VIII. Give tan 30+ tan 20 + tan'00; find tan 0.

IX. In any triangle the sides are proportional to the sines of the opposite angles.

X. Find the radius of a circle which touches one side of a triangle and the other sides produced,

If 01, 02, 03 be the centres of the escribed circles, show that

XI. Two rows of houses of equal height are at right angles to each other; on a sun shiny day the distance of the corner of the shadow from the corner where the rows meet is observed twice, and found to be a and b respectively; if h be the height of the houses and a the difference between the altitudes of the sun on the two occasions, then h2 + (a - b) h cot a + ab = 0

THURSDAY, 17TH FEB., 2 TO 5 P.M.

GEOMETRY.

E. P. METCALFE, M.A.

I. If two triangles have two sides of the one equal to two sides of the other each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides equal to them of the other: the base of that which has the greater angle shall be greater than the base of the other.

II. The angles in the same segment of a circle are equal to one another.

From the intersection of the diagonals of a quadrilateral inscribed in a circle, perpendiculars are let fall upon the sides; prove that the semi-sum of two opposite angles of the quadrilateral formed by joining the feet of these perpendiculars is equal to one of the angles formed by the diagonals of the former quadrilateral.

III. Triangles of the same altitude are to one another as their bases.

ABCD is a square and the side AD is bisected in E. If BE be joined cutting the diagonal AC in the point F, show that of the triangles thus formed

AEF CEF ABE BCF:: 1 2 3 4

IV. Every solid angle is contained by plane angles which together are less than four right angles.

The sides of a pyramid consist of the greatest possible number of equal equilateral triangles. Determine the form of its base.

V. In the fig. Euc. 1.22. "To make a triangle of which the sides shall be three given straight lines, &c.," if D F, F G, G H be taken equal to the given straight lines and F K G be the triangle required : show that the circles described about the triangles DK G, FKH both pass through the centre of the circle described about the triangle DKH and their common chord bisects the angle F K G: also if this chord meets F G in L, and the straight line bisecting F G at right angles in M, the rectangle F K, K G is equal to the rectangle K M, K L.

VI. If the tangent to any conic at a point P intersect the directrix in the point Z, then PS Z is a right angle.

Hence show that if the normal at P meet the axis in G
SG SP::SA: AX.

VII. If QV be an ordinate to the diameter of a parabola at P

Q V24 S P. P V.

If the ordinate pass through the focus and G be the intersection of the normal and axis show that P G is a mean proportional between the segments into which the ordinate is divided at the focus.

VIII. If from the foci S, S' of an ellipse S Y, S' Y' are drawn perpendicular to the tangent at P; show that

SY. S' Y'
also S Y

SP:: BC: CD where C D is conjugate to C P.

IX. If through any point in the diagonal produced of the rectangle formed by the tangents at the vertices of a hyperbola and its conjugate an ordinate be drawn cutting the curve in P and the other diagonal produced in r, show that the rectangle R P. Pr is constant: and deduce the characteristic property of an Asymptote.

If the Asymptotes be given in position, and one point on the curve determine the position of the foci and directrices.

X. Investigate the nature of the section of a cone made by a plane whose inclination to the axis is greater than half the vertical angle of the cone.

Prove that the section of a cylinder made by a plane which is not at right angles to the axis nor parallel to it, is an ellipse.

FRIDAY, 18TH FEB., 10 A.M. TO 1 P.M.

PHYSIOLOGY.

WM. MACRAE, A.M., M.B., C.M.

I. What is Protoplasm? Where does it occur? What are its properties?

II. What are the chief forms of Epithelium? Mention one locality of each kind.

III. Describe shortly the skin and its functions in man.

IV. What are the differences in the circulation of the blood and in the blood itself, of Mammals, Reptiles and Fishes?

V. Describe shortly the nature of the processes by which the heat of warm-blooded animals is sustained.

VI. What are the orders of Insects? Give an example of each order? Describe the Oral apparatus of Insects generally.

VII. Whence do plants derive their food? In what form and by what organs do they absorb it? Where do they digest it? VIII. Describe the Mammalian Ovum and the Mammalian Placenta.

PHYSICAL GEOGRAPHY.

I. Define Physical Geography. What terrestrial phenomena owe their origin to the sun's influence?

II. What is a glacier? Describe its formation, its mode of motion, and some of its effects.

III. What are the chief forms of clouds? Describe the causes of their formation and dissipation.

IV. What is Dew? Explain its formation. On what surfaces and in what kind of weather is it most abundant ?

V. Define River-basin, and Water-shed. What becomes of all the rain that falls to the ground?

VI. What are meant by Flora and Fauna? What animals and what plants are characteristic of Australia? What is the general form of the surface of that country.

VII. What are the distinguishing features of the Hindus, Chinese and Negroes?

VIII. Explain the causes and phenomena of tides.

IX. Describe the ordinary course of Cyclones in the Indian Ocean,

FRIDAY, 18TH FEB., 2 TO 5 P.M.

CHEMISTRY.

W. MACRAE, A.M., M.B., C.M.

I. Give your reasons for supposing that matter consists of Atoms. What is meant by a Molecule? What do you understand by the Atomicity of an element and the Basicity of an acid?

II. A Litre of Hydrogen at 0° C. add 760 Millimetres Barometric pressure, weighing 0869 grammes :-What volume of oxygen under these conditions may be obtained from 150 grammes of Chlorate of Potash ?

III. What is the composition of Gunpowder? Describe the Chemical changes that occur on igniting it, and give an idea of the amount of energy put in action.

IV. In the manufacture of sulphuric acid on the large scale what substances must be collected, and what must be done with them? Show by equations the various chemical changes that take place.

V.

Describe the structure and use of the blowpipe flame.

VI. Given a mixture of organic and inorganic matter: mention two ways of getting rid of the former and retaining the latter.

VII. Whence is Alcohol derived? What are the conditions favourable for its formation? What is the action of sulphuric acid upon it? N.B.-Laboratory experiments performed in addition to the above

paper.

ELEMENTS OF PHYSICS.

I. What is a Balance? What are the conditions of accuracy and of delicacy of the ordinary Balance ?

II. What are meant by the specific gravity and the elastic force of Gases? On what does the volume of any given quantity depend?

III. A little water gets into the vacuum above the Mercury in an ordinary Barometer:-State clearly what will happen in consequence. IV. Describe a Daniell's Hygrometer; What is the use of it?

V. Describe the changes in volume and state of H 2 O in passing from 10° Fh. to 240° Fh. at the ordinary Barometric pressure.

VI. Construct a diagram illustrating the use of the simple microscope, and explain it.

VII. A horizontal wire conducts a strong current of electricity from South to North, and a magnet free to move in a horizontal plane is placed close beneath it. What position will the magnet assume, and why?

VIII. Describe a Leyden jar and its use.

FRIDAY, 18TH FEB., 10 A.M. TO 1 P.M.

LOGIC.

W. E. ORMSBY, M.A., LL.D.

I. Write a note on the Definition and Province of Logic.

II.

What is Mr. Mill's view of the functions and logical value of the syllogism?