B;—1a.

12

4. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it. Show that, if the diagonals of a parallelogram are equal, the figure is a rectangle; if the diagonals are perpendicular to one another, the figure is a rhombus; and if they are both equal and perpendicular to one another, the figure is a square. 5. In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle. 6. If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. 7. To describe a square that shall be equal to a given rectilineal figure. Show how to divide a straight line into two segments such that their rectangle may be equal to a given square.

Class D.—Chemistry (Optional). 1. What is the effect of heat on the following compounds:—Nitrate of ammonium, red oxide of mercury, black oxide of manganese, chlorate of potash? 2. How much oxygen can be got from 100 grammes of mercuric oxide? (Hg=2oo.) 3. 10 grammes of ammonia (NH 3 ) are dissolved in water. How much pure nitric acid (HNO 3 ) is required to neutralize the solution ? 4. In what different ways could you cause an explosion of a mixture of hydrogen and chlorine in a clear glass vessel ? 5. How much carbon dioxide (carbonic acid) can be produced by the combustion of 1 ton of coal containing 70 per cent, of carbon ? 6. Arrange the following gases in the order of their specific gravity : —C0 2 , CO, S0 2 , H, O, Cl, fl.O, CH 4 , H 2 S, NH 3 . 7. What is the " firedamp "of coal-miners? What becomes of it in a colliery explosion? 8. Describe fully (using equations) how the following bodies are made : —Chlorine, nitric acid, ammonia, sulphuretted hydrogen, hydrogen. 9. State what you know of the composition of the atmosphere. 10. State clearly the points of difference between red phosphorus and yellow phosphorus ; and explain how the one can be converted into the other.

Class D.—Electricity (Optional). 1. Describe an electrophorus, and state the use of the tinfoil that is generally placed under the sole. 2. How would you make experiments to show the distribution of a charge of electricity on a sphere, a dish, and a cube respectively ? 3. Describe exactly how to make the experiment to prove that the charge of a Leyden jar is chiefly confined to the glass jar rather than to the covers. 4. Describe experiments to show that different dielectrics possess each a " specific inductive capacity " of its own. 5. Describe a one-fluid and a two-fluid galvanic cell, and state the advantages of using the latter. 6. How may experiments illustrating the phenomena of magnetism be made by a wire bearing an electric current, without the aid of any magnetic metal ? 7. Describe Siemens's or Becquerel's electric pyrometer. 8. Describe and explain Bell's telephone. 9. Make a sketch illustrating the principle of some form of apparatus for reversing a current of electricity. 10. Draw a section through a submarine telegraph cable, and describe any form of recording instrument used with such cable,

Class D. —Sound and Light (Optional). 1. What are respectively the effects of heat, of pressure, and of the presence of water vapour, upon the velocity of sound in air ? 2. Describe all the essentially different ways in which sound may be made to interfere. 3. What are the laws of the vibration of strings? State all the circumstances that influence the character of the tone of a stringed instrument. 4. In what several ways has the velocity of light been determined ? Describe one celestial and one terrestrial method in detail. 5. Draw diagrams illustrating a total eclipse of the sun and a partial eclipse of the moon. What is the difference in the shadow cast by an object when a disk and a point of light are respectively used to produce it ? 6. The reflection of a lamp in water is generally a long wavy line of light; draw a diagram to explain this phenomenon. 7. Explain total reflection, and describe experiments to illustrate it. 8. Describe the eye, and state the functions of its several parts. How is the achromacy of the eye usually explained ? 9. Show by a diagram how an opera-glass makes an object appear nearer. 10. Describe two different ways of polarizing light. How may polarized light be distinguished from common light ?