a cruel execution. When the little mournful procession arrived at the school the apparatus had to be deposited in one of the school lavatories, where it will remain when not in use, until the long-rumoured reduction of salaries takes place, when, of course, it will have to be sold, along with all the other accessories of science teaching that I have managed to get together.

'A

Probably some or my fellow-teachers have, like myself, one of their rooms fitted up as a workshop; of course I mean at their own private homes, not at the school. Those that have not I should advise to set about getting it at once. Some hard work at carpentering and the lathe will help to throw off the old and worn-out material of both body and mind. To those who possess a workshop the construction of this apparatus is easy. The outer frame is about four

and a half feet high, three feet wide, and is made of one-and-a half-inch-square pine, mortised at the corners, and let in at the bottom to a much stouter piece. To give it greater steadiness, iron brackets may be placed at the rear of the uprights at the base. The lever (Fig. 1) is of the same material as the sides of the frame, four and a half feet in length, of uniform thickness, and weighs exactly two pounds. It is marked off into equal distances, counting from each side of the centre C. When in use it rests upon the handle V (Fig. 2) as a fulcrum. The pulleys T and U are ordinary brass screw-pulleys: they can be bought at any ironmonger's. S, R, and Q are the same, but the threads of the screws are filed off, and the remaining short piece of iron heated and bent to form a hook. The cord from T to U passes through the frame for greater convenience in showing the running down of the weight P. Where the cord passes through the frame I have let in a small piece of brass piping jointed into iron plates on either side. Below Fare two of the commoner kinds of block pulleys. The sheaves (wheels) are brass, the frames iron, and other details steel. They are really beautiful pieces of engineering work, made by the father of one of the boys. It took him two weeks of evening work to complete them, and I could not prevail upon him to take a single halfpenny for his trouble. He is an engineer. If any teacher is not able to get this done so cheaply, he can easily make it himself if he has a

'slide-rest' to his lathe. At G is seen the wheel and axle. For the two-grooved wheel H get a piece of two-inch pine, cut it roughly round, and turn it up on the taper-screw chuck of the lathe. Let the larger wheel be eight inches in diameter, and the smaller one two inches. They are both in one piece, and are three-quarters of an inch thick. Turn the axle to one inch in diameter. For bearings, run on to each end of the axle a piece of brass piping half inch on the outside; fit into the frame pieces of iron piping half inch in the inside. One end of the axle runs through the centre of the wheel, into which it is fixed by a wooden peg through the smaller wheel. The whole should run easily. A pound weight, J, suspended by a cord passing round the large wheel, should exactly balance a weight, I, of eight pounds upon the axle. Fig. 3 is the inclined plane, removed, however, from its place on the apparatus in order to show the large screw W. When the plane is in use the screw W and the block X are removed; then the lower end, A5, of the plane is placed at Z, and the upper end, A4, rests upon the brass rod of which the handle is V. This brass rod may be inserted into any of the holes represented, and thus give various elevations to the plane. These holes, which are three inches apart from centre to centre, are drilled through iron plates screwed on to the uprights. The length of the plane is a little over three feet, and the height of the top hole one foot. The little carriage A6, which is to carry the weights to be drawn up the plane, weighs exactly one pound: it has four brass wheels upon steel axles. The wheels are grooved to run upon two lines of iron rails screwed down to the plane by this means there is so little friction that one penny piece at the end of a cord passing over the pulley, just above A 4, is sufficient to draw along the truck when the plane is level. A weight of five pounds placed in the truck should exactly balance a weight of two pounds at A 3 when the plane is in position, elevated to the top hole at V. At W (Fig. 2) I have arranged the screw. All that can be shown here is the enormous power gained by the use of this simple machine. It is an ordinary wooden bench-screw, which, with its block, can be bought at any ironmonger's. The block X slides easily backwards and forwards upon a smooth table that also serves to connect the lower part of the frame. The plain part of the screw near its shoulders Y turns in a pla'n bored hole in the fixed block Z. In actual working the shoulder is of course close up against this block. Looped on to the movable block X are two stout cords: these unite, and pass over the pulley A 1. Upon turning the handle or lever of the screw at Y the weight A 2 is raised. A little child has by means of this screw easily lifted one hundredweight. graduated rod or lever (Fig. 1) can also be used as a sale. If, for instance, it be placed against the upright on the right-hand side of the frame, it will mark the distance to which the weight P falls, and the height to which O is raised thus serving to illustrate that whatever gain there is in power is accompanied by a corresponding loss in distance.

The

The cost of materials for such an apparatus is about thirty shillings; but any school-furnishing firm would probably charge about five pounds for the complete machine.

I will now reproduce a lesson upon the Lever,' to illustrate the use of this contrivance.

Jones, come out here, and try to lift that cupboard. You can't move it? Well, place the end of this rod a little way under it; now put this little block of wood under the rod close up to the cupboard; press down the other end of the rod; be careful. You see, boys, the cupboard is now being tilted up. Have you ever seen men lifting heavy things in that way? Ans.—Yes, sir: I saw a man getting up the flagstones in that way. (Another boy)-I saw a grocer getting a large barrel

of

sugar into his shop in that way. Just so. Embery, you seem stronger than Jones; come here; put the iron under the cupboard as before. Now I will bring the block a little farther out away from the cupboard. Now try to lift it. What! can't you move it? Ans.-No, sir; I can't shift it; there is not enough handle. What do you mean by 'not enough handle'? Ans. (Embery) The distance from the block to my hand. is not enough. Very well, then alter it. Ah! don't overturn the cupboard. You see how easily he tilts it. Try to lift the cupboard without the rod. You can't do it. You see, therefore, what an advantage there is in using this rod; and what must you do to lift the weight the more easily? Ans.-Have a long handle. Very good. Now you say that the distance from the block to your hand is the handle: what do you call the distance from the block to the other end of the rod? You don't know? You want a name for it; well, I will give you one, and also names for the other parts of this simple machine. Here is the picture of such a rod, with the names of the parts written. The rod itself is called a 'lever;' the block is the 'fulcrum ;' the cupboard or whatever we want to lift we will call the 'weight;' the force you apply to lift it is the 'power;' the distance between the fulcrum and the power, which Embery called the handle, is the 'powerarm,' and that between the fulcrum and the weight is the 'weight-arm.' How much do you think that cupboard, with all the books and slates in it, weighs? Ans.

More than a hundredweight. Yes; I should think about two. Embery, do you think you could lift two hundredweight? Ans.-No, sir; not without that lever. (A boy)--He couldn't lift it with the lever at first. (Embery)-No, because there was not enough handle. (Teacher)-Don't say handle. (Embery)The power-arm was not long enough. Just so. Do you think these boys pressed the lever downwards with a force of two hundredweight? Ans.-No, sir; much less. And can you tell me exactly how much less? Ans. It depends upon how long the power-arm is. How do you know that? Ans. From trying it, and from our common sense. Exactly so. Now we will carry our common sense a little farther, and after making a few experiments with this apparatus, find out the true or scientific relationship between the various parts of that mechanical power called the lever. Howell, you come here; place this lever on that fulcrum. (Fig. I is placed on V.) Balance it. You see the lever is marked so that you can easily find the centre. Do you know the name of that balancing point? (A boy)-The centre of gravity. (Another boy)-You said the centre of gravity was somewhere in the middle of the earth. Yes; so the centre of gravity of the earth is. (Another boy)-You said everything had a centre of gravity. And so it has. The centre of gravity of that lever is just about where Howell has balanced it. Now, Howell, put a four-pound weight on the lever, say three distances from the fulcrum. Hold up the lever.

Smith, take this two-pound weight; put it on the other arm; see where it just balances. (Smith)-It balances now. How far is it from the fulcrum? Ans.-Six distances. Cox, come and write that on the blackboard. 'Two pounds six distances from the fulcrum balances four pounds three distances.' Now take the weights off. Dedden, you come out; place this sixpound weight one distance from the fulcrum. Drayson, see where you have to put this two-pound weight in order to maintain equilibrium. Here it is, sir, three distances from the fulcrum. Very good. Cox, write that on the board. 'Six pounds one distance balances two pounds three distances.' Just so. Now all go to your places. Look, boys. I place eight pounds on the lever two distances from the fulcrum: tell me where I must put this two pounds in order to balance. Ans.-Eight distances. You are right. You see how exactly it balances. I will write that on the board. I want you all now to look upon the blackboard. Think carefully of what we have done. Tell me whether, in these experiments, the results show a likeness in any respect. Ans.—Yes, sir: it's all the same thing. What do you mean, Richards, by 'all the same thing'? Ans. (Richards)-The arm that is shortest has the greatest weight. Very good. (Another boy) The smallest weight is always on the longest Yes; but that is almost the same as Richards has said. (Another boy)-If you call the arm on the left the weight-arm, and the one on the right the power-arm, then the weight is just as much greater than the power as the power-arm is greater than the weight-arm. (Howell)-If you multiply the weight by the weight-arm, it always equals the power multiplied by the power-arm. That's capital, Howell. Come out here, and show the boys that what you say is true. (Howell comes out greatly delighted.) In the first experiment four times three is the same as six times two; in the second, six times one equals twice three; in the third, eight times two equals twice eight. Very good. Now I want to write out these four quantities as a proportion: you can, I know, easily tell me how to do it, as you have lately heard a good deal about ratio and proportion. Ans. (Smith.)— The power is to the weight as the weight-arm is to the power-arm. Just so. I will write that on the board. P W :: w.-a. p.-a.'

arm.

STANDARD II.-(dictated : two sets). A (1) 67,894 × 85. Ans. 5,770,990. (2) 40,016÷7. Ans. 5716-4. (3) 41,302-34,067. Ans. 7235. B (1) 67,894 X 94. Ans. 6,382,036. (2) 40,016÷6. Ans. 6669 - 2. (3) 41,302 - 40,819. Ans. 483.

STANDARD III.

(1) If 198 nuts be divided equally among 7 boys and 11 girls, how many will each receive? Ans. 11.

STANDARD IV.

(1) Multiply nineteen pounds thirteen and eightpence halfpenny by 109. Ans. £2145 14s. 2d. (2) If a man's wages are 3s. 7d. a day, and a boy's IS. 3d. a day, how much will a farmer, who employs 8 men and 3 boys, pay per week of 6 days in wages? Ans. £9 14s. 6d. (3) Divide £18,907 4s. 10d. (given in words) by 84. Ans. £225 1s. 8d. – 64. (4) In 763,972 inches (words), how many miles, fur., yds., etc.? Ans. 12 m. o f. 101 yd. I ft. 4 in. (5) Subtract £12,907 17s. 6d. from £22,382 75. 101d. (words). Ans. £9474 10s. 3 d.

(7) Name an island south of England. (8) In what river is it?

(9) Other islands in the English Channel? (10) To which country are they the nearer ? (11) What is south of Wales?

(12) Through which English county does the Dee run?

(13) In what lake does it rise?

(14) Through which counties does the Wye run? (15) Where is the Isle of Man ?

(16) What separates Anglesea from the next county?

(17) What is the county on the other side of Menai Strait ?

(18) Name the highest mountain in that county. (19) What town stands on the Dee?

(20) Name seaports on or near the Bristol Channel. (21) What strait joins the English Channel with the North Sea?

(22) Name a town on Cardigan Bay. (23) On what river is Liverpool?

(24) Through what counties does the Thames flow? (25) What is Anglesea besides an island?

(26) What country is on the other side of the English Channel?

STANDARDS IV. TO VI.

(1) What is another name for Tasmania?
(2) Name the parts of Australia.
(3) What are they called?

(4) What is the chief town in Victoria ?
(5) What is the chief town in New South Wales?
(6) Chief river in Australia?

(7) Between what lakes are the Falls of Niagara ? (8) What is the largest river in North America? (9) Name the strait between Tasmania and Australia.

(10) How many islands form New Zealand? (11) Name a town in New Zealand.

(12) What do we get from there?

(13) Why do people go there?

(14) What is the distance of Australia from England ?

(15) What was Australia formerly called?

(16) Name some of our possessions on the west of Africa.

(17) Why not emigrate to that part?

(18) Name an island in the Pacific Ocean belonging to England.

(19) What do we get from Australia? (20) Where is Canada?

(21) How did we get it?

(22) When did we get it?

(23) Name the provinces in Canada.
(24) Name some towns in Canada.
(25) What is Nova Scotia?

(26) Where is it?

(27) Name a seaport of Nova Scotia.

(28) Name some lakes in Canada.

(29) What group of islands are east of Australia ? (30) How many islands form New Zealand? Name them.

(31) What do we get from Mauritius?

(32) Where is it?

(33) Name an island east of Africa belonging to England.

(34) Name an island in the Atlantic belonging to England.