SECTION B. PROFESSOR TOWNSEND. 6. Make a vertical section of a hanging stone stair-case, with spandril or feathered-edged steps and moulded nosings. Show how the steps are supported and the iron balusters secured to the steps. 7. Make a sketch of a roof, covered with Duchess slates nailed at centre, showing the rafters, battens, margin, lap, and tilting fillet, and specify the weight or number of slates required for 10 squares. 8. Describe the mode of forming a street with asphalt, and also the footways. 9. Find the cant in inches in a railway curve with a radius of half a mile, the gauge being 4 ft. 8 inches and the speed 40 miles an hour. 10. Make a sketch of a modern double-headed or bullhead rail for carrying heavy, fast, and incessant traffic, and specify its weight per yard. Sketch also a flange-rail suitable for the the above purpose, and describe their relative merits. EXAMINATION FOR THE B. E. DEGREE. MATHEMATICAL PHYSICS. PROFESSOR MCCLELLAND. 1. Show that a system of forces can be reduced to a single force acting through any given point and a couple. If X, Y, Z are the rectangular components of the force, and L, M, N the rectangular components of the couple, show that LX + MY + NZ is independent of the origin and of the direction of the system of rectangular axes. 2. Explain how to examine the stability of a system in equilibrium from a knowledge of the work function. A rod rests in equilibrium on a smooth cycloid whose axis is vertical and vertex downwards. Is the equilibrium stable or unstable? 3. A solid is composed of attracting matter of volume density p. If V, denote the potential outside the attracting mass, and 2 the potential inside, show that outside the body da V d2 V1 d2 V1 Vi = 0, dz2 and inside the body dx2 dy? If a finite surface density existed anywhere in the region, what modification would you introduce in the above equations? 4. Taking any point of a body as origin, prove the existence of three mutually rectangular planes passing through it, such that the products of inertia with respect to them vanish. 5. Define an apse of a central orbit. Show that there can be only two apsidal distances and one apsidal angle. 6. Rain is falling vertically on a hemispherical umbrella. Compare the pressures at various points of the surface. 7. A sphere is supported in stable equilibrium by a horizontal axis which passes through the sphere at a distance from the centre, and about which the sphere is free to turn. Determine the smallest blow which would cause it to turn completely round the axis, supposing the direction of the blow to pass through the centre of the sphere. 8. Knowing the surfaces of flotation and buoyancy, and the centre of gravity of any body, show how you would examine the stability in any position. 9. Show how to find the position of the centre of pressure of a plane area immersed horizontally in a rotating liquid. 10. A cone floats in a liquid with its axis vertical and vertex downwards. Determine the condition of stability, and examine the apparently neutral case. CIVIL ENGINEERING. SECTION A. PROFESSOR FITZGERALD. [Lithograph fig. 12 to be supplied with this paper.] 1. Draw the stress diagram for the frame fig. 12 and load shown, finding the tensions in the sides of the inner and outer octagons. 2. In a parallel flange girder, consisting of eight bays of isosceles bracing at 60°, loaded with 10 tons at each vertex of the lower flange, span 120 feet, find the maximum load on the fourth brace from left hand abutment when the bridge has, in addition to the above, a rolling load of 1 ton per running foot brought on it. 3. Describe and illustrate methods of construction for breakwaters, with superstructure founded below low water on a rubble mound. 4. Illustrate quay foundations on concrete cylinders, as used in Plantation Quay, Glasgow, and mode of sinking them. t 5. Illustrate the application of different arrangements of regulating dykes in rivers, their functions, materials and construction. SECTION B. PROFESSOR TOWNSEND. 6. Describe by sketches the siphons constructed by Mr. Baldwin Latham for conveying the sewage under the Mottlaw and Keel-graben rivers at Dantzic, and also the method which he adopted for laying the siphons. 7. Describe the experiments made by Mr. Dibdin with a filtering bed, an acre in extent, at the northern outfall works of the London drainage. State the quantity of sewage that this bed is capable of purifying in 24 hours, and the degree of purification attained. How, according to the Massachusetts experiments, would the quantity purified be affected if raw sewage were run on the filler bed? 8. Describe the peculiar features of the compound engines designed by Mr. Webb, and represented by the "Black Prince," for heavy express passenger trains; and state the advantage of the compound principle. 9. Make a sketch of Allan's valve gear, and state its advantages. 10. Describe the construction of the indicator, and show how it is used to ascertain the work done by an engine. SECOND PAPER. PROFESSOR FITZGERALD. 1. In the Manchester pipe line, what arrangement replaces curved pipes for making bends in the line? 2. In the Vyrnwy waterworks, different arrangements were adopted in crossing the Weaver Navigation, the Manchester Ship Canal, and the Mersey. Sketch these, and describe mode of construction. 3. Describe and illustrate a construction of valve suitable for waterworks' pumps working against a considerable pressure. 4. Sketch and describe two arrangements of lifts suitable for barges in canals, where the height from lower to upper reach is considerable. 5. Give approximate cross-sections of large ship canals, and state what minimum bottom width seems, from the Suez Canal experience, to be advisable if two ships are to be permitted to pass one another anywhere. SECTION B. PROFESSOR Townsend. 6. A wrought-iron shaft 12 feet long and 6 inches in diameter is under a torsional stress of 4 tons per square inch, and the angle through which it is twisted is 24 degrees: calculate the coefficient of torsional elasticity in tons per square inch. 7. A beam uniformly loaded, rests on two horizontal points how would you adjust the inclination of the ends, so that the moment at the centre would equal the moment at the ends? 8. Describe the mode of producing each of the following materials-Plaster of Paris, Roman cement, Keene's cement, and state the purposes for which they are used. What is the composition of hard bronze for bearings for machinery? 9. Describe the defects that are found in timber after being cut down. What are the diseases to which timber is liable? Describe some of the processes adopted for their preservation. 10. Make figured cross-sketches of the Blackwall tunnel under the Thames, and describe the method in which it was carried out. |