and nine hundred, seven hundred and twenty thousand, and four million forty-nine thousand and forty-five; from the sum take away three hundred and thirty-four thousand one hundred and forty-three; and divide the difference by three hundred and forty-five.

SECTION II. 1. Multiply 456978 by 789.

2. Divide 302129168 by 6704.

SECTION III. 1. How many days, hours, and minutes, in 505680 seconds?

2. How many ounces in 1 ton 7 cwt. 13 lbs. ?

6468

SECTION IV. 1. Reduce to the simplest form 2772 and (2%).

67

150

6 17 19 31

3.

2. Add together 27, 36, 240, 480' 35'

SECTION V. 1. Find the value of the sum of £453125, 1.14843753s. and '7185d.

2. Subtract 90-41 from 300, and divide the difference by '62.

SECTION VI. 1. If th of a ship be worth £36 10s. 7 d., what share will be worth £125 5s. ?

2. A bankrupt has assets to the amount of £1020, and debts to the amount of £3225: what will his creditors receive in the £?

SECTION VII. 1. How many yards of carpet 25 inches wide will cover a floor 19 ft. 7 in. long by 18 ft. 9 in. wide? Find the cost of the carpet at 5s. 6d. a yard.

2. Two partners with a capital of £800 gained £312 88. in two years; one had put into the business £352, and the other the rest: how much of the profit should fall to each ?

SECTION VIII. 1. How much must I invest at 4 per cent. per annum to secure a yearly income of £30?

2. At what rate must I invest £60 to obtain the yearly sum of £3 12s. ?

SECTION IX. 1. In working sums in the first four rules respectively, say whether you begin on the right or left, and give your reasons.

2. Explain, as to a class, your method of working the following sum:-Divide £15 among three persons so that the first may have £3 10s. more than the second, and the second £2 10s. more than the third.

3. Show that the product of two proper fractions is always less than the quotient.

DOMESTIC ECONOMY.

You are not permitted to answer more than one question in each section.

SECTION I. (Household Work.) 1. Describe clearly the work required of a housemaid; and explain the way in which a grate should be cleaned, a bed made, and bedroom furniture kept.

2. Write down a list of household furniture and kitchen ware which would be requisite for a school teacher in fitting up a schoolhouse; and give an estimate of the cost of the different articles.

SECTION II. (Investment.) 1. Describe with accuracy some investment from which a school teacher would be likely to derive benefit; and state the money interest to be secured from such investment.

2. Why should elementary school teachers be specially advised to make some sacrifice year by year by way of investment? Show clearly the wisdom of such advice, and the need there is that teachers should comply with it.

SECTION III. (Cooking.) 1. Mention different ways by which odds and ends of bread may be utilized, and write out, as for a young school teacher, the receipts for half a dozen inexpensive and nutritious dinners for a mistress and her pupil teacher.

2. Give receipts for making a meat pudding, for cooking cheap fish, for boiling potatoes, and for doing a rasher of bacon.

SECTION IV. (Sickness.) 1. Write out full instructions for a person who is to act as nurse in a sick room.

2. Explain clearly what precautions should be taken in any cottage where a case of infectious fever has broken the disinfectants which should be provided, and the manner in which they should be used.

out;

SECTION V. (Clothing and Washing.) 1. What teaching have you received in laundry work? and what benefit do you hope to derive from such instruction ?

2. Explain as to a class of children the difference between cotton, wool, linen, and silk; and show the adaptation of each of these materials for clothing.

SCHOLARSHIP QUESTIONS,

1876.

Candidates are not permitted to answer more than one question in each section.

The solution must in every instance be given at full length. A correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value.

ARITHMETIC.

SECTION I. 1. Multiply three millions seven thousand and five by four hundred and seven.

Prove the sum by casting out the nines.

2. Divide eight hundred and sixteen millions eight hundred and eighty-seven thousand six hundred and sixty-five by four hundred and seven.

Why do you begin at the left-hand side ?

3. Divide £404 8s. 04d. among 17 women and 19 men, giving each woman twice as much as a man.

SECTION II. 1. How many turns does a hoop, 2 yds. 16 in. in circumference, make in a quarter of a mile? 2. How many 9-oz. packets of tea are there in 40 chests, each containing 24 lbs. P

3. Find the value of the silver at 4s. 5d. per oz. in a bar containing 19 lb. 7 oz.

SECTION III. 1. Make out the following bill:27 lbs. of beef at 111⁄2d. per lb.

19 lbs. of mutton at 1s. 1d. per lb.

17 lbs. of suet at 9åd. per lb.

16 lbs. of pork at 71⁄2d. per lb.

2. Divide £2944 9s. 7d. into an equal number of shillings, sixpences, fourpences, and threepences.

3. A table, five feet square, is covered with halfpence, placed in rows; find the value of the halfpence, each

halfpenny being one inch in diameter, and no one touching more than four others.

SECTION IV. Find by Practice the value of—

1. 5098 articles at £15 14s. 94d. each.

Or 2. 17 cwt. 3 qrs. 4 lbs. at £5 15s. per cwt.

Or 3. The assets of a bankrupt on debts amounting to £595 at 7s. 23d. in the £.

[The sum should be worked so as to be intelligible to a class learning Practice.]

SECTION V. 1. What is meant by ratio and proportion? Find the fourth term in the proportion 118, 130, 177, and a mean proportional to 1764, 2304.

2. If 9 cwt. 3 qrs. 5 lbs. of cheese can be bought for £31 19s. 11d., what will 8 cwt. 2 qrs. 8 lbs. cost?

3. If 575 men perform a piece of work in 180 days of 10 hours each, how long will it take 115 men working 9 hours a day?

SECTION VI. 1. Add together 615, 17, 321, subtract from this sum 512, and divide the remainder by 51 of 3. 2. A job can be finished in 25 days by 30 men; at the end of each week (consisting of 6 days) 5 men are with drawn. How many weeks must the last five men work by themselves to finish the job?

3. Three fields are bought for £240, £270, and £470 respectively; they contain 4 ac. 3 r., 5 ac. 2 r., 9 ac. 3 r. respectively find the average cost per acre, and the highest priced field.

SECTION VII. 1. Divide 15 by 30, 1500 by 005, 015 by 003. Prove the second result by vulgar fractions. 2. A's share is 09 of B's, B's is 308 of C's, C's 1·1 of D's; C's share is £2750: find A's, B's, and D's.

3. 1,802,830 gallons of wine, value £658,405, were imported in 1874; 1,902,415 gallons in 1875, value £671,374: find the increase per cent. in quantity and value to two places of decimals.

SECTION VIII. 1. Define interest, principal.

Find the simple interest of £1575 10s. for 4 years at 8 per cent.

2. Define discount, present worth.

Find the present worth of £1296, due 9 months hence, at £10 138. 4d. per cent.

3. A man invests £1585 108. in 3 per cents. at 944,

brokerage is charged at the rate of 3th per cent.: what income does he derive?

SECTION IX. 1. A labourer's wages some years age were 15s. 2d. per week, and he could save 1s. weekly; his wages are now 18s. 6d., but the cost of living has increased 17 per cent.: what can he save now?

2. The rates of a parish amount to 3s. 6d. in the £; 3rd is poor rate, ths highway rate, the rest is schoolboard rate. What will a man pay for school purposes who is rated at £170 per annum ?

SECTION X. 1. A cubical space containing 941,192 cubic inches is exactly filled by 64 cubical boxes: find the length of the side of each box.

2. How many deals 4 feet long and 8 in. wide are required for the floor of a room 16 feet long and 12 feet wide ?

3. Find the cost of papering a room 18 feet long, 12 feet wide, 12 feet high, with paper 18 inches wide, at 11⁄2d. per yard.

EUCLID, ALGEBRA, AND MENSURATION. Candidates in Scotland may answer two questions out of Section IV. if they omit Section IX. With this exception Candidates are not permitted to answer more than one question in each section. (Marks are given for portions of questions.)

EUCLID.

Capital letters, not numbers, must be used in the diagrams. The only signs allowed in Geometry are + and =. The square on AB may be written "sq. on AB," and the rectangle contained by AB and CD, "rect. AB. CD."

SECTION I. 1. Define a "superficies," a "circle," a rhombus," and write out the three postulates of Euclid.

2. What is meant by saying that one proposition is the converse of another? Give examples from the first book of Euclid.

3. Into how many sections would you divide the first book of Euclid ? To what properties of figures do the last fourteen propositions refer?

SECTION II. 1. To bisect a given rectilineal angle.