EUCLID.

(Three Hours allowed for this Paper).

Books I. to IV.

Section 1.

1. Upon the same base and upon the same side of it there cannot be two triangles which have their two sides terminated at one extremity of the base equal to one another, and likewise those which are terminated at the other.

2. 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 of them, 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.

3. To a given straight line to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Section 2.

1. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the two parts.

2. If a straight line be divided into two equal and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. 3. To describe a square that shall be equal to a given rectilineal figure.

Section 3.

1. If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

2. The diameter is the greatest straight line in a circle; and of all others that which is nearer to the centre is always greater than the one more remote: and the greater is nearer to the centre than the less.

3. If from any point without a circle two straight lines be drawn, one of which cuts the circle and the other touches it; the rectangle contained by the whole line which cuts the circle and the part of it without the circle, shall be equal to the square of the line which touches it.

Section 4.

1. About a circle to describe a triangular equiangular to a given triangle. 2. To describe an isosceles triangle, having each of the angles at the base double of the third angle.

3. To inscribe an equilateral and equiangular pentagon in a given circle.

MECHANICS.

(Three Hours allowed for this Paper.)

Section 1.

1. Define the unit of work, and prove that if a pressure of 5 lbs. be exerted through 7 feet, the number of units of work done is represented by 7 x 5. 2. State the principle of the parallelogram of pressures, and describe fully an experiment by which it may be proved.

3. Prove that in a straight lever the power and weight are inversely as their distances from the fulcrum.

Section 2.

1. What is the strength of a wire, inch in diameter, of iron which will bear 25 tons per square inch?

2. A train weighing 50 tons travels on a railway at the rate of 20 miles an hour, the resistances of friction and the air being estimated at 8 lbs. per ton; at what horse-power does the engine work?

3. The piston of a steam-engine is 36 inches in diameter, the length of the stroke is 6 feet, and it makes 6 strokes per minute; under what effective pressure per square inch must it work in order to yield 75 horse-power at the piston?

Section 3.

1. A bar of iron 15 feet long, and supported at its extremities, has 3 cwt. suspended from a point distant 6 inches from one point of support, what is the pressure on the other point of support, first when the weight of the bar is neglected, and secondly, when 15 lb. is allowed per foot for the weight of

the bar?

2. Exhibit, by means of diagram, any useful combination of three pullies, and determine the relation between the power and weight in that combination. 3. A weight is suspended from a given point in a cord whose extremities are fixed to any two given points; show how the tensions on the two parts of the cord may be determined by means of a scale and compasses.

Section 4.

Describe fully one of the following machines, illustrating your description by a diagram. 1. A thrashing machine. 2. A gas meter.

Section 5.

Describe one of the following machines, illustrating your description by a diagram.

1. A flour mill.

2. An organ.

1. Multiply 4 a2---6 a + 9 by 2 a + 3.

2. Show that a × a" = am+" and am÷a" = am-"; and divide q3 — 3aTM c2 + 2c2 by aTM―c".

a + x a

+

+ a2 X

1. Reduce to its simplest form

2. Show that /24 + √54− √6, = 4√6, and extract the square root of 4x-12x+25 x2·

-24x+16; proving the principal steps of the process.

3. Prove the rule for finding the greatest common measure, and find the greatest common measure of

3x-1, and

3. (a) √ (1 + a)2 + (1 − a) x + √ (1 − a) 2 + (1 + a) x = 2a.

1. Find two consecutive numbers such that the half and the fifth parts of the first taken together shall be equal to the third and fourth parts of the second taken together.

2. What two numbers are those whose sum is 40 and the sum of their cubes 19000?

3. If 18 oxen, in five weeks, eat 6 acres of grass, and 45 oxen eat 21 acres in nine weeks, the grass growing uniformly; how many weeks' food for an ox were there on each acre before they began to feed, and how many grew on an acre per week?

Section 6.

1. There are three schools, boys', girls', and infants', containing together 266 children. There are four times as many in the infants' school and twice as many in the girls' as there are in the boys'. How many are there in each?

2. A square room requires 576 superficial feet of paper to cover its walls; but if it were 3 feet higher this quantity of paper would only cover three of its walls. What are its dimensions?

N.B.-Windows, doors, &c. are to be neglected in the calculation.

3. A book is published at a cost of 5s. per copy and sold at 10s. per copy. Now if it had been sold at 6s. 8d. per copy the annual sale would have been 200 copies more, the edition would have been sold off two years sooner, and it would have begun to pay profit one year later. How many copies were published and what was the annual sale?

N.B.-The interest of money is to be neglected in the calculation.

WELSH.

(Three Hours allowed for this Paper.)

1. Translate into English one of the two following passages:

Fy mol, fy mol; gofidus wyf o barwydenau fy nghalon; mae fy nghalon yn terfysgu ynof; ni allaf dewi, am i ti glywed sain yr udgorn, O fy enaid, a gwaedd rhyfel. Dinystr ar ddinystr a gyhoeddwyd; canys yr holl dir a anrheithiwyd; yn ddisymmwth y distrywiwyd fy lluestai i, a'm cortenni yn ddiattreg.

Hai! lleisiwch yr udgyrn ar goppa bryn Sion;
Dadgenwch gân molawd, chwi fedrus gantorion,
I'n Blaenor cadarnaf, a hollol orchfygodd
Dywysog yr Awyr, a'i aml fyddinoedd.
Daeth heddyw o'r frwydr, âi ddillad yn gochion;
A'i gleddyf yn llifo gan waed ei elynion;

A llefodd "Efengyl, sef rhyddid trag'wyddol,
Iwch feibion caethiwed, mewn teyrnas ddymunol,
Ennillais i heddyw, 'r ol ymdrech anhydyn,

A'r dieflig ormesdeyrn, oedd beunydd eich gelyn."

2. Parse fully, in English, the first two lines of whichever of the above passages you have translated; and explain the literal mutations of the whole passage.

3. Translate into Welsh one of the two following passages:

Come let us walk abroad and see the wonderful works of God. Let us behold the earth, the sky, the sea, the animals, the birds, the fishes, and the plants. Do they not all bear witness to the goodness of our Creator? Do they not all show his handiwork, and his providence? Examine them well, O man; try to understand them; and be thankful!

He was a young man, born in a humble position, who, thanks to the institutions of his country, had been able to gain a slight amount of general knowledge. He was placed in a situation, fairly remunerated, which tended to separate him from his fellow-parishioners. Such a rapid rise completely turned his head; he gave himself airs, disdained his equals, became insolent to his employers, aspired to an higher occupation, and, like the frog in the fable, thought that by puffing himself up, he should become as big as an ox. 4. Explain fully the construction of the following phrases:—

Bod eisiau arno sydd eglur.

Nid yw hyd yn nod y cyfoethogion heb drallod.
Yr hon yr oedd ei brawd yn glâf.

MALE STUDENTS (continued).- SECOND YEAR.

1. THE ACTS OF THE APOSTLES.
II. THE EPISTLE TO THE GALATIANS.

(Three Hours allowed for this Paper.)

Section 1.

On what occasions was St. Peter cast into prison at Jerusalem, and under what circumstances was he set free? In what words did he address the council on his second appearance before them?

2. Describe geographically the countries from which those persons came who heard the Apostles preach on the day of Pentecost.

3. "And all that believed had all things common" (Acts ii. 44). In what sense are the words "had all things common," to be received? Give Scriptural grounds for your answer to this question.

Section 2.

1. Relate, shortly, the history of the Church, between the conversion of St. Paul and the departure of Barnabas from Antioch to Tarsus to seek Saul (Acts xi. 25).

2. Give some account of the chronology of the Acts of the Apostles.
3. Have you any observations to make on the following passages?—
"Which was with the deputy of the country Sergius Paulus"
(Acts xiii. 7).

Philippi which is the chief of that part of Macedonia and a colony"
(Acts xvi. 14).

"For as I passed by and beheld your devotions I found an altar with this inscription, TO THE UNKNOWN GOD" (Acts xvii. 23).

Section 3.

1. What is recorded of St. Paul's last visit to Jerusalem?

2. What probable account may be given of St. Paul's labours during his confinement at Rome, and after his release?

3. What is known of the following persons mentioned in the Acts of the Apostles?

Apollos, Titus, Erastus, Aristarchus, Tychicus, Trophimus, Gallio, the high priest Ananias (Acts xxiii. 2), Herod the king (Acts xii. 1), King Agrippa (Acts xxv. 13).

Section 4.

1. Describe Galatia geographically, and give some account of its history. 2. What is recorded in the Acts of the Apostles, concerning St. Paul's visit to Galatia?

3. "I marvel that ye are so soon removed from him that called you " (Gal. i. 6). To what period does the expression "so soon" probably refer Assign reasons for the answer you give to this question.

Section 5.

1. What difference is observable in respect to the authority with which St. Paul addresses the Galatians and the Romans? How do you account for the difference?

2. St. Paul does not in the Epistle to the Galatians lay down the doctrine of the Gospel at large as he does in that to the Romans. Assign a reason for this.

3. The church of the Galatians included Jews and Jewish proselytes. How does this appear from the Epistle?

Section 6.

1. "When the brethren knew, they brought him down to Cæsarea and sent him forth to Tarsus a city of Cilicia" (Acts x. 30). What passage in the Epistle to the Galatians refers to this journey, and what argument may thence be derived for thinking that the journey in question was made by land?

2. "And I, brethren, if I yet preach circumcision, why do I yet suffer persecution? Then is the offence of the cross ceased" (Gal. v. 11.) Explain this passage and illustrate it by passages from the Acts of the Apostles.

3. "Then after three years I went up to Jerusalem to see Peter and abode with him fifteen days" (Gal. i. 18.) Prove from the Acts of the Apostles that St. Paul abode but a short time at Jerusalem on this visit, and show how he was employed.

Section 7.

1. Explain the following passages:

Brethren, if any man be taken in a fault, ye which are spiritual restore such an one, in the spirit of meekness, considering thyself lest thou also be tempted" (Gal. v. 1).

"Brethren I beseech you be as I am; for I am as ye are: ye have not injured me at all" (Gal. iv. 12).

2. Explain the following passage :-" Having begun in the spirit are ye now made perfect by the flesh?" (Gal. iii. 3). In what sense are the words spirit and flesh used in this Epistle?

3. What reason is to be assigned for the use of the following words by St. Paul in the commencement of his Epistle?" Paul an Apostle, not of man neither by man" (Gal. i. 1)! Give other passages in which he asserts his apostleship to have been derived immediately from Christ. From what other Apostle was he distinguished in this respect?