8. If a map, plotted on the metric system, but of which the scale is not attached, the distance between two distinct points R and S, measured on the ground, is found to be 505.55 English yards; determine the scale of the map expressed as a decimal fraction, and compute thence the number of Hectares contained in the rectangle BACD.

[See Diagram, p. 267.]

9. The centre lines of a road survey are found to intersect at an angle of 144° 26', and the radius of the curve by which they are to be joined is 1749 ft.; compute the tangent lengths, the secant point, and the length of the arc of the curve from one tangent point to the other.

10. A span of 80 ft. is to be crossed by a stone bridge, it is required to ascertain the vertical height of the soffit above the level of the springing, at a point 10 ft. from either abutment, when the curve of the elevation of the arch is a semicircle, a semiellipse, and a segment of a circle; with the two latter curves the rise is proposed to be one-fourth of the span.

II. The abutments of an oblique bridge being built up to the springing, and the centering in its place with close laggings prepared, describe the lines which are necessary to be pencilled on these laggings, and the whole process of obtaining them.

12. If the centre lines of an existing road and intended line of railway intersect at a part where the latter is on a curve, describe the method of obtaining the angle of intersection for an intended bridge crossing; the line of railway being marked on the ground by pegs at every 100 ft. distance, and the axis of the road passing between two of these pegs, describe, first, how you obtain the exact point of intersection, and the radius being 1000 ft., give all the requisite calculations.

13. Calculate the quantity of brickwork in the arch sheeting of the three proposed arches in No. 3.; each having, at both elevations, ring pens of aisler alternately 2 ft. 9 inches and 2 ft. 3 inches, the width from one face to the other being 45 ft.; the depth of the key in each case being 3 ft.

JUNIOR CLASS.

MR. W. ROBERTS.

1. If sin 43, find sin 24, cos 2A.

2. If tan A = 1, tan B = 2, tan C=3, find the value of A+ B+ C.

3. Draw a line dividing the vertical angle of a triangle so that the ratio of the sines of the parts may be equal to that of the sines of the angles at the base.

4. Find the angles of a triangle whose sides are 5, 6, 7.

5. If in a triangle_A = 26° 38′ 50′′, B=34° 32′ 13′′, c=170, find a and b.

6. If in a triangle a=6. b=7, C=75° 31′ 22′′, find c, A, B.

1. P is a point in a line AB: AP = 326.9, BP=673.1, and AP, BP subtend at a point C angles which are respectively equal to 49° 12′ 6′′ and 80° 10'; it is required to find the lengths of AC, BC, PC.

2. A base line AB is measured equal to 1000 yards; it is required to determine the distance of two points C, D, from the following values of angles, ascertained by observation:

CAB = 31° 46′ 10′′, DAB = 28° 5′ 26′′, ABC= 60° 42′ 48′′,

ABD = 67° 20′ 40′′.

3. The sides of a triangle are given respectively equal to 32, 40, 45.95; at a point P within the triangle, the side 32 subtends an angle 79° 8' 26", and the side 40 an angle 105° 58′ 58′′. Find the distances AP, BP, CP.

6. Find the minimum value of 13 sec x- 12 tan x.

7. Draw through a given point a plane parallel to two given right lines. 8. Draw a tangent plane to a given cylinder through a point outside it.

CHEMISTRY AND MINERALOGY.

DR. APJOHN.

1. Explain the mode of producing liquid hydrochloric acid, the composition of the gaseous acid, and the reaction which ensues when it is passed into a solution of nitrate of silver.

2. Give in a few words a description of the process for making oil o vitriol, and the products formed when it is heated in contact with mercury.

3. Give the usual process for preparing nitric acid, and the action which it exerts upon metallic copper.

4. What is the composition of Laughing Gas, and what is the process for preparing it generally adopted?

f

5. Sulphate of ammonium is the ammoniacal salt at present made in largest quantity. What is the formula of this salt, and what the process by which its ammonia may be separated from it?

6. How would you develope sulphide of hydrogen, and what action would it exert if passed into a solution of sulphate of copper?

7. Write the formula of grey antimony, and of galena, and state how these minerals may be distinguished from each other.

8. Native gold always includes silver. How is the analysis of the alloy effected ?

9. 30 volumes of a mixture of nitrogen and oxygen, after being mixed with 15 volumes of hydrogen, were exploded in a eudiometer by an electric spark. The residual gas now measured 27 volumes. From these data deduce the percentage of oxygen and nitrogen in the original mixture.

ENTRANCE EXAMINATION.

MR. W. ROBERTS.

1. Prove that the rectangle under the segments of a chord of a circle, which passes through a fixed point, is constant.

2. If a line be cut in extreme and mean ratio, prove that the rectangle under the segments is equal to the difference of their squares.

3. If two equal triangles have an angle in each equal, the sides about the equal angles will be reciprocally proportional.

4. Two triangles have an angle in each equal, and the sides about the equal angles are respectively 17, 19, and 119, 133; find the ratio of the areas of the triangles.

5. The sides of a triangle are 15, 17, 19; find the segments into which the side 19 is divided by the bisector of the angle opposite to it.

6. What are the sine and cosine of a right angle, of half a right angle, and of the third part of a right angle?

7. Find the diameter of the circle circumscribed to the triangle whose sides are 85, 204, 221.

2. Write the following radical expression, with fractional and nega

5. Find the values of x and y from the equations

х

17x+16y=200

4x - y = 28.

6. Solve the quadratic equation

x2 - 36x + 323 = 0.

7. Write down the expansion of (x + y)" by the binomial theorem. 8. Being given log 2 = 0.30103, calculate the logarithm of 64.

LLOYD EXHIBITION EXAMINATION.

PROFESSOR JELLETT.

1. If a heavy beam rest upon two smooth inclined planes, show that their line of intersection must be perpendicular to the beam and parallel to the horizon.

a. Show that the equilibrium is unstable.

2. If the planes be rough, and equally inclined to the horizon, to which their intersection is parallel, show that the beam will be in equilibrium in any horizontal position, if the common inclination of the planes to the horizon be not greater than the angle of friction.

3. If a heavy rough body rest upon two others, which themselves rest upon a horizontal plane, show that the three centres of gravity and the four points of contact are situated in the same plane.

4. A uniform beam rests with one end against a smooth vertical plane, its other end being supported by a string attached to a fixed point in the plane; show that if the length of the string be equal to or greater than twice the length of the beam, the beam must be vertical.

5. A heavy body slides down a smooth inclined plane, which itself moves on a smooth horizontal plane. Determine the pressure on the plane.

6. A heavy particle is projected along the concave side of a paraboloid of revolution whose axis is vertical. Determine the conditions necessary in order that its path may be horizontal.

7. Investigate the series for the time of vibration in a circular pendulum.

THEOLOGICAL EXHIBITION EXAMINATION.

Hilary Term.

REV. GEORGE LONGFIELD, D. D.

The Book of Zechariah.

1. Zech. i. 1. "Zechariah, the son of Berechiah, the son of Iddo the prophet." What difficulty is suggested by a comparison of these words with the Book of Ezra, and what solutions of it have been proposed ? How does the version of the LXX. here differ from the Masoretic text?

2. What traces have been observed in the writings of Zechariah of the prophet's education in Babylon ?

3. Examine the grounds on which chaps. ix.-xi., and chaps. xii.-xiv., have been assigned to different authors.

4. What is the fact which led De Wette to conclude that the latter chapters, ix.-xiv., must belong to the age of Zechariah?

5. What peculiar forms of expression have been remarked as common to the two chief divisions of the prophecy?

a. Discuss the different opinions as to the signification of the stone

.in this passage האבן

-and illustrate the sym על אבן אחת שבעה עינים Explain the clause .6

bolism.

a. Translate this passage, pointing out a mistake in the rendering of the Authorized Version.

b. Explain the imagery of the vision.

e. The Masorets suggest a different reading of one word in the passage? How has the Kethibh been explained?

d. Give the derivations of and . How is the latter word expressed by Jerome, and the LXX. ?