ARITHMETIC AND ALGEBRA.

1. State in order the truths on which the working of a sum in Simple Proportion depends. Give a short illustration, showing how you would render the theory intelligible to a class of children.

2. Transform the fraction

21 te 7
et 956

in the duodecimal notation into the form of a decimal fraction.

3. What principles will you think it necessary to establish before teaching the rule for the Extraction of the Cube Root? Find the Cube Root of 7263, (a) to the third place of decimals; (3) by the method of approximation, so that it shall be true to .

4. Give contracted rules for mental computation in the following cases, and explain the reason of the processes.

(a) To find the price of a hundred, a gross, or a score of articles.

(3) To find the price of a ton when that of a pound is known, or that of a pound when an ounce is known.

(y) To find the square of a number.

(8) To find the interest for any number of months at six per cent.

5. Make a list of the units of weight, measure, and value employed in the French Système Métrique. State what is the meaning of each term, and how the several units are related to one another,

6. Give the formula for determining (a) the Compound Interest on £a for n years; (B) the present value of an annuity for the same term; and (y) the time in which £a would amount to £na at per cent.

3

7. What is the net annual income of a man who possesses 79a. 3r. 27p. of land, for which his tenant pays 15s. 6d. per acre; who has £7,560 in the 3 per cents., and has just laid out £2,300, his remaining capital, in the purchase of 4 per cent. stock, at 98? Deduct fourteen pence in the pound for Income Tax.

8. Distinguish between true and ordinary Discount. Find both on a bill for £720 10s., drawn on September 27, and payable on the 13th of the following February, at 3 per cent. Express your answers in the proposed decimal coinage.

9. If a shopkeeper each year double his capital, except an expenditure of £240 per annum, and at the end of four years be worth only of his original capital, what did he commence with?

12. Expand (1-a3)—2 to six terms. Write down the twentieth term of the expansion, and find the difference between the whole series and the first n terms of it.

(a+b)2 — (c + d) a
(a + d)3 — (b + c)2

2

14. Find the sum of 12 terms of the series 15, 12, 9, &c., and of an infinite number of terms of the series 108 +36 + 12 . . . .

15. Given log.10 2 = 30103, and log.10 5.743491 = 759176; find the fifth root of 0625. State, also, the advantage of choosing 10 as the base of the system.

(3) If A's money were increased by 10s. he would have twice as much as B, but if B's money were diminished by 15s. he would have a third as much as A; find how much each possessed. 18. Solve one of the equations :

(4) A sharcbroker sold 70 shares of a railroad (A) and 120 of another (B) for £500. He sold 30 more of the railroad (A) for £100 than he did of (B) for £60. Required the price of each share.

1. Describe the state of this country as regards religion at the time of the Saxon invasions, and further state how Christianity was introduced among the Saxons themselves after they had settled in England.

2. What power in the State can suspend the operation of the Habeas Corpus Act? Under what circumstances is this power exerted, and what is its effect?

1. Give some account of the Seven Years' War, or of Cromwell's Campaigns, or of the Conquest of England by William the Conqueror.

2. What account can you give, either of the progress of commerce or of the useful arts and manufactures, during the latter half of the eighteenth century?

1. Name the primates of England who have opposed themselves to the civil power, and give some account of their proceedings.

2. Say how the following officers receive their appointments, and what are the duties connected with their office:-Sheriffs, Coroners, Justices of the Peace.

1. Give a detailed yet not diffuse account of the following battles:-Tewkesbury, Neville's Cross, Plassy, Helvoetsluys, Culloden, the Standard, the Herrings, and the Spurs.

2. When was the power of bequeathing lands by will first exercised in this country? Why should any difference so long have existed in this respect between land and other descriptions of property?

1. Give a list of all the premiers of the reign of George III., and set against each name the most remarkable events of his premiership.

2. Give some account of the progress of commerce, and of the state of national industry, during one of the following periods:

1. From the accession of James I. to the Restoration.

2. From the restoration to the Revolution of 1688.

1. Say when there have been some wide-spread risings of the peasantry in England. State the causes and give some account of the same.

2. What were the chief feudal burdens, and when were all such entirely removed from land?

1. Give a brief but not meagre account of one of the following sovereigns:-Ethelred the Unready; Richard II., or James II.; and also of one of the following nobles: --Godwin Earl of Kent, Thomas Cromwell Earl of Essex, or Ashley Earl of Shaftesbury; as also of Fitzosbert, surnamed Longbeard, Titus Oates, or Wilkes.

2. Trace out the course of proceedings against an offender from his first detention to his punishment, particularly distinguishing between the functions of the Grand Jury and Petty Jury.

1. Give the nature of the claim of the first sovereign in each family that has reigned in England since and including William the Conqueror. Show also in what respects the claims of Lady Jane Grey, Lady Arabella Stuart, and the Pretender were defective.

2. Give what particulars you can respecting the condition of the people, as regards their dwellings and furniture, clothing, food, and employments during one of the following periods :

1. The Norman Period.

2. The Tudor Period.

3. From the Revolution of 1688 to the accession of George III.

:1

1. In a constitutional and legal point of view, say what makes the following reigns interesting:Henry II., Edward I., and William III.

2. Say what were the most important constitutional events in the period between Edward I. and Henry VIII. inclusive.

1. Trace the course of a Bill through parliament till it becomes the law of the land.

2. What account can you give of the manners and customs of the various classes of the population during the period from the accession of George III. to the commencement of the present century.

1. Explain the following expressions:-Convention. The Family Compact. Jacobin and Jacobite. Lord George Gordon's Riots. The Exclusion Bill. The Board of Control.

2. Explain the following expressions :-Alien. Denizen. Homage. The Act of Settlement. Moveable Property. Knight's Fee. Domesday Book. Felony. Murder. Manslaughter.

LETTERS TO THE EDITOR.

CHEAP SCHOOL APPARATUS.

SIR,-In answer to the inquiries of one of your correspondents respecting cheap models, objects, specimens of Natural History and manufactures, I perhaps can render him some information and assistance. I am possessed of a set of models, three glass cases, and a number of drawers full of said specimens, including Minerals, such as fossils-Metallic Ores, a few of the most common precious stones, &c.-Animal productions, as Silk, Coral, &c.-Vegetables, as Sugar-cane, Maize, &c. Petrifactions, Coins, Shells, Leather; curiosities in art and nature on a small scale, and about 100 sorts of birds' eggs, &c. &c.; and I have obtained the whole without the aid of my school committee. Now for the way of obtaining them. The models I had made by a young man (a former pupil) in his leisure hours, from drawings I made; he charged for little more than the materials, and was pleased to render a good turn to the school; and the money, ten shillings, was gained by some of my pupils for map drawing, from a country society. I painted them, and they look very well indeed. With reference to the other things:-I live in a mining district, and collected those of the neighbourhood on Saturdays and holidays. Some of the boys' parents would present me with a nice specimen occasionally. Some of these (the duplicates) I exchanged with my friends for specimens of their neighbourhood. I employed my leisure hours in making myself acquainted with the nature and properties of the things around me; and was, and am, frequently applied to for information respecting any curiosity that falls in the way of my townsfolk, and have many given to me in consequence. I hold that specimens are of no use unless the possessor knows how to use them, and when a person collects for himself additions are constantly being made; some few I bought. The eggs I collected, while studying that branch of natural history, and brought the boys to respect birds' nests at the same time, as I only took one, and sometimes two eggs from each nest. In conclusion, I have to inform your correspondent that the collection has given me more real pleasure, brought me more health and more friends, than ten times the value of all my specimens, and has done my school no harm, but I hope much good; and I shall be happy to assist him, by exchanging one of my specimens for the productions of his neighbourhood; or I shall be happy to render him assistance, by sending him a few specimens, if he will write me (and perhaps you will be kind enough to furnish my address). Perhaps it might be attended with too much trouble to the Society's depository department, to act as medium for these exchanges, but perhaps you may be enabled to suggest some means; or if not, the carriage of parcels by rail or water is very cheap, and much might be done at little expense. I am, Sir, yours respectfully,

Liskeard.

J. P.

ON TEACHING READING.

SIR, I send you a hint, chiefly founded on my own school experience, on a very important subject.

In teaching reading, first see the monitors are well acquainted with the lesson which has to be taught. In order to test this, select the lessons to be read by the classes on Friday evening; let the monitors take the books home, study the lessons, and write the difficult portions, or words, in their copy books, to be explained on Monday morning.

To secure the progress of the children, and to test whether the monitors teach, set but one reading lesson per week, or even a part of one, if it be long or difficult. On Friday examine each class, giving that monitor the highest marks who has succeeded in teaching each boy to read the lesson well, to be able to spell any of the words in it, and to know their meanings.

For variety, but chiefly for recapitulation, every sixth week let them read over again the lessons they have had during the preceding five weeks; so that there will be a different lesson each day.

In teaching reading, impress on each boy's mind the necessity of attending to the three following points :-(1) To look carefully, in order to be sure of the word before he speaks it, and also to learn how it is spelt. (2) To speak distinctly; hence the necessity of aspirating the h, of sounding the d in and, and the g in ing, &c. (3) To read in such a manner as to convey the sense.

With the youngest children, teach the alphabet and the sounds of the letters in the following way :—

(1) The different kinds of letters A a, A a, &c, naming them the capital printing A, the small printing a, the capital writing A, and the small writing a, &c.

(2) When they know their letters, take one of the vowels, write it on the black board, and place consonants before it, drawing from them the proper sounds, as a, ba, da, ray, &c.; then, by placing the y after, telling them the same letter is added each time, about half-a-dozen words may be taught during each lesson-bay, day, ray, &c.

(3) Also, for variety and interest, as well as to teach them spelling and encourage thought, take some common thing, as a cáp, and describe in a simple and interesting manner its parts, colour, how it is made, &c.; at the same time taking some of the most important and easy words, and wishing to know how they are spelt. For instance, in writing down what the subject of the lesson is, namely, the cap, place before them the alphabetical board, drawing from them the sound of the first letter, c. Now, let one of them point out c on the alphabetical board, then write it distinctly on the black board, and proceed in the same way with the other letters. When the word cap is written down, let them spell it together, and not leave it before it is well known. Proceed in the same way with any other word that is written down, as colour, black parts, peak, &c., not writing on the board more than half-a-dozen words, so that there may be enough only to learn well, and plenty of time for recapitulation. With a little training the monitors, who can naturally explain and describe common things in simple language, may be taught to adopt this plan.

With the middle classes of children, the plan with common things may be used advantageously. In reading the lesson appointed for the week, it will be found a good plan (1) to let each boy spell a word; (2) to let each boy say a word without spelling; and (3) to let each boy read the sentence. The advantages of this are, (1) it gives variation; (2) tends to improve the spelling, and fix each word on the mind; and (3) gives good scope for questioning.

With the elder boys, pay particular attention to the posture while reading, to the tone of voice, the pronunciation, and easy style, as if they understood what they were reading about. Also, if a mistake be made, be very careful to have it thoroughly corrected; the one correcting the error he has made. Check inattention, by telling

any boy in the class to read, and by challenging the careless with the place. Encourage looking carefully at each word by occasionally asking a boy to spell one of the words in the sentence just read; and if he fails, let him be taken down by one who can. Also discourage careless reading, by causing the one who does so to be shown how to read by a careful boy, and to be made, if possible, to feel the disgrace. I am, Sir, very respectfully yours, G. R.

Finsbury.

BOOK DEPOSITORY, BOROUGH-ROAD, SOUTHWARK.

Open daily, from 9 a.m. till 6 p.m. (On Saturday, from 9 till 3 o'clock.)

In issuing a new Catalogue of Lesson Books, Maps, Slates, and other School Material, to the Committees, Managers, and Teachers of British and other Schools, attention is respectfully called to the greatly reduced prices at which all articles are now sold at the Depository.

It will be perceived that the Lesson Books are offered at about half the retail price, and that nearly every other book in the Catalogue can now be obtained at a discount of 25 per cent., or one-fourth less than it is published at.

The Committee are anxious that their friends should be able to obtain everything that may be required of an educational character, at the Borough-road, on the lowest terms; and as the degree in which this can be accomplished necessarily depends on the amount of their sales, they trust that both the committees and teachers of local schools will see the importance of sustaining the attempt by making all their purchases at the Depository.

Catalogues will be sent by post, gratis, on application.

Particular attention is requested to the notices found in the front page of the Catalogue, as, if disregarded, it is impossible to avoid delay.

To meet the convenience of teachers and others, arrangements have been made for the gratuitous delivery, where practicable, of parcels in London.

HENRY DUNN, Secretary. N.B.-All remittances should be enclosed to Mr.SAMUEL BRADFORD, Accountant, and Post Office Orders made payable to him, at the Borough Post Office, London. Borough-road, December, 1855.

BRITISH AND FOREIGN SCHOOL SOCIETY.

DONATIONS, AND NEW ANNUAL SUBSCRIPTIONS.
From September 1st, 1855, to November 30th, 1855.

Remittances from Auxiliary Societies and Corresponding Committees, &c., from September 1st, 1855,

to November 30th, 1855.

Subscriptions and Donations will be thankfully received by SAMUEL GURNEY, ESQ, Treasurer, 65, Lombard-street; Messrs. HANBURYS and Co., Bankers to the Society, 60, Lombard-street; and at the Society's House, Borough-road.

Printed by JACOB UNWIN, of No. 8, Grove Place, in the Parish of St. John, Hackney, in the County of Middlesex, at his Printing Office, 31, Bucklersbury, in the Parish of St. Stephen, Walbrook, in the City of London; and Published by THE SOCIETY, at the Depository, Borough Road.-TUESDAY, JANUARY 1, 1856.