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by 68 men; how many men, working at the same rate, could build a wall 32 feet high in 8 days?

SECT. V.-1. Give the meaning of the words fraction, integer, mixed number, and proper fraction. Subtract 73 from 85.

2. Reduce of a pound to the fraction of a penny; of a week to the fraction of an hour; of a yard to the fraction of a mile.

3. If oz. cost ., what will 1 oz. cost? 4. Divide 14 by '7854.

5. Reduce 19s. 54d. to the decimal of a pound. SECT. VI.-1. What is the interest of 477. 10s. for 4 years and 52 days, at 4 per cent?

2. A person invests 75007., and receives 23 per cent upon his investment; what is his rent?

3. By selling 26 yards at 3s. 44d. per yard, a draper gains 6s. 5d,; what was the prime cost per yard, and what is the gain per cent?

SCHOOL-MANAGEMENT.

1. Give a copy of your own time-table, and mention what means you employ to ascertain whether it is working well.

2. What faulty habits are boys most apt to contract when learning to write? How do you guard against them?

3. What expedients do you use to bring particular boys up to the rest of their class when they fall behind in penmanship?

4. Give a specimen of what you consider the most difficult kind of sum in subtraction, not

going beyond tens of thousands.

5. How do you prevent boys from forgetting numeration and notation while they are going on to higher rules?

6. What use can you make of the simultaneous method in teaching children to read? Describe a reading-lesson conducted on that method?

7. What lessons do you give to children to learn by heart? and why do you select those lessons in particular?

8. What lessons do you give to be prepared at home? Explain what principles should guide the teacher in setting such lessons. Point out their advantages?

9. How do you endeavour to secure (a) punctual attendance on each day, (b) regular attendance from day to day?

10. Do you give special instruction to your monitors? and if so, at what time? How do you superintend them when they are in charge of classes?

11. Do you make the same classification of your school for all subjects, or do you make one classification for arithmetic, another for reading, and so on? If the latter, state what is the ordinary number of your scholars, and the exact steps which are gone through in order to change the grouping of the scholars?

12. Describe the registers that you use? When and how do you fill them up? What is the use of keeping accurate registers?

13. Fill up the last column on the right hand, and the three lines at the bottom, in the following

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SCHOOL-MANAGEMENT.

For Students in Taining as Infant-School
Teachers.

1. Describe exactly the best shape and arrangements for a school of 120 infants.

2. What assistance would you require in teaching this number of infants? Show very precisely the way in which you would employ your assistants, and the means by which you would provide for their own instruction and training.

3. Describe very exactly and assign reasons

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seven years old? Show exactly at what special objects you aim in each of these exercises.

7. Describe the best apparatus for a playground, and the use for which each part of the apparatus is intended.

8. By what means do you propose to cultivate the senses of sight, hearing, and touch?

9. What are the chief difficulties in teaching children to articulate distinctly? By what means are those difficulties most effectually surmounted?

10. What combinations of letters are most easily learned? Upon what system do you propose to teach the elements of reading? Give reasons and examples.

11. Explain clearly the system on which you propose to teach arithmetic, and the progress which you would consider satisfactory in children between four and five, and between six and seven years old. Explain clearly the common rule for subtraction.

12. What is the best system of teaching the elements of geography? How would you explain the use of a map to young children?

13. What are the best subjects for collective lessons in the first division of a good infant-school?

14. Explain the different objects which you have in view in giving lessons upon some animal to two classes of children between three and four and between six and eight years old.

15. In what order are the mental faculties of children usually developed? By what lessons are the principal of these faculties best exercised?

16. Give a clear account of the substance of lectures which you have heard on causes affecting the health of children.

Extra Paper.

N.B. This paper contains three subjects (viz. geometry, algebra, and mechanics), one or other of which must be taught to male Pupil-teachers in the later years of their apprenticeship. Candidates are not permitted to answer questions in more than one of the three sections into which this paper is divided. No marks will be given for papers in which this direction is not observed.

No Pupil-teacher is allowed to commence apprenticeship with Masters who have neither obtained certificates nor passed for registration (including this paper).

Mistresses are not required to attempt this paper.

Masters declining this paper, but passing satisfactorily in others, will be accepted in fulfilment of the conditions of the Minute of 2d April 1853, and will not be disqualified to remain in charge of all Pupil-teachers apprenticed to them before 1st January 1855.

I.-EUCLID.

1. Define a plane rectilineal angle, and show how to bisect one, that is, to divide it into two equal angles.

2. Any two sides of a triangle are together greater than the third side.

Is the same proposition true of the angles of a triangle?

3. What is a parallelogram? Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the diagonal bisects it.

4. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts are together equal to the square of the whole line.

5. Describe a square that shall be equal to a given rectilineal figure.

6. When are circles said to touch one another? If one circle touch another internally, they have not the same centre.

7. The opposite angles of any quadilateral figure

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8. The head of a fish is 5 inches long; the body is as long as the head and tail together; and the tail is as long as the head and body together. What is the length of the fish?

III. MECHANICS AND MENSURATION. 1. If a door be 7 ft. 6 in. high, and 4 ft. 3 in. broad, what does it cost at 2s. 9d. per square foot?

2. Give a rule for finding the area of a trapezium.

What is the acreage of a field in the form of a trapezium, of which the diagonal is 1375 links, and the two perpendiculars on that diagonal from the opposite angles respectively 295 and 417 links?

3. The pit of a theatre is in the form of a semicircle, with a diameter of 58 feet: how many persons may be seated in it, allowing two square yards for every three seats?

4. How many cart-loads of clay will there be in a drain 90 ft. long, 2 ft. wide, and 3 feet deep, allowing 1 tons for each load, and assuming the weight of a cubic foot of clay to be 2160 ounces? 5. Describe the mechanical power called the "Wheel and Axle;" what advantage would be gained if the diameter of the wheel were 3 feet, and that of the axle 6 inches?

6. In the handle of a common pump the piston rod is fixed at a distance of 3 inches from the fulcrum, and a force of 90 lbs. is applied at a distance of 28 inches from the fulcrum: what is the force lifting the piston?

7. How is mechanical work estimated? Calculate the work done in raising a ton of coals from a pit 160 fathoms deep.

8. What is friction? If the friction on a railway be 8 lbs. per ton, at what uniform rate will a train of 90 tons be drawn, by an engine of 60 horse-power?

PAPERS AND CORRESPONDENCE.

[The Committee of the National Society are thankful for any communication likely to assist School-managers and Teachers, or otherwise promote the cause of Church Education; but they do not necessarily hold themselves responsible for the opinions of the Editor's correspondents.]

PUPIL-TEACHERS' OBLIGATIONS AND PROSPECTS.

The following is an Address to Pupil-teachers at the close of their apprenticeship, by Rev. Derwent Coleridge, M.A., Principal of St. Mark's College, Chelsea:

MY YOUNG FRIENDS,-You have now come to the end of your apprenticeship, and have to consider whether you will go on in the way of life for which you have to a certain extent been prepared-in plain terms, whether you wish, or at least are willing, to be a schoolmaster, or whether you mean to seek a livelihood in some other way. This is the most important question which, in all probability, you will ever be called upon to decide: if it is settled for you by the force of circumstances,—which is as much as to say, by the will of Providence,-do not regret this, rather make it an occasion of thankfulness; for then you will only have to do your duty, steadily, earnestly, and cheerfully, committing yourself to the guidance of your Heavenly Father: come what may, you will have no cause for self-reproach. But if, as more commonly happens, you have to make a choice, then you will do well to weigh the matter carefully, to seek for information, to listen to advice, and above all, to ask the help of God in prayer. If you make up your mind to be a schoolmaster, you will probably seek to enter a training college, as well for the advantage of further instruction, as that you may obtain a Government certificate; but before you take this step, you are bound, as a point of duty, to consider the obligations which you will incur; and ought, as a matter of prudence, to consider the prospect which it will open to you. And first, what will be your obligations?

You will, in the first place, bind yourself to follow the calling of a schoolmaster, unless prevented by ill-health, or by other circumstances beyond your own control. Before you enter a training college, you are free to make a choice. You have done your work, and have received your wages. There is no claim against you for further service, and you have no claim for any further payment. It matters not whether you consider yourself to have been well-paid, or ill-paid; whether you could have earned more or less in any other situation; whether you would have been better off, or not so well, had you not been a pupil-teacher. You have had all that was promised, and have done no more than you agreed to do. The advantages offered to a pupil-teacher in a good school are indeed very considerable, the annual stipend being the least part of his remuneration; but whether these advantages have been greater or less, whether they have been improved by diligence and good conduct, or lost by negligence or incompetence, the bargain is now closed. You must look for nothing more, except the opportunity of entering a training college, and so turning to the best account the skill and experience which you have already gained as a teacher. If you resolve to avail yourself of this opportunity, and present yourself as a candidate for admission into a training college, you do in fact renew your engagement. A large sum of money, supplied partly by the Government, partly from charitable sources, will now be spent upon your maintenance and education, in order to fit you for the calling of a schoolmaster; and you cannot, without gross dishonesty, make use of this money, or of

the advantages which it procures, for any other object than that for which it is offered. It does not follow that you will be bound to continue a schoolmaster during the whole of your life, or for any given number of years. Circumstances may occur, which might justify, or even require you, to seek your livelihood in some other way; and you are not expected to fetter your liberty of action in such a case: but if you are truly honest, you will have no difficulty in understanding the nature of your obligation. You will feel that you are bound to carry out the objects of the institution, the benefits of which you enjoy, to the best of your ability. You will enter into the college with this intention, and you will suffer no prospect of present advantage, nor any fancied change of inclination, to alter your purpose.

Similar considerations will make it plain to you that you will be bound to conform to the rules and discipline of the institution with which you connect yourself, because it is obvious that you would not be admitted except on this understanding. You will comply with the regulations of the college, not because you think them necessary or expedient, but as your part of an engagement from which you expect to receive considerable advantages.

Among these rules the most important is that which binds you to comply with the injunctions which you may receive from those who are placed in authority over you, in all matters within their proper jurisdiction. It matters not whether it be the principal himself from whom you receive an order, or one to whom he has delegated a portion of his authority, and who acts in his name. Your obedience is as much due to a. monitor, or other delegate, so long as he is acting in his proper place, and performing the duty which has been assigned to him, as to the master by whom he has been: appointed to his post. If you suffer any wrong, you have your remedy; you may make your complaint in the proper quarter, when your case will be fairly considered:. but you must not refuse to comply with an order merely because you do not think it to be necessary, just, or expedient. In this, as in every other case, you must conform to the rules of the place. No community, from the greatest to the least, could be governed on any other principle. You will see and acknowledge this when you are yourselves the masters of schools, and have pupil-teachers and monitors assisting you. in your work: it is right and necessary that you should acknowledge it now. Till you have learnt to obey, you will not be fit to govern; meanwhile it is sufficient to remind you, that compliance in this particular forms part of your engagement.

On precisely the same grounds, you must resolve to give your best attention to the lectures of the several masters, and to follow exactly the course of study which may from time to time be prescribed to you. You may or may not think a particular lecture well adapted for its purpose; you may perhaps sometimes think that you might employ your time more usefully in some other way: you have voluntarily placed yourselves under guidance, and are bound to comply with the directions which you may receive, not only in form, but truly and heartily. You must remember that you come to a training college, not simply for the acquirement of knowledge, but of such knowledge as will fit you for the business of elementary instruction. Your information had need be rather accurate and well-grounded than extensive; you must know both the principles, and to some extent the details, of the subject-matter which you will have to teach; and the process by which this sort of knowledge is to be gained may perhaps be more tedious and elaborate than would be necessary if your object. were merely to inform your own minds. I hope that you will soon be convinced of this, and will see more and more plainly as you go on that the method of learning pointed out to you is well adapted to the end proposed. But whether you see this or not, it will still be your duty to make the best of the means placed at your disposal for the acquirement of knowledge in a docile and earnest spirit; because you will by your own act and deed have placed yourselves under guidance, and in so doing will have surrendered for the time the right of self-direction in this matter.

Again, as regards the art of teaching, do not imagine that the experience which

you have gained as a pupil-teacher will enable you to dispense with further practice. You will have both to study the science and to practice the art of teaching under special direction, and the two must go on together. The theory cannot be learnt to any purpose apart from the application. This is indeed the leading study in a training college, to which all others are subordinate. You will carry it on in the schools connected with the college under peculiar advantages; but whether you see this or not, you must understand that the cheerful and zealous performance of your allotted task in the practising schools is a duty which you will have voluntarily taken upon yourself.

In all these particulars you are bound to act according to the spirit of your engagement: and I put the case before you in this form because, when you see this to be a duty, there can be no further dispute or doubt about the matter, and because I think it is far better in every way that you should consider what is right, not what you may fancy to be expedient. But it would have come exactly to the same thing if I had addressed you with a reference solely to your own advantage. The rules and discipline, the course of instruction, the mode of life which the students are required to observe, have, and can be supposed to have, but one object, namely, the general welfare. There neither is, nor can be, any private interest to be served by any thing that is allowed or forbidden, given or withheld, done or left undone; all is intended for the advantage of the college at large, and of the students in particular. The whole course, and every part of it, is the result of much consideration, grounded upon long experience, expressly with a view to your benefit. You will therefore act not only more honestly, more honourably, and more gracefully, but more prudently, more wisely, even in a worldly point of view, by simply doing what you must know to be your duty, than by seeking to benefit yourself by any devices of your own.

Hitherto I have spoken to you of your obligations; I will now say a few words to you of your prospects; and here, as in the former case, I believe that by referring to your sense of duty, rather than to your hope of worldly advancement, I shall appeal not only to the nobler, but to the more influential motive, while at the same time it will not be difficult to show that your duty and your interest, even in a worldly sense, really coincide.

Your term of residence in the college will extend to one, to two, or to the full period of three years. If your stay be limited to one year, I cannot hold out to you any strong inducement, beyond the desire which you may feel to fill a post of humble usefulness, to seek the calling of a schoolmaster. You will, in the first place, be entitled only to the lowest of the three classes of certificate, according to which the augmentation of your salary by the Government will be regulated; but this is not the only nor the most important consideration. Your training will in itself be incomplete; so much so, that you will find the knowledge and ability with which you may leave the college decline in most cases, and wear out in a few years, lying, as it mostly does, almost entirely on the surface. Of this I have been assured on very high authority, as well as by the reason of the case; and consequently you will not, under ordinary circumstances, be furnished by the college with a testimonial of competency. Still, if you can do no otherwise, there is scarcely any amount of outward disadvantage which may not be overcome by resolution and force of character; and you will certainly carry with you the best wishes and prayers of those who have had, though for so short a time, the charge of your education. Only, be it observed, that this force of character, where it really exists, will in almost every case have made provision for a second year's training, considering the helps that are now afforded to the pupil-teacher and to the Queen's scholar by the Government; or if unexpected difficulties occur, will find the means of overcoming them.

But you will most probably remain at least two years; and then you will obtain the highest augmentation of salary from the Government which your place in the

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