Section 7.

1. Show that the character of our Lord, as represented in the gospel, affords strong grounds for believing that he was a Divine person.

2. Give a short summary of the evidences of Christianity, as stated by Bishop Porteus.

ARITHMETIC.

Each step in the solution of those questions which are marked with an asterisk, is to be fully explained.

*1. Subtract 69 from 88.

*2. Multiply 137 by 90.

*3. If 27 quires of paper cost 10s. 6d., what is the cost of 45 quires?

*5. Bought quills at 4s. 7d. the hundred, and sold them so as to gain of the selling price: what is the selling price?

7. Eggs are to be sold at the rate of 3 for 2d.; how must they be bought to gain 25 per cent.?

8. What is the true discount on £124, payable in 2 years, at 44 per cent. per annum !

9. Bought wheat at 61s. per quarter, pavable in 4 months, and sold it the same day at 65s. per quarter, payable in 7 months; what is the gain per cent. per annum ?

10. Suppose the grass in a meadow to be of uniform quality and growth, and that, when the whole pasture is equivalent to 12 weeks' growth, 48 sheep will crop it down in four weeks; how long would it take 28 sheep to do the same?

ENGLISH HISTORY.

Section 1.

1. Enumerate the sovereigns named Plantagenet. Under what circumstances did they first ascend the throne ?

2. Who were the sovereigns of the Tudor race, and what were

the circumstances under which they first ascended the throne of England?

Section 2.

1. Give dates for the following events:-The Norman Conquest, the ascension of Edward I., of Edward III., Charles I., William and Mary.

2. Give some account of the feudal system. Under what circumstances was it first introduced in England? In what respects was its operation controlled by the influence of the Saxon aristocracy, and by the old Saxon institutions of the country?

3. Give some account of the authority exercised by the Pope in England before the Reformation; and of the troubles to which, at different times, it gave rise.

Section 3.

What is the history of the Liturgy of the Church of England?

Section 4.

1. Under the authority of what Act of Parliament did George I. derive his right to the throne? What was his claim by descent? The claims of two other families, by descent, were superior to his; what families were they, and why were they set aside?

2. Give some account of the war of the "Spanish succession." In what circumstances did it originate, who were the principal leaders, and what the chief battles fought in it, and how did it terminate?

Section 5.

1. Enumerate the great naval engagements of the time of George III., and give the names of the commanders.

2. Give some account of the Peninsular war, and of the circumstances in which it originated.

1. Of Chester and its environs.

2. Of England, showing distinctly its river system. 3. Of Europe.

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Section 2.

1. Describe the county of Kent.

2. Describe the principal mountain ranges of England.

3. Contrast the objects familiar to our observation in England with those which surround the inhabitant of a tropical climate.

Section 3.

1. What places in England are historically the most remarkable? 2. Describe the mountain and river systems of Spain.

3. Describe an Arctic winter.

Section 4.

1. What is meant by the distinction of castes among the Hindoos? What are the names of their principal deities, and what the characteristic features in their religious belief?

2. Give some account of the climate of Hindostan, and of the periodical rains.

3. What are the principal groups of islands in the Pacific Ocean; by what races of men are they inhabited; by whom were they discovered, and what has been their subsequent history?

Section 5.

1. Account for the formation of clouds and rain; to what regions of the earth is the formation of clouds limited ?

2. State what are the prevailing currents of the atmosphere, and account for them. Would a vessel bound to New Zealand and back make the voyage in an easterly or a westerly direction, and why?

3. The extreme summer heat of Nova Zembla is, probably, not less than that of London. Explain this.

GEOMETRY AND ALGEBRA.

Section 1.

1. Show that 2 x + 3y (x

2 g)

= x+5y.

2. Multiply 3 2 x + 5 by x-7.

(a + b) x + ab by x — a.

Section 2.

1. A farmer buys a flock of sheep at 20s. each, and after having kept them until the expences incurred upon them amount to £10 (during which time he has lost ten of them), he finds they have cost him 30s. each. How many were there in the flock?

2. The food of part of the inmates of a union-house is made of wheaten flour, and that of the rest of oatmeal. When the whole number of inmates is n, they eat a sacks of flour per day, and b of oatmeal; and when the number is N, they eat A sacks of flour per day, and B of oatmeal. How many will one sack of flour feed for one day, and how many one sack of oatmeal?

3. A passenger train and a luggage train, the one travelling at 10 miles per hour less speed than the other, set out at the same time, the one from London and the other from Carlisle, 210 miles apart, and pass one another at a certain station on the road. The passenger train sets out from Carlisle to return, two hours after the luggage train sets out to return from London; and it is observed that they pass one another at the same station. At what rate do they travel, and how far from London is the station?

1. The greater side of every triangle subtends the greater angle. 2. Right lines which are parallel to the same right line are parallel to one another.

3. Equal triangles on the same base and on the same side of it, are between the same parallels.

Section 5.

1. If a right line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole line and that part, together with the square of the other part.

2. If two circles cut each other, they shall not have the same

centre.

3. The angles in the same segment of a circle are equal.

MECHANICS.-(TATE.)

ASTRONOMY.-(COMSTOCK.)

Section 1.

1. Define the unit of work, and show, that if a pressure of m pounds be exerted over a space of n feet, the number of units of work done is represented by m x n.

2. How many tons of coals can be raised in 24 hours from a depth of 90 fathoms by a winding engine of eight-horse power? 3. A shaft 256 feet in depth, and full of water, is to be pumped dry by three men working in succession; to what depths must they, respectively, sink the surface of the water, that each may do an equal share of the work?

Section 2.

1. A train weighing 90 tons descends a gradient of 1 in 400 steadily, at the rate of 40 miles per hour; what is the horsepower of the engine?

2. How many horses, each exerting a traction of 200 lbs., would be required to draw a waggon weighing with its load five tons, up a hill whose inclination is 1 in 18, the friction being 1 in 25 ?

3. How many units of work must be expended in carrying a ton of goods along a line of railway which ascends 3000 feet on a gradient of 1 in 50, then runs 10,000 feet on a level, afterwards descends 1000 on a gradient of 1 in 180, and lastly ascends 6000 feet on a gradient of 1 in 300 ?

Section 3.

1. A uniform bar three feet in length, and weighing 10 lbs., has weights of 20 lbs. and 10 lbs. suspended from its extremities; on what point will it balance ?

2. Show that the distance of the centre of gravity of a triangle from its base is one-third of the height.

3. In the compound wheel and axle, if the diameters of the two axles be 12 inches and 9 inches, respectively, and the length of the handle 20 inches; what is the relation of the power and weight?

Section 4.

1. Investigate an expression for the work accumulated in a body of a given weight, and moving with a given velocity.

2. A train which weighs 400 tons, is travelling at the rate of 20 miles an hour; what friction must be put upon it by the breaks,