Higher Mathematics.

Women.

STATICS; DYNAMICS; ASTRONOMY.

1. Find the conditions of equilibrium of any system of forces acting on a rigid body in one plane. (Express these both by the use of moments, and also by resolving each force into two components at right angles.)

2. Define the centre of gravity of a body. Having given the positions of the C.G.'s of a body and a given portion of it, find that of the remainder.

3. A square is divided into four equal triangles, by having its diagonals intersecting in ; if one triangle be removed, find the C. G. of the figure formed of the three remaining triangles.

4. A particle slides from rest down a rough inclined plane, of inclination a and co-efficient of friction μ; find the velocity after a time t, and the space passed over.

5. A point P is at a distance of 12 feet from a plane inclined 30° to the horizon, and is above the plane. Find the time of quickest descent in a straight line from P to the plane.

6. A particle has been falling for 40 seconds, find the force which will stop it in 10 seconds, and also the force which will stop it in 10 feet.

7. How would the phenomena of the seasons be altered if the earth's axis were inclined to the plane of the ecliptic at an angle of 90°, or of 45°, or of 0°, the axis being always supposed to remain parallel to itself?

8. Explain and illustrate by a diagram the apparent motion of the sun in R.A.

2. Show that if

π

A

+tan √tan 4/4 = 1.

2

π

1 = 4 sin

2

π B

π 1

sin

sin

4

4

be the circular measure of a positive angle

less than sin 0, 0, tan 0, are in ascending order of magnitude,

us to calculate nearly the sine of any small angle, say 10"? 3. What are inverse trigonometrical functions?

4. Given a 18 b = 24 c = 30, find sin A, sin B, sin C, and the area of the triangle.

=

If a 70, b = 35, C = 36° 52′ 12", find the other angles and side having, given

log 34771213, L cot 18° 26' 6" = 10.4771213.

5. What is the ambiguous case in the solution of triangles? Illustrate your answer by diagrams.

6. If tangents be drawn at the ends of any chord of a conic, the point of their intersection, the middle point of the chord, and the point of contact of the tangent parallel to the chord, all lie in one straight line.

7. The circle passing through the points of intersection of three tangents to a parabola, passes also through the focus.

8. Define the terms diameter, ordinate, parameter, used in reference to a parabola.

By means of the general proposition proved above for all conics, prove that if QVQ be a double ordinate of a diameter PV of a parabola, QV is a mean proportional between PV and the parameter of P.

9. Find the equation of the chord of contact of tangents to the circle x2 + y2= from the point (xy). Show that this chord is perpendicular to the line forming the centre to the point (x1 y1). 10. Find the pole of 3x + 4y = 7 with regard to the circle x2 + y2 = 14.

11. Show that if a point A lie on the polar of B, then B lies on the polar of A.

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), (ƒ), (g), (k).

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

(a)

1. Explain what is meant by the Atomic Theory.

2. What is Silica? How is it employed in manufactures ? 3. Describe the chief compounds of Tin.

(b)

4. Given copper sulphate; show that it contains sulphuric acid.

5. What are the characteristic tests for H2S?

6. How are oxalic and tartaric acids recognised?

(c)

7. Weights of 2 lb. and 1lb. are attached to the ends of a string which passes over a fixed smooth pulley; find the velocity acquired and the space passed through by one of the weights in two seconds, and, if the string is then cut, determine the subsequent motion of the lighter weight.

8. Find the range of a projectile on the horizontal plane through the point of projection.

If the angle of projection is 450, find the velocity of projection, in order that the range should be 128.8 feet.

9. Explain carefully the difference between Statics and Dynamics, and define the word force, describing the different ways in which a force may be exerted.

10. Enunciate the three laws of motion, giving any illustrations of them that may occur to you.

(d)

11. If a man suddenly tries to lift a weight which he cannot move he experiences a flush of heat through his body. Explain this phenomena.

12. Explain the origin of convection currents in fluids. How would you avoid their formation ? How are they useful in warming a house?

13. Why should a kettle be kept free from soot at all points, and polished bright at the top, but not at the bottom?

14. State the various peculiarities of ice and water, and how these peculiarities are of special use.

(e)

15. Describe some form of Dynamo-electric Machine suitable for electric lighting.

16. One end of a sub-marine cable is put to earth, and the other connected with the positive pole of a battery, the negative pole of which is put to earth. Describe fully the electrical condition of the several parts of the cable.

17. Describe a good form of quadrant electrometer. What particular electrical quantity is measured by the electrometer? How does the sensibility of the instrument depend on the distances between the extremities of the two threads of the bifilar suspension ?

18. Give an account of (i) electrolysis; (ii) the thermoelectric pile.

(f)

19. Give the course of a drop of blood in passing from the left to the right side of a frog's heart.

20. State the chief points to be noticed in examination of a drop of frog's blood or a piece of muscle.

(g)

21. Write out a list of all the British shell-fish you have observed; refer them to their places in classification, and describe the habits of each.

22. Describe the structure of Hydra; contrast it with that of any jelly-fish, and give the life-history of the latter.

23. What is a "dental formula"? Give the dental formulæ of the cat, pig, horse, sheep, and man. State the meaning of the terms, "monophyodont," "diphyodont,' "carnassial tooth,"

"diastema."

24. Describe the parts of any skull you know, and explain the following terms: condyle, zygomatic arch, suture, foramen, fontanel.

(h)

25. Describe, in botanical language, without reference to books, any two flowers which you can obtain, referring each to their natural order.

26. Describe three examples of plants, modified so as to facilitate or necessitate cross fertilization, and explain the meaning of the term.

27. State the function of roots, and show their importance in an ordinary plant.

28. Draw up, from memory, a classification of the vegetable kingdom, giving examples of all the principal groups.

(k)

29. Describe carefully the course of an ordinary river from its source to its mouth. What is the peculiarity of the Cañons of Colorado, and how is it caused?

30. Enumerate the more important salt lakes. Under what circumstances may salt lakes be produced?

31. Describe the construction and use of the barometer.

32. Give an account of the distribution of mountains, tablelands, and plains in North and South America.