13

E.—la.

another at Studholme Junction 6 hours afterwards: if the train from Christchurch travels 3 miles an hour faster than the Dunedin one, and the whole distance between the two places is 230 miles, find the distance from Christchurch to Studholme Junction. 10. A grocer, having purchased two kinds of tea, finds that if he mixes them in the proportion of 71b. of the better kind to 31b. of the inferior, and sells the mixture at 2s. per lb., he will make a profit of only 2d. per lb.; but that if he mixes them in the.reverse proportion, and sells at the same price, his profit will be 33* per cent. Find the cost per lb. of each kind of tea.

Class D.—Euclid (Optional). f Time allowed: Three hours. 1. Define a plane, an angle, a circle, parallel straight lines, a parallelogram. Cite Euclid's axiom with reference to parallel straight lines. 2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise the angles contained by those sides equal, their bases or third sides shall be equal, and the triangles shall be equal, and the other angle of the one shall be equal to the remaining angle of the other, each to each—namely, those to which the equal sides are opposite. State exactly what is meant by the expression " the triangles shall be equal." 3. Given three straight lines, any two of which are together greater than the third, show how to construct a triangle with its sides severally equal to the three straight lines. Where does the necessity for the limitation, that any two of the straight lines must be together greater than the third, appear in the construction ? 4. What is meant by a regular polygon ? How does Euclid enable us to find the magnitude of an angle of a regular polygon ? Give the necessary proof. How many degrees are there in an angle of a regular octagon, and how many in that of a regular polygon of fifteen sides ? 5. Show how to describe a square on a given finite straight line. Construct a square which shall be three times a given square. 6. 'If a straight line be divided into two equal parts and likewise into two unequal parts, the rectangle contained by the unequal parts together with the square on the line between the points of section is equal to the square on half the line. When is the rectangle contained by the two segments of a given line greatest ? 7. Divide a straight line into two parts such that the rectangle contained by the whole and one part may be equal to the square on the other part.

Class D.—Chemistry (Optional). Time allowed: Three hours. 1. Describe experiments to show the chief properties of oxygen. 2. A jar is full of one of the following gases; Oxygen, nitrogen, chlorine, carbon dioxide, hydrogen, ammonia. How would you find out which of these gases it is ? 3. The chief constituents of coal are carbon, hydrogen, oxygen. What becomes of these when the coal is burnt ? 4. What is atmospheric air ? Is it a mixture or a compound ? Give reasons for your answer. How is the air affected by plants and animals ? 5. What are the constituents of water? How many ounces of each do one hundred ounces of water contain ? 6. Describe two experiments to show how water can be formed from its elements. 7. Explain how ammonia can be made from any of its compounds. 8. Describe a process for the manufacture of sulphuric acid. 9. Describe the various modifications (allotropic forms) of carbon. 10. What weight of hydrogen can be made by the action of sulphuric acid on 100 ounces of zinc? (Atomic weight of Zn = 65.) 11. Give the names and formula} of all acids that contain (a) chlorine, (b) sulphur, (c) phosphorus.

Class D. —Electricity (Optional). Time allowed : Three hours. 1. What is the distribution of a charge of electricity on a sphere, a cube, and a cone respectively ? What effect have points and flames on the discharge of electricity ? Describe the action of a lightning-conductor. 2. How would you prove the electricity of the clouds, of an electric machine, and of a galvanic battery to be identical ? 3. How is a gold-leaf electroscope charged by induction ? Describe some form of electrometer. 4. Describe and explain Holtz's electric machine. 5. Make a section showing the arrangement of a Grove cell. Describe the chemical changes that occur, and show how you would join a battery up when there was a large and a small external resistance respectively. 6. How is an electro-magnet made? What experiments can be performed with it? 7. Explain the advantages of an astatic galvanometer over an ordinary multiple galvanometer. 8. Describe the process of electro-plating and electrotyping, and state the changes that occur when sulphate of copper is decomposed by platinum electrodes. State the changes that occur when the current is reversed.