Sir-Would any of your kind correspondents inform a young certificated Master of a Boys' National School how he might acquire a knowledge of Drawing? say, sufficient for a high first class. The inquirer would not begrudge labour or moderate expense. Sir, yours obediently,

P.

[In many Towns a School of Art has been established. Where there is not one in the neighbourhood, and where there is no Schoolmaster already certificated in drawing, there seems no present remedy.-ED.]

Gramination Papers.

HIGHER MATHEMATICS.-(SECOND YEAR.)

ALGEBRA AND TRIGONOMETRY.

(Three hours allowed for this Paper.)

SECTION I.

1. If any two quantities partly rational and partly quadratic surds, be equal to one another, the rational parts of the two are equal and also the irrational parts.

2. Prove the formule for finding the sums of arithmetical and geometrical progressions.

3. A farmer bought a lot of oxen, sheep, and horses for £127; each horse eost £15, each ox £10, and each sheep 30s., and the number of sheep was equal to twice that of the horses and oxen together. How many did he buy of each?

SECTION II.

1. Show how to find the greatest term in the expansion of (a + x)n.

2. If two numbers are prime to each other they are the least in that proportion.

3. Resolve into partial fractions 1−x+x*. 14x3 + 6x2

1

(1 + x) x31

(x-1)(x-4)

SECTION III.

1. The product of any r consecutive number is divisable by 1.2.3:....r, 2. Express 7 and 18 in continued fractions.

3. Reduce to a vulgar fraction in the senary scale, without passing into the decimal scale, the following recurring senary fraction 434343 ad inf.; and then express the vulgar fraction so obtained in the decimal scale.

SEOTION IV.

1. Prove that sin (A + B)

+ sin A cos B + sin B cos A.

2. Prove that coseo 2 A+ cot 4 A cot A

Tan A+ 3 eot A = 4.

Cosec A, and find A when

3. If two circles touch externally, the diameter of one of which is four times that of the other, the sine of the angle between their common external tangents is

24

25

SECTION V.

1. Write out the algebraical proof of the arithmetical rule for finding the square root, and find by first principles, without Algebraical symbols, the square root of 14641.

2. Prove, as you would to a pupil teacher in the fifth year, by algebra and geometry, without the use of trigonometry, the rule for finding the area of a triangle when the three sides are given.

3. Point out exactly how far algebra corresponds to arithmetic, and at what point, not merely a peculiar notation, but new principles or conceptions are introduced.

SECTION VI.

1. Describe exactly the successive steps in the process of teaching algebraical multiplication to a pupil teacher in his fifth year.

2. Explain the means that you would adopt to give your first class a clear idea how distances can be measured by trigonometry.

3. Compare the effect of teaching boys of seventeen algebra, &c., and teaching them geometry.

ARITHMETIC.-[FEMALES.]

You are not allowed to answer more than one question in each Section but when there are two Sums in the same question, both should be worked.

(Three hours allowed for this Paper.)

SECTION I.

1. What is meant by a system of Numeration? What by a system of Nota-. ion? When is a system said to be decimal

2. Show how you can divide by 10, 100, 1,000, &c., more easily than by any other number. If in multiplying by 7,000, we multiply by 7 and add three figures, what principles are illustrated by the process?

3. What do you mean by reducing fractions into lowest terms? Show the correctness of the process employed. Prove by means of a diagram that

=

SECTION II.

1. If a piece of ribbon measures 21 yards 2 nails, how many bonnets can be trimmed with 17 such pieces, suppose each bonnet requires 2 yards? How many crowns, half-crowns, shillings, and groats, amount to £99 16. 4d. taking of each an equal number?

2. A man spends £155 5s.7d. per year, how much will he lay by in 37 years, out of £200 per annum ?

If 6 million visitors entered the Crystal Palace in 26 weeks, what was the average attendance per day

3. Find by Practice the value 8,632 articles, at £1 14s. 3 d.

£1,280 is divided among three persons, so that their portions are as 5, 3, 2, respectively, how much does each receive?

SECTION III.

1. Find the sum, difference, product, and quotient of 2 and 5.

The sum realized by a bankrupt's estate is £7,848, being the amount of the debts, and the dividend paid.

of his debts, find

2. How long will it take 17 men to earn £50, if twelve men in 6 days can earn 13 guineas?

3. Divide 71 by 635. Find the value of 178 of a mile. Express '75 of a shilling as decimals of such of the coins of the realm.

1. THE HISTORY, CHRONOLOGY, AND GEOGRAPHY OF THE

BIBLE

2. THE GOSPEL ACCORDING TO ST. MATTHEW.

(FIRST YEAR.)

Three hours allowed for this Paper.

SECTION I.

1. Describe the course of the Jordan.

2. What tribes or nations occupied Canaan when Abraham and Joshua, respectively, crossed the Jordan?

3. Draw a map of Syria, inserting the mountains and rivers, Antioch, Damascus, Tyre, Jerusalem, and the six cities of refuge.

1. Write a history of Gideon,

SECTION II.

2. Distinguish between trespass offerings, peace offerings, and burnt offerings. Give the rules for each.

3. Give an analysis of one of the prophetical Books in the Old Testament, with some account of its author.

SECTION III.

1. What do we know of St. Matthew from the Bible? What is the com.. monly received opinion on the date, and original language of his gospel? What circumstances mark for whom it was written?

2. Mention any miracles, parables, or phrases peculiar to this Gospel.

3. Narrate the parable of the labourers in the vineyard. What circumstances led to the parable? What is its doctrinal meaning? Can you find anything parallel to it in ordinary life?

SECTION IV.

1. When did our Lord first begin to foretell his own sufferings?

2. Mention the occasions on which the disciples are said to have quarrelled mongst themselves. State in each case what circumstances seem to have led directly or indirectly to the quarrel.

3. Give an analysis of the 'sermon on the Mount, showing its unity and coherence. What leading doctrines or precepts of the gospel find no place in it ?

SECTION V.

What is the best teaching that can be given to children between the ages of seven and nine, out of the Old Testament? Illustrate your answer by a sketch of a specimen Old Testament lesson.

SECTION VI.

Write an explanation for a class of children between 11 and 13 of the Leaven and the Mustard seed. Be careful to point out the difference as well as parables of the the similarity of meaning in the two parables.

SECTION VIL

Write such notes on the following passage as will give an illustration of the preparation that you would make for hearing it read by your first class, and explaining it to them;

"And when they were come to Capernaum, they that received tribute money came to Peter, and said, Doth not your master pay tribute?

"He saith, Yes. And when he was come into the house, Jesus prevented him, saying, What thinkest thou, Simon? of whom do the kings of the earth take custom or tribute? of their own children, or of strangers?

"Peter saith unto him, Of strangers. Jesus saith unto him, Then are the children free.

"Notwithstanding, lest we should offend them, go thou to the sea, and cast an hook, and take up the fish that first cometh up, and when thou hast opened his mouth, thou shalt find a piece of money: that take, and give unto them for me and thee."-Matthew xvii., 24 to 27.

No. 72.

FEBRUARY 1, 1857.

PAPERS FOR THE SCHOOLMASTER.

Children's Gertificate.

Two

Practical men know well enough that Popular Education is not so much impeded by want of School-buildings, as by the irregular and scanty attendance of children. How lamentably small a per-centage of children is found to attend above half the days of the year. or three years ago, a minute was passed by the Committee of Council on Education, which allowed a capitation grant to the managers of every School under inspection, for every child who had been present 194 days out of the 365, but the advantage was so contemptible, in consequence of the paucity of children, who were found to have attended even this amount of time-that the number of days has been reduced to 176. But how few are the instances of Schools, where the returns show that a half or even a third of the children have attended during the past year, 176 out of 365 days. Carelessness and indifference, and the interruption of desultory employment have produced this state of things. Abroad, the parental authority of the legislature forbids this infliction of wrong, but at home we have an instinctive abhorrence of any interference with individual privilege, though it be the parental privilege to injure his child now, the child who will become the citizen hereafter. Meanwhile, intermediate efforts are being made to offer inducements to children's regular attendance at School, by an appeal to the parent's cupidity. There may be, and there are abstract objections to the system which has the direct tendency to lessen the parent's sense of duty to his child, and