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ECCLESIASTICAL HISTORY.

(Three Hours allowed for this Paper.)

I. The 15th and the first half of the 16th centuries.

2. The Reformation in England.

Section 1.

1. Give some particulars of the life of one of the following persons:(a) Wickliffe; (b) Huss; (c) Erasmus.

2. Give some account of those communities of Christians who, before the Reformation, repudiated fundamental doctrines of the Church of Rome.

3. What circumstances in the political state of Europe, and in the progress of knowledge and the arts of civilization, towards the close of the fifteenth and the beginning of the sixteenth centuries, favoured the Reformation, and in what way?

Section 2.

1. Give some account of the early life of Martin Luther.

2. Who were the three principal sovereigns of Europe at the time of the Reformation in Germany? What were their characters respectively, and in what relation did they stand to each other?

3. Who were the Popes during the first quarter of the sixteenth century? Give some account of their history. Name the great commercial state of that age, and state who were is greatest merchants, writers, and artists?

Section 3.

1. Give some account of one of the following reformers :--

(a) Zuinglius; (b) Farel; (c) Calvin.

2. What were indulgences? Give some account of the measures taken by Tezel to promote the sale of indulgences in Germany, and their results.

3. What means were taken by the Pope to silence Luther? Who were his chief antagonists? Give some account of his appearance at the Diet of Worms. What testimony does his early life afford to the existence of piety and learning among the monastic orders in Germany?

Section 4.

1. What, before the reign of Henry VIII., had been the chief grounds of collision between the the Popes and the Sovereigns of England? What were the objects of the statutes of Provisors and of Præmunire?

2. What measures were taken for the suppression of Wickliffe's translation of the Scriptures? Give some account of the history of the Lollards in the reigns of Henry IV. and Henry VII.

3. What general councils were held in the fifteenth and sixteenth centuries, and under what circumstances?

Section 5.

1. Give some account of one of the following persons:

(a) Sir T. More; (b) Tyndal; (c) Latimer.

2. Give some account of the books issued by authority in the reign of Henry VIII. By whose authority were they issued? What three great principles of the English Reformation were established in that reign?

3. What bishops of Henry the Eighth's reign were on the side of the Reformation; and what on the side of the Pope? How did Cranmer act in regard to the Six Articles? What did he advise in regard to the revenues of the monasteries?

Section 6.

1. How long did the reign of Edward VI. last? What were the first acts of his reign in favour of the Reformation?

2. Give some account of the history of the Liturgy in the reign of Edward VI. What controversy was raised by Hooper, and with what results? 3. Give some account of the history of Cranmer during the reign of Mary.

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LOGARITHMIC ARITHMETIC.

(Two Hours allowed for this Paper.)
Section 1.

1. Define a logarithm; and show that the logarithm of the product of two numbers is equal to the sum of their logarithms; and the logarithm of their quotient, to the difference of their logarithms.

2. Show that the integral portion or index of the logarithm of an integral number is equal to one less than its number of integers.

3. One person out of 46 is said to die every year in England, and one out of 34 to be born; if there were no emigration, in how many years would the population double itself?

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1. What will a capital of 1207. amount to in 10 years at 6 per cent. per annum compound interest?

2. In how many years will 17. become 27. at 4 per cent. per annum compound interest?

3. What is the present value of an annuity of 201. to continue 40 years, reckoning interest at the rate of 6 per cent. per annum?

HISTORY OF ENGLAND.

(Three Hours allowed for this Paper.)

The constitutional History of England.

The history of manners and customs in England.

Section 1.

What particulars can you give of the manners and customs of the people in England in one of the following periods?

1. The Anglo-Saxon period.

2. From the reign of Henry IV. to that of Richard III.

3. The reigns of Charles II. and James II.

Section 2.

What account can you give of the condition of the people as regards their habitations, their clothing, and the relation of the employers to the employed, in one of the following periods:

1. The Norman Conquest to the death of King John.

2. The reign of James II. and Charles II.

3. From the accession of George III. to the commencement of the present century.

Section 3.

What general account can you give of the progress of arts and manufactures, and of the state of national industry and commerce, in one of the following periods ?—

1. From the revolution of 1688 to the accession of George III.

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2. The period from the accession of George III. to the commencement of the present century.

3. The present century.

Section 4.

1. Into what six periods does Blackstone divide the history of the laws of England.

2. What great department of law does he state to be of Anglo-Saxon parentage? What principal changes in the law were introduced at the Norman conquest? Of what classes of persons did the nation then consist? In what terms does Blackstone describe the violence and oppression of that period? In what respects were these mitigated in the reign of Henry I.

3. Mention some of the chief of our liberties established by Magna Charta. In what respects were these violated by the Tudors and the Stuarts? What circumstances favoured the encroachments of power under the Tudors? What does Blackstone say of the reign of James Î?

Section 5.

1. Under what circumstance were knights of the shire first called to Parliament? How were they elected? When did the two Houses begin to sit separately?

2. Give some account of the Petition of Right, the Habeas Corpus Act, the Bill of Rights, and the Act of Settlement.

3. What is the right of the House of Commons in regard to taxes; on what constitutional principle is it founded? What is the method of bringing a Private Bill into the House of Commons; and what is that of bringing in a Public Bill? What is done at the first, and what is done at the second reading? What is a Committee of the whole House?

Section 6.

1. How did the feudal system originate? What were the qualifications of knighthood in feudal times?

2. Give some account of the conditions under which the barons held lands of the crown, and particularly of the money payments to which they were subject.

3. What was Doomsday Book? What was the distinction between free soccagers and villeins? Give some account of the condition of the latter. What causes led to their emancipation?

HIGHER MATHEMATICS.-No. I.

(Three Hours allowed for this Paper.)

Section 1.

1. If the angle of a triangle be bisected by a straight line, which also cuts the base; the segments of the base shall have the same ratio which the other sides of the triangle have.

2. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

3. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means, and conversely.

Section 2.

1. To describe a rectilineal figure which shall be similar to one, and equal to another, given rectilineal figure.

2. To cut a given straight line in extreme and mean ratio.

3. If an angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to

the rectangle contained by the segments of the base, together with the square of the straight line which bisects the angle.

Section 3.

1. Show that equal triangles on equal bases have equal altitudes, whether they be situated on the same or on opposite sides of the same straight line. 2. Divide a given straight line into two parts such that the squares of the whole and of one of the parts shall be equal to twice the square of the other part.

3. From a given point without a circle, at a distance from the circumference of the circle not greater than its diameter, draw a straight line to the concave circumference which shall be bisected by the convex circumference.

Section 4.

1. Describe a levelling instrument. Explain the method of using it for determining the difference of level of two distant objects, and give an example of a level book, making the calculations indicated by it.

2. Prove the formula for determining the area of a triangle in terms of the sides.

3. There is a rectangular plot of land of two different qualities, one portion of it being £m, and the other £n per acre; the boundary of the two is a straight line whose intersections with the side and one end of the rectangle are at the same distance a from one of its angles. A portion of this land, of a given value £c, is to be cut off by means of a straight fence parallel to the end of the rectangle whose length is b. Where must this fence be drawn? Section 5.

1. Describe and explain the use of (a) The Vernier scale.

(b) The prismatic compass.

2. Give an example of a field book, lay down the corresponding field, and calculate its area.

3. Prove Thomas Simpson's rule for determining an area bounded by a curved line.

Section 6.'

1. Given the meridian altitude of a heavenly body whose declination is known; show how the latitude of the place of observation may be found. 2. Given the mean time at any place, and also the Greenwich time; explain fully how the longitude of that place may be found.

3. There are two points A and B, situated due north and south, 21 feet from one another; and there is a third point C, half way between them. Supposing to be exceedingly small as compared with the radius of the earth, determine how much less a distance A is carried round in an hour by the rotation of the earth than C, and how much greater B. Apply the resulting formula to explain Foucault's Pendulumn experiment.

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2. Find the series in arithmetical progression of which 2 and 10 are the 4th and 7th terms.

3. Investigate expressions for the number of permutations of n things taken r together and of n things taken altogether when the quantities recur, and calculate the number of permutations that can be made with the letters taken all together of the word characteristic.

Section 2.

1. Prove the binomial theorem in the case in which the index is a positive integer.

2. Show that a number and the sum of its digits leave the same remainder when divided by 9.

3. Show that converging fractions are alternately too great and too little; deduce the law by which any continued fraction may be converted into a series of converging fractions, and show that the difference between any two consecutive convergents has 1 for it numerator.

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1. If an event may happen in a ways, and fail in b ways, determine the chance of its happening or failing; and apply it to determine the probability of a person's death in his 23rd year; the number of persons out of 586 of the age of 22 who attain their 23rd year being 579.

2. A sum of money £a is to be raised in n years by the investment of £ b at £r per £1 compound interest for a certain portion of the term, and of Le, at the same rate of interest, for the rest of the term. At what period of the term must the £ c be substituted for the £b?

3. The toll of a bridge is one penny; it is proposed when the decimal coinage shall be introduced to fix the toll at 5 mils for a part of the n years which the lease will have to run, and at 4 mils for the rest of the term. How long should 5 mils be paid that its excess over the penny toll may compensate for the deficiency of the 4 mils; compound interest being allowed at £r per £1 per annum?

Section 5.

1. Show by means of a diagram under what circumstances the sine, cosine, and tangent of an angle become negative quantities; and prove that sin. (A+B)= sin. A cos. B cos. A sin. B.

2. Having given sin. 18° ‡ (√/5 — 1) and sin. 30° = 4, find sine 48° and sine 129.

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1. Having given three sides of a plane triangle, show either angle may be determined.

2. Having given two sides of a plane triangle, and the angle they contain, show how either of the other angles may be determined.

3. Standing on a line of railway I can see each of two distant objects, but if I move either way along the line I lose sight of one of them. By what observations and calculations may I determine the distance of those objects

from one another?

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