ultimo raggio della sua stella che stava per ecclissarsi per sempre, velocemente marciava alla volta di Parigi, accrescendo successivamente le sue schiere con quante schiere erano successivamente contro di lui inviate; giacchè niuna fra tante volle o potè trattar de nemico colui che tante volte l' avea condotta alla vittoria, tutte lo salutarono qual loro imperadore. DR. ATKINSON. Translate the following into English :: Oh! ce sont là les grands et les heureux du monde ! O magnifique orgie! ò superbe appareil ! 1. Write a notice on V. Hugo as a lyric poet (quoting in illustration any passages you remember). 2. Influence of the French drama as an instrument of European culture ? 3. Write out an analysis of any chapter of Guizot. 4. Guizot's position as a historian? Compare with Thiers or Michelet. 5. Give some account of French epic poetry from the earliest times, 6. Of French ballad poetry. 7. Of the state of modern French (nineteenth century) literature in any one branch. 8. Trace the growth of the French system of conjugation out of the Latin. 9. What new modes of formation are peculiar to the Romance languages? 10. Give the derivation of-moutarde, moule (m. and f.), nièce, jusque, cercueil, danger, coucher, dîme, épée, renard. Translate the following into Italian, French, or Spanish : For instance, suppose a number of travellers proceeding through some nearly desert country, such as many parts of America, and journeying together in a large party for the sake of mutual security: when they came to a resting-place for the night, they would be likely to agree among themselves, that some should unlade and fodder the cattle, while others should fetch firewood from the nearest thicket, and others water from the spring; some in the meantime would be occupied in pitching the tents, or erecting sheds of boughs; others in preparing food for the whole party; while some again, with their arms in readiness, would be posted as sentinels in suitable spots, to watch that the rest might not be surprised by bands of robbers. Now, but for such an arrangement, each man would have to go both to the spring for water, and to the wood for fuel-would have to prepare his own meal with almost as much trouble as it costs to dress food for the whole-and would have to encumber himself with arms while performing all these tasks, lest he should be suddenly attacked by an enemy. SCHOOL OF ENGINEERING. MIDDLE CLASS. DR. DOWNING. 1. For the gauge of 1 ft. 11 in., which is that of the Festiniog Railway in North Wales, compute the length of the line AB, which being strained from any two points in a continuous curve, will give a distance at the centre CD equal to the necessary superelevation of the outer rail; the highest velocity permitted being 25 miles per hour; and together with the length of the line AB, give a full proof of the rule by which it is determined. כן A C B 2. What is the length of offset to be used with a curve of 54 statute chains radius, it being set out by the method of offsets at the chain end? and describe fully the mode of proceeding in setting out a curve, and also give a detailed proof of the rule employed. 3. It becomes necessary, in setting out the curve in the last question, to increase the radius, after a certain point, to 70 chains; what is the offset to be used for the first point in this new curve, when the centre is at the same side as in the original curve, and what is the offset for the succeeding points in this curve of 70 chains? 4. In setting out a curve by means of a theodolite and chain, the springing point is at 89 chains 32 links, and the radius 53 statute chains; what is the angle for the first odd distance, and for the following chain points?—and add a proof of the approximate formula you employ. 5. If both springing points are such that the theodolite cannot be set up on them, but the intersection of the tangents is quite accessible, how may we proceed to set out the curve? Take a radius of 5247 ft., and the angle of intersection 144° 26', so that in the answer you may give the values of the several quantities to be used when describing the method of proceeding. 6. Two planes, inclined respectively at 45° and 30° with the horizontal, are so placed that their traces make an angle of 120° measured on the horizontal plane; describe the mode of drawing the horizontal projection of the line of intersection of the two planes, and also of determining the angle which that line makes with the horizon; and apply this to the drawing of a plan of the intersection of two retaining walls, one of which batters at an inch to the foot, and the other 1 inch to the foot, the plans of the two walls being inclined to each other at 110°. 7. Give, with proof, the general construction for drawing a regular polygon of n sides upon a given line, and the construction for an octagon particular to that figure; also an approximate construction for a heptagon. 8. The lower part of a portion of an excavation has the following dimensions:- Breadth of base 24 ft., slopes to one, and the depths at A=2, at B 15 ft., at C = 10 ft., and at D=21 ft. Calculate each of these three portions separately, and in cubic yards; the lengths being from A to B 270 ft., from B to C 135 ft., and from C to D 216 ft. 9. The harder ground in the last question, standing at that steep slope, is covered by loose gravel requiring a slope of 2 to one; calculate the volume with these following depths: at A = o, at B = 6 ft., at C = 18 ft., and at D = 3 ft. 10. Give a full proof of the formulæ employed in questions Nos. 8 and 9. 11. If the depths in No. 8 had been taken by scale from a Parliamentary section, what would have been the cubical content of the poitions B to C, and C to D? 12. A turnpike road is found to be 28 ft. wide where it crosses the centre line of a railway; what width may be given between the parapets (or between the abutments)? and give a statement of every circumstance either in the wording of 8th Vic., chap. 20, or prudential, which may influence this part of the design. 13. A bridge over a line of railway has a curved string course and parapet; the design shows that the horizontal distance from the key to the newel is 34 ft., the inclination of the road on each side being one in 28; what is the radius of the curve of the string course, and the vertical depth of the point where the arc meets the newel below the middle point over the key and prove the approximate formula you employ. 14. An oblique bridge with girders over a stream has the angle of intersection of the axis or direction of the stream with that of the road equal to 47°; the width of the stream is 18 ft., and that of the road 22 ft., each taken on the square; compute the length of the abutments, and the length of the girders, adding 2 ft. 6 in. for bearing at each end of the girders. 15. Compute the discharge of a channel the dimensions of the transverse section being 1st part, a segmental invert 3 feet wide, and having a dip of 9 inches in the centre. 2nd part, a trapezium, the lower side being 3 feet wide (the width of the invert), and the width at the water-surface being 3 ft. 6 in., and the distance between these two parallel lines 2 ft., the side walls having a batter of 1 in. to the foot. The area of the segmental portion at the invert, and also the length of the curve, may be taken, either by the approximate methods or exactly. The inclination is 4 ft. per mile, the discharge to be given in cubic feet per minute, and in gallons per 24 hours. 16. A square orifice, 6 inches in the side, discharges 286.5 cubic feet per minute with a head of water-measured from still water surface to centre of orifice-equal to 12.25 feet; compute the coefficient of contraction which was acting at this opening, it being supposed that the contraction is identical on all the four sides. 17. If this orifice were altered so as to suppress altogether the contraction on the lower side, the other three sides remaining the same, what would now be the discharge per minute? 18. If in question No. 16 the head of water were only 125 ft. above the centre of the orifice, what formula would you employ to give exact results? and give a proof of it. Also, compute the depth at which the velocity would be mean. 19. A weir, 12 ft. long, and having a metal plate or edge for its crest, is discharging water at a depth of 0.45 ft., compute the discharge; show how the formula you employ is derived. 20. If it were required to send down only 40 per cent. of this quantity, what should now be the depth at which it flows over the crest? The discharge may be given in cubic ft., per second or per minute. 21. Describe all the precautions to be used in constructing such a measuring apparatus, and how you would actually measure the depth of water flowing over. MR. LESLIE. 1. State and prove the expression for the relative density of steam. 2. What is the relation between the temperature and pressure of steam? What experiments illustrate the connexion? 3. Find the latent heat of steam at 80 lbs. pressure. 4. What weight of water can be raised from the freezing to the boiling point by the condensation of steam produced from a cubic foot of water at 212° ? 5. The combustion of 1 cwt. of coal is able to convert 84 gallons of water at 68° into steam at 250°; what is the evaporating power of the fuel? 6. Calculate the mechanical effect produced by the evaporation of water. 7. Prove that the greatest possible useful effect is produced when steam admitted into the cylinder of an engine has the same pressure as that in the boiler. MECHANICS. MR. GALBRAITH. 1. Find the moments of inertia of a cube round one of its edges, and round one of its diagonals. 2. If a heavy body revolve on an axis, prove that the centre of gyration acquires a velocity due to the descent of the centre of gravity. 3. Let a cube of cast iron, whose side is 18 inches, be used as a tilt hammer acting at the end of a handle 6 feet long; calculate the angular velocity and momentum with which it will strike an anvil at its centre of percussion after falling through an angle of 30°. Let the weight of the handle be neglected, and the weight of iron be taken at 450 lbs. to the cube foot. 4. The centres of percussion, pressure, and oscillation are identical; what is the expression for their distance? Give a construction for finding them. 5. If the tilt hammer, described in question 3, strike the anvil close to the remote edge, calculate the shock on the axis. 6. A prism of oak (58 lbs. to the foot), which is 6 feet high and I foot square, stands on its square end; find the momentum with which it must be struck in a horizontal direction through its centre of percussion so as just to overset it. 7. If S be the modulus of rupture, and ƒ the tearing or crushing strain of the fibres, prove that according to theory S = tf. 8. Show that the centre parts of solid round girders or pillars are of little use in resisting transverse strains. |