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2. A ladder, 120 lbs. weight and 20 feet long, rests against the face of a vertical wall at a point 17 feet from the ground; if its centre of gravity be 8 feet from its base, required its pressure against the wall.
3. A wall of brickwork, 20 feet high and 14 feet thick, is acted on at every foot of its upper internal edge by a force P inclined at an angle of 30° to the ground; assuming the weight of a cubic foot of brickwork to be 112 lbs., required the greatest value of P that will just not overturn the wall.
4. In the same case, if the wall be supported at every 20 feet of its length by a triangular buttress of its own height, it feet in breadth, 3 feet in thickness at the ground, and tapering to nothing at the top; required the greatest value of P that will just not overturn the entire structure.
5. In a rectangular reservoir of water, 20 feet deep, 50 and 36 feet broad at the surface and base, respectively, and 100 feet long throughout; assuming the weight of a cubic fathom of water to be 6 tons, calculate the entire pressures on its sloping and vertical faces.
6. In the same case, calculate the moments of both pressures to overturn the retaining walls, supposed both vertical outside, and 3 feet thick at the top.
7. In the equilibrium of a suspension bridge under the action of gravity, if the roadway be perfectly flexible, uniform, and of considerable weight compared with that of the supporting rods and chains, show that approximately the forms of the latter are parabolas.
8. Given, in the same case, the span and central deflection of the supporting chains, required the variation of the latter consequent on a small variation in the length of the chains, arising from change of temperature or any other cause.
9. Investigate the formula for the central deflection of a uniform rectangular beam of given dimensions, weight, and elasticity, supported, but not fixed, in a horizontal position, by two props placed under its extremities, and bent by its own weight.
10. For a girder of uniform thickness, and uniformly loaded, required the best form of vertical section to resist fracture by bending.
1. Calculate the radius of a segmental arc 28 ft. span, 6 ft. rise.
2. Calculate the radius of a cast iron segmental arch 179 ft. span, and 17.9 ft. rise, and give the rule for readily determining the radius with that proportion of rise to span.
3. Compute the vertical ordinate in No. 1 at a point 5 ft. from the springing; and if the arch had been a semiellipse with same span and rise as in No. 1, calculate the vertical ordinate at that point.
4. Calculate the number of cube yards in the cutting of the section be. low :-Base 30 ft., and side slopes i to
5. If a portion of an excavation have the two end heights equal, each being 30 ft., the base being 20 ft., and slopes 2 to r; the ground on the surface having a transverse slope of 12 to 1; calculate the increase of excavation in cubic yards caused by this slope above that of level ground, the length being 297 ft.
6. In a portion of a cutting, 200 feet in length, base 30 feet, slopes if to 1, the heights at each end being 40 feet and io feet, respectively ; calculate the distance from either end at which a vertical plane being drawn, it will divide the block into equal portions.
7. In the annexed sketch map of contoured ground, show how you would obtain the height of any point as A situated between two figured contour lines.
8. Draw a line across the contours drawn on the annexed plan which shall have an inclination of 1 in 12.
9. State the number of feet per mile ascent in the following gradients : i in 270, gth inch in a yard, 7 inches per statue perch.
10. On a map whose scale is gooo, a square is drawn 3} inches in the side, calculate the number of acres it encloses.
11. A railway has to be carried over a road 25 feet square width, the axis of the road and railway intersect at 38°; calculate the length of the girders required, the bearing upon the abutment being 2 feet on each end.
12. In an oblique arch, being a semicircle 30 feet on the square span; calculate the angles B and o, the angle of intersection of the axes of road and railway being 40°, using the letters in the same signification as in the Text-book.
1. When three forces equilibrate at any point in a plane, show that their moments equilibrate round every point in the plane.
2. For any system of parallel forces, show that the sum of their moments round any line perpendicular to their common direction is equal to the moment of their resultant round the same line.
3. Given the masses of any number of material particles, and their distances from any plane, required the distance of their centre of gravity from the same plane.
4. A uniform beam of given length and weight is supported from a fixed point by cords of given lengths attached to its extremities; required the tensions on the cords.
5. A ladder supported on a rough floor rests against a smooth wall, vertical or inclined; given its weight, dimensions, and position, required its pressure against the wall.
6. In a rectangular reservoir of given dimensions, filled with water, required the entire pressures on the vertical faces and their moments to overturn the retaining walls.
7. If two opposite sides of the reservoir slope, the remaining two continuing vertical; required, as before, the entire pressures and moments for the vertical faces.
8. Explain the most accurate method with which you are acquainted of determining the specific gravity of a solid lighter than water.
9. Required what statical force, acting freely for one second on the mass of a ton weight, will get up in it a velocity of 100 feet per second.
10. Required the centrifugal force of a mass a ton weight performing one revolution per second in a circle of 6 feet radius.
11. If a body be projected vertically upwards with a velocity of 1000 feet per second, required the extreme height to which it will ascend, and the time it will take to reach it.
12. If a body be projected obliquely with the same velocity at an elevation of 45°, required its range on a horizontal plane passing through the point of projection, and the time it will take to reach it.
EXAMINATION FOR PREMIUMS IN IRISH.
1 Cor. iii. 9-15.
Translate the following passages from Irish into English :
i Cor. ix. 24-27.
1. Discuss briefly the question of the antiquity of letters in Ireland.
2. Mention some of the principal features which distinguish the Irish from the other living Celtic dialects.
3. Give the modern and ancient Irish for the following words : Servant, ministry, faith, contrary, image, comparison, conscience, persecution, circumcision.
4. In what respects chiefly does the modern Irish differ from the more ancient language ?
5. It is often said that the Irish wants words for gratitude and profess; show that such is not the case.
6. Derive the words, fognań, cungnań, imreas, fortaót.
7. The derivation and composition of Irish words is frequently obscured by the use of a comparatively modern rule in orthography?
8. To which of the classical languages has the Irish, as it now exists, the greatest resemblance? Give instances, and account for the fact.
9. Give a general account of the verb system of the Irish; and conjugate at length the verb cím.
10. In what circumstances does the substantive not modify the form of the adjective?
11. Mention some of the idiomatic meanings of the prepositions ar
12. Give some instances of the use of the impersonal passive in Irisk.
GENERAL DIVINITY EXAMINATION,
PROFESSOR OF DIVINITY'S LECTURES.
1. The divergence of the Romish and Reformed dogmatic systems begins with the state of man before the fall ?
2. What is the fundamental distinction between the Romish and Reformed doctrines respecting Justification ?
3. Explain exactly what the Schoolmen meant by meritum de congruo and meritum de condigno.
4. “Faith” has very different significations in the Romish and Reformed systems, respectively?
5. What is meant by “fides formata”? _Refute the argument in support of it adduced by Romanists from the Epistle to the Galatians.
6. The dogma of Papal Supremacy de jure divino is intimately connected with another fundamental article of the Romish Creed
7. The argument by which the former is sought to be established consists of three propositions, not one of which can be proved ?
8. The Papal Bulls down to the eleventh century exhibit decisive evidence against the dogma of the Supremacy of the Pope ?
• The greater part of these Examinations is conducted viva voce.
9. The history of Heresy and Schism also furnishes an unanswerable argument against it?
10. The foundation of the Papal power is mainly due to three of the early Popes?
11. Even as a theory, Infallibility is defective in two essential points ?
12. What is the Archbishop of Dublin's argument against Infallibility, founded on a well-known passage in the Acts ?
13. Enumerate the Seven Romish Sacraments in their proper order, and point out their mutual relations.
14. Who first introduced the word “Sacramentum" into Ecclesiastical language? Corresponding Greek word ?
15. Which of the five so-called Sacraments was first promoted to the rank of a Sacrament; and what was the cause of its being so exalted ?
16. The scholastic terms, materia and forma, applied to the Sacraments, are derived from a well-known definition of Augustine :
17. The doctrine of Intention is based on a principle of the Aristotelian philosophy adopted by the Schoolmen?
18. According to the Romish theory, the Eucharist differs essentially, in one respect, from all the other Sacraments ?
19. As regards the mode of the presence of Christ in the Eucharist, the Roman Catechism is at direct variance with the Council of Trent!
20. What is the difference between impanatio and consubstantiatio ? and in what sense do the Lutherans not hold the latter ?
21. What is meant by communicatio idiomatum, and for what purpose was it invented !
22. The Lutheran Formula Concordia says: “Rejicimus ... externa visibilia elementa panis et vini in sacramento adoranda esse.” Why so ?
23. The Romish doctrine respecting the Rule of Faith necessarily involves that of the Infallibility of the Church ?
24. What is the distinction between inhesive and declarative Tradition ? Show that the Tradition sanctioned in the fourth Session of the Council of Trent is different from both.
1. What is meant by the Masoretic Recension? Give a brief account of its origin.
2. What is meant by “the Hebrew tongue" spoken of in Acts, xxi. 40, and elsewhere in the New Testament? Give a sketch of its history.
3. What are the characteristic constituent elements of the New Testament Greek, as compared with Classical Greek ?
4. Whether are the most ancient known MSS. of the Greek or Hebrew Scriptures the older ? What is the difference in age between them?
5. Give a sketch of the history of the LXX. Version.