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 figure do the last fourteen proposi tions refer?

SECTION II.

1. To bisect a given rectilineal angle.

In what particular case will the quadrilateral figure required by the construction be a rhombus ?

2. Given two points. Find two other points that shall be at the same given distance from each of them. What is the least possible length of the given distance?

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

Construct the triangle when each side is equal to half the sum of the other two.

SECTION III.

1. The three interior angles of every triangle are together equal to two right angles.

What ratio does the angle of a regular hexagon bear to a right angle?

2. Triangles upon the same base and between the same parallels are equal.

A line drawn through the middle points of the sides of the triangle is parallel to the base.

3. In any right-angled triangle the square described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.

SECTION IV.

1. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal

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parts together with the square on the line between the points of section, is equal to the square on half the line.

Construct a rectangle equal to the difference of two given squares.

2. If a straight line drawn through the centre of a circle cut a straight line in it which does not pass through the centre at right angles, it shall bisect it.

Lines drawn at right angles to the sides of any figure inscribed in a circle from their middle points meet in one point.

3. The angles in the same segment of a circle are equal to one another.

Given three points in the circumference of a circle, required to find a fourth.

ALGEBRA.

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.

=

SECTION V.

1. If a 2, b=3, c=0, find the value of 3a + 4b, 3a-4c a2+b2 + c2, abc, (a+b+c)+(a+b−c), (a2 + b2 + c2+3)3. 2. Multiply x3- 5x2 - 3x - 18 by x2 + 3x − 4,

3. Divide x-y by x -y.

SECTION VI.

1. Find the G. C. M. and L. C. M. of x2+5x+4, x3 + 4x2 — 2x - 8.

Solve the equations

1. (a) 5x+6=7x-10.

(b) 3 (2x-1)+4(3x-2)=5 (3x+2).

Or 2. 2x-3y+2-7x-8y-3=0.
Or 3. 32x2-3=20x.

SECTION VIII.

1. The length of a garden exceeds its breadth by 50 yards; the garden contains 9,375 yards; find its length and breadth.

2. Two numbers are in the ratio of 5:6; show that four times their sum 44 times their difference, whatever the numbers may be.

3. A labourer can save out of his weekly wages 10 per cent.; his wages rise one shilling a week, but his expenses increasing also 10 per cent. he can now only save 5 per cent. of his increased wages; find his weekly wages.

MENSURATION.

SECTION IX.

1. Find the number of turfs, 4 ft. by 8 in., required for a garden plot 50 ft. by 75 ft., allowing for four circular beds, diameter 6 ft.

2. A triangular piece of ground, whose sides are 800, 500, and 500 yards respectively, is let for £30 a year; find the letting price per acre.

3. A schoolroom is 60 ft. long, 20 ft. broad, 10 ft. high to the wall plate, 16 ft. high to the ridge of the roof. How many children would it contain, allowing 80 ft. of cubic space for each child? By how much does this exceed the workable number at 8 square feet per child.

Female Candidates for Admission.

DOMESTIC ECONOMY.

THREE hours allowed for this Paper.

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

SECTION I. (Household Work.)

1. What are the special qualifications and duties of a house and parlour maid? Describe the general requisites for good waiting at table.

2. Write down rules of practical advice to a young girl entering on her duties as nurse maid.

SECTION II. (Investment.)

1. Name any safe investments for a school-teacher; state clearly

the benefit of such investments and the percentage thus obtained, and give your reason for thinking these investments safe.

2. The salary of a young school-mistress at the present date is greater than the expenditure naturally demanded of her; on what principle, and to what extent, may she fairly be expected to lay by for her support in later life?

SECTION III. (Cooking.)

1. Describe various methods by which eggs may be used in cooking, and explain their value and nourishment as food.

2. Show clearly the difference between roasting, boiling, frying, and baking meat; explain which plan is most economical, and which renders the food most easy of digestion.

SECTION IV. (Sickness.)

1. Describe the qualifications and duties of a sick nurse; and write down instructions to be observed in a sickroom with regard to (a) "noise," (b) "hours of food," (c) "cleanliness," (d) "light," (e) "temperature of room."

2. Describe the common symptoms in any, or all, of the following diseases whooping-cough, measles, roserash, ringworm, chicken-pox; and give recipes for making arrowroot, barley-water, lemonade, beaf-tea, barley-gruel.

SECTION V. (Clothing and Washing.)

1. Give recipes for the following:

To remove fruit-stains, ink, and iron-mould from linen.
To wash flannel so that it may retain its colour and not shrink.
To clean woollen cloth.

2. Calico, flannel, cotton print, and coburgs are the principal materials of dress which are useful for cottage wear; and there is a material called derry, which is cheap and strong, and therefore suitable for working dresses.

Describe these different materials, and show their suitableness for the objects stated, and give the width and the price per yard of each.

Answers to the Mathematical Examples will be inserted in our next.

America and the Oceans.

By R. C. BUCK.

Immigration, Labour, &c.-There is one feature of American immigration which calls for special remark-the recent enormous influx of Chinese. After the general emancipation of slaves, which began in the English possessions, it was found necessary to import labour from either Europe or Asia. Perhaps it is a natural result of the former servile condition of the negro that his present idea of the blessings of freedom is to enjoy the pleasure of looking on while others work. To such an extent does he indulge in this taste, that in most parts he is infinitely worse off than when he was in bondage, eating worse food, living in worse houses, sucking more canes, chewing more tobacco, and rearing less children (child murder being common because children cause expense and trouble). Where white men could not and negroes would not work, natives of S. Asia (especially from Hindostan) were tried, being indentured for five years. This new introduction has met with considerable success, the labourers, (who, if possible, always return to their native country), often carrying back with them considerable wealth for them, and America being much enriched by their industry. The "Coolie system has, however, received an immense impetus since the ports of China have been opened to the world, and wherever the labourmarket is understocked, there "John Chinaman" makes his appearance, ready for any clime or work, existing where perhaps no other living being could preserve himself from starvation, and promising to oust all competitors from the field. No part seems

to have so much attraction for him as the N. Pacific coast line, which, beside being within easy distance of home, offers to him peculiar chances of success; its rapid development, and, consequently, the extraordinary demand for labourers and domestic servants, opens a rare field to the half-starved millions of China. (The scarcity of white women, and hence the impossibility of getting servants except at fabulous wages, brings "John" into great requisition, for the Chinaman here fills most of those offices which in England are considered feminine, the Anglo-American of the Far West looking upon the effeminate and womanly-dressed "celestial" in such a manner as to make no account of the "proprieties.") The cheapness of the labour, the adaptability of the