Higher Mathematics.

Women.

STATICS, DYNAMICS, ASTRONOMY.

1. Find the relation of the power to the weight in the three kinds of levers.

2. Prove that the effect of a couple cannot be counteracted by any single force.

3. Define the terms, conservation of energy, potential energy, kinetic energy.

4. Find the mechanical advantage of a system of four moveable pulleys in which the strings are all attached to the weight, and each pulley weighs of the weight.

5. Prove that when a body is suspended from a point round which it can swing freely it will rest with its centre of gravity in the vertical line through the point of suspension.

6. Prove that the velocity acquired by a body in falling down an inclined plane is the same as that of a body which has fallen freely through the same vertical distance.

7. A particle falling from rest through I feet with acceleration fint seconds acquires a velocity m. What are the units of time

and length?

8. A body has fallen through a distance of 140 feet. Find the distance through which it fell in the last second and in the last second but one of its fall.

9. Define a tropical, sidereal, and anomalistic year. To which of these does the civil year most nearly correspond?

10. What is meant by solar and lunar nutation?

Explain the reasons why the latitude of all stars remains sensibly constant, whilst the longitude of all has a yearly increase of about 50".

11. How are we led to the conclusion that the earth is not flat, but that it is approximately spherical?

12. Describe the apparent path in the heavens of an inferior planet as seen from the earth, and shew how its real motion round the sun may be deduced from observation of its apparent motion.

Higher Mathematics.

Women.

TRIGONOMETRY AND CONICS.

1. Define the sine of an angle, and shew how all the other trigonometrical ratios may be deduced from the sine.

2. Trace the changes in sign and magnitude of varies from 0° to 270°.

cos 2 A

sin 2 A

as A

3. Prove that the circumference of a circle varies as its radius, and find the ratio of the circumference of a circle to its diameter. Explain what is meant by the circular measure of an angle. 4. Prove that

and give the reason why for one value of cos A there are two

5. Shew that in any triangle c2=a2+ b2 - 2ab cos C.

6. Prove geometrically that tan (C+D)

=

tan C+tan D

1 tan C. tan D'

7. The focus and directrix of a parabola being given, find any number of points on the curve.

8. In the parabola the rectangle under the latus rectum and the abscissa is equal to the square of a semi-ordinate.

9. Find the condition that the straight line x cos 0+ y sin0=p should touch the circle x2+ y2 = 2 (ax+by).

10. If from a point O a pair of tangents OP, OP' be drawn to an ellipse, then OP and OP' will subtend equal angles at either focus.

11. Prove that the equation y2+ Axy-x2 = 0 always represents two straight lines through the origin at right angles to each other.

geometrically and analytically.

22 12. Find the equation to the tangent to the ellipse a2

13. Define the polar of a point with respect to a circle both

y2 b2

+ = 1.

Natural Philosophy.

Junior and Senior.

(a) CHEMISTRY; (b) PRACTICAL CHEMISTRY; (c) STATICS, DYNAMICS, AND HYDROSTATICS EXPERIMENTALLY TREATED; (d) THE EXPERIMENTAL LAWS OF HEAT; (e) ELECTRICITY AND MAGNETISM; (f) ELEMENTARY BIOLOGY; (g) ZOOLOGY; (h) BOTANY; (k) PHYSICAL GEOGRAPHY.

Junior Students will only be examined in three of the subjects (a), (b), (c), (d), (g), (h). Senior Students will only be examined in three of the subjects (a), (b), (c), (d), (e), (f), (g), (k).

NOTE.-(b) cannot be taken with (a), nor (g), nor (k), without (f).

(a)

1. Define the terms, chemical element, compound, and mechanical mixture, and say to which head the following substances belong, giving your reasons: air, gunpowder, brass, copper, common salt, sugar, coal gas.

2. Name the non-metallic elements. Which of them occur free in Nature, and which are most important to animal and vegetable life, either free or in their compounds?

3. What is meant by the "atomic weights of the elements"? In expressing these weights, what is taken as unity? What are chemical symbols?

(b)

4. Describe experiments, shewing that in order to combine chemically substances must be in close contact. In what ways can this contact be best effected? Prove that chemical action is most strongly exerted between dissimilar substances.

5. Shew that an entire change of properties is the result of chemical union. Give examples of change of colour, state, taste, and smell.

(c)

6. Define the terms, mass, velocity, momentum, uniform motion, variable motion.

7. What sort of motion has a falling body? Find the space described in the sixth second by a falling body. What will be its velocity at the end of the sixth second?

8. A man is walking at the rate of 4 miles an hour. Express this velocity in feet per second.

9. What is the force which causes bodies to fall to the ground? Do all substances fall at the same rate? Give reasons for your

answer.

(d)

10. What theory is held with regard to the nature of heat? Explain what is meant by temperature.

11. State the common effects of heat on substances, and prove them by examples. Mention an exception to the law that substances expand under influence of heat. Name substances that expand on solidifying, and can therefore be cast.

12. What is meant by the term, coefficient of expansion? If an iron bar is 150 feet in length at 0° C., what will be its length at 50° C. ?

(e)

13. Explain the terms, conductor and insulator of electricity, giving four examples of each.

14. What is meant by vitreous and resinous electricity? Shew their different effects by describing experiments with the electric pendulum.

15. If wood be rubbed with flannel, is positive or negative electricity produced in the wood? Is the same produced in the flannel?

16. Describe three experiments in which electrical separation is effected.

(f)

17. Explain the terms, anatomy, morphology, embryology, physiology. Distinguish between growth, development, evolution.

18. "The body consists of a double tube." Explain what this means, and how it is true of all vertebrates.

19. Explain the structure and growth of cellular tissue.

(g)

20. Describe the nervous system of an earthworm, and contrast it with that of a typical lamellibranchiate mollusc.

21. Name the various divisions of the lamellibranchiata. State their characteristics, and name as many genera belonging to each as you can remember.

22. Describe a typical mammalian vertebra, and contrast it with the vertebræ of (i) a crocodile, (ii) an osseous fish.

23. Give a tabular list of the bones of a dog's skull, and give a short description of the position and letations of each.

(h)

24. Enumerate the parts of a plant. Give examples of plants in which one or more of these parts is wanting.

25. Distinguish in all the parts of the plant the difference between monocotyledons and dicotyledons.

26. Explain the terms, phanerogam, cryptogam, vernation, venation, placentation, gymnosperm, angiosperm.

27. Examine and describe technically the root and flower of the primrose.

(k)

28. Describe the exact shape of the earth, and give some proofs of its being the shape you indicate.