Higher Mathematics.

Women.

STATICS, DYNAMICS, ASTRONOMY.

1. Enunciate and comment upon the first law of motion.

2. Find the conditions of equilibrium of a heavy rod of mass m which is suspended by two strings of lengths l and l' attached to its end and attached to the same fixed point.

3. Assuming the parallelogram of forces for the magnitude of the resultant, prove it for the direction of the resultant.

4. Shew how to find practically the coefficient of friction between two substances.

5. "The path of a projectile in space is a parabola."

A body is projected with a velocity of 12 ft. per second at an inclination of 45°. Find the greatest height to which it will rise and the horizontal range.

6. A body descends uniformly down a plane 12 ft. long inclined at an angle of 30° to the horizon in 9 seconds. Find the vertical velocity.

7. Define energy, and name the different kinds of energy. What kind of energy is that possessed by compressed air? Give reasons for your answer.

8. If one foot be the unit of length and one second the unit of time, what is the measure of the velocity of light which requires 8 minutes to pass from the sun to the earth, taking that distance to be 91,000,000 miles?

9. Discuss the nature of comets and the formation of tails on their approach to the sun, and account for the fact that these tails always point away from the sun.

10. Define parallax, and shew how the sun's parallax may be found accurately by observations of the transit of Venus.

Higher Mathematics.

Women.

TRIGONOMETRY AND CONICS.

1. The sides of a plane triangle are 12 ft., 13 ft., and 14 ft. respectively. Find the area of the triangle.

2. Find an expression for all the angles which have a given tangent. Write down the general value of 0 when tan20=3.

3. Find the radius of a circle inscribed in a triangle. The sides of a plane triangle are 4, 9, 12. Compare the radii of the inscribed and circumscribed circles.

4. Find an expression for the sine of the sum of two angles in terms of the sines and cosines of the angles themselves.

5. Determine the value of the trigonometrical ratios of an angle of 435°.

6. Find the circular measure of an angle of 15° 33′ 25′′.

7. Trace the form of the parabola from its equation y2 = 4ax.

8. Find the equation to the common tangent of the circles x2+ y2 = (c+a)2 and x2 + y2 — 2ax = (c+a) (c− a).

9. Find the co-ordinates of the intersection of

x cos ay sina-p=0 and x cos ẞ+ y sin 6-p=0.

10. The sum of the distances of any point from the foci of an ellipse will be less or greater than the major axis according as the point is inside or outside the ellipse.

11. The tangent to a parabola at the vertex is perpendicular to the axis.

12. If from any point P of an hyperbola PH, and PK be drawn parallel to the asymptotes, meeting them in H and K respectively, then 4PH.PK = CS2.

Natural Philosophy.

Junior and Senior.

(a) CHEMISTRY; (b) PRACTICAL CHEMISTRY; (c) STATICS AND HYDROSTATICS EXPERIMENTALLY TREATED; (d) THE EXPERIMENTAL LAWS OF HEAT; (e) ELECTRICITY AND MAGNETISM.

Junior Students will only be examined in three of the subjects (a), (b), (c), (d). Senior Students will only be examined in (a), (b), and one of the subjects

(c), (d), (e).
(a)

1. Does oxygen occur free in nature? What volume will 200 grammes of oxygen occupy? How much of it by weight can you obtain from 500 grammes of potassic chlorate ?

2. What are the chief properties of hydrogen? When it burns in the air what is formed?

3. How much oxygen and hydrogen do 200 cubic centimetres of water give if completely decomposed?

(b)

4. By means of what metals can you decompose water and obtain free hydrogen? Describe the process.

5. Describe the preparation of nitrogen (i) from air, (ii) from ammonia.

(c)

6. Explain the term, force. What forces are acting upon a book lying on a table, a piece of iron in the neighbourhood of a magnet, a ball falling from a height, a ball bounding after touching the earth?

7. State the theorem of the parallelogram of forces. Prove the same theoretically, or describe an experiment by which it may be practically proved.

8. Explain why a force, acting upon a rigid body at rest, may be supposed to act at any point within the body in the line of its direction.

9. Distinguish between solids, liquids, and gases. Describe the experiment by which the compressibility of liquids has been proved.

10. What conditions must be fulfilled before a liquid can be in equilibrium? Describe the hydraulic press, and note the principle of which it is the practical application.

(d)

11. State the theories as to the cause of heat known as the "Theory of Emission " and the "Theory of Undulation."

12. Suggest any reason why bodies expand under the action of heat. Which substances are the most expansible? Describe a method of measuring the expansions of solids.

13. Account for a small space being left between successive rails in laying down a railway, also for a glass into which hot liquid is suddenly poured cracking.

(e)

14. Distinguish between frictional and current electricity, in the manner in which they are obtained, and the practical uses to which they may be put.

15. Account for each fraction of a broken magnet being a perfect magnet. Shew by a diagram the hypothesis of the twofluid theory.

16. Describe a Wollaston voltaic cell. Explain the polarization of a cell, its disadvantages, and the method by which Daniell, to a great extent, overcame them in the construction of his cell.

Science.

Junior and Senior.

Junior: (a) BOTANY; (b) ZOOLOGY.

Senior: (a) BOTANY; (b) ZOOLOGY; (c) PHYSICAL GEOGRAPHY AND GEOLOGY.

No Student will be examined in more than one of the subjects (a), (b), (c).

1. Describe a moss.

(a)

2. Compare the spore-bearing organs of the fern, horsetail, and stag's-horn moss.

3. Give an account of the development of selaginella. How does it differ from that of a fern?

4. What is the minute structure of the stem of the horse-tail and the bracken?

(b)

1. Describe a hydra and a sea-anemone, drawing diagrams shewing the difference of structure between the two.

2. What is a thread-cell? How do sense organs occur in the cœlenterata?

3. Explain the meaning of a "polypite" and a "cœnosarc," giving descriptions of examples (including a common jelly-fish) shewing the different forms in which they may be arranged.

4. What are "dead-men's fingers"? Describe the chief forms of cœlenterata which build coral islands.

(c)

1. Explain why more rain falls in the west of England than in the east.