2. What kind of land, and what situation, are suitable for (a.) Corn growing? (b.) Hop growing? Illustrate your answer by examples from the counties of Great Britain and Ireland. 3. Describe minutely the colonial trade of Great Britain, showing the articles traded in, the colonies traded with, and (if you can) the average amount of exports and imports. SECTION V. Write a short essay, or give notes of a lesson, on one of the following subjects, viz.: 1. A Canadian Winter. 2. The Life of a "Squatter" in Australia. 4. The Tea Trade. N.B. Fullness and exactness of statement will be of more value than general descriptions. SECTION VI. 1. What causes affect the temperature of any country? Give examples, showing how the different causes counteract each other. Explain the phrase "Isothermal lines." 2. Why are degrees of latitude and longitude not equal in length? What is the difference between a degree of latitude and a degree of longitude in the latitude of London? 3. Explain, with illustrations, the terms "Equinox," "Solstice," "Precession of the Equinoxes," "Eccentricity of the Earth's Orbit;" and show how each of them is connected with the seasons. EUCLID. Capital letters, not numbers, must be used in the diagrams. The only signs allowed are + and -. The square on AB may be written "sq. on AB," and the rectangle contained by AB and CD, "rect. A B. C D." SECTION I. 1. To draw a straight line perpendicular to a given straight line of unlimited length, from a given point without it. Through a given point within an angle BAC, to draw a line cutting off equal parts from AB, AC. 2. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. The alternate sides of a polygon are produced to meet; show that the angles at their points of intersection together with four right angles are equal to all the interior angles of the polygon. 3. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Produce a given line so that the rectangle contained by the whole line thus produced and the part produced may be equal to the square on half the line. SECTION II. 1. If in a circle two straight lines cut one another, which do not both pass through the centre, they do not bisect each other. The only parallelogram that can be inscribed in a circle is rectangular. 2. To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. CA, C B are tangents at A, B, and A D is a diameter. Shew that the angle ACB is twice the angle BAD. 3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles. The lines bisecting any angle of the inscribed quadrilateral and the opposite exterior angle meet in the circumference. SECTION III. 1. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. 2. From a given circle to cut off a segment which shall contain an angle equal to a given rectilineal angle. Divide a circle into two segments, such that the angle in one of them shall be five times the angle in the other. 3. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other. Through any point in the common chord of two circles, which intersect one another, draw two other chords, one in each circle, and shew that a circle can be described through their four extremities. SECTION IV. 1. In a given circle to inscribe a triangle equiangular to a given triangle. If the triangle be equilateral, the radii drawn to the angular points will bisect the angles. 2. To inscribe a circle in a given triangle. Inscribe a circle in a given sector of a circle. 3. To inscribe an equilateral and equiangular hexagon in a given circle. Inscribe a regular hexagon in a given equilateral triangle, assuming the trisection of a straight line. SECTION V. 1. The sides AB, AC of a triangle are bisected in D,E respectively, and BE, CD are produced till EF=EB, and GD-DC; show that the line GF passes through A. 2. From the angles C,B of a parallelogram ABCD, CE, BE are drawn parallel to the diagonals, which EA, ED intersect in H,K. Show that HK is half BC. 3. On AC the hypothenuse of a right-angled isosceles triangle ABC a square ACED is described, and BE meets AC in F. Join DF, and show that the square on BE is five times the square on a side of the triangle. Show also that nine times the square on DF is thirteen times the square on the hypothenuse. SECTION VI. 1. Circles are described on the sides of a right angled triangle. Shew that the square on their common tangent is equal to the area of the triangle. 2. Given the perpendiculars from any point on the three sides of a triangle and two of the angles, construct the triangle. 3. ACB is a diameter of a circle, CD a radius perpendicular to it. The chord AD is bisected in E; BE meets CD in F and the circle in G. Show that three times the rectangle contained by BF, EG is equal to the square on the radius. POLITICAL ECONOMY. Candidates are not permitted to answer more than six questions. 1. Detail the functions of money, and explain the difference between money and capital. 2. What do you understand by the value of money? Discuss the effects of recent gold discoveries upon it. 3. Examine the consequences of the conversion of circulating into fixed capital. 4. Distinguish between productive and unproductive consumption, and show whether the latter is beneficial to society or not. 5. Tell how wealth is divided, and discuss the relations of landlord, labourer and capitalist. 6. Discuss the causes and consequences of strikes and lock-outs. 7. Examine the effects of foreign commerce on the countries concerned, and discuss the relative importance of imports and exports. 8. Enumerate the received canons of taxation, and classify the legitimate objects of national expenditure. 9. Investigate the various modes of investing small savings, with their comparative advantages. 10. Write a short essay on the conditions under which popular education promotes national wealth. 11. Write Notes of a Lesson, such as you would give to an intelligent first class of children on one of the following subjects: (a). A Savings Bank. (b). A Co-operative Store. |