greater than the radius, and show that the length of the object the length of the image where u is the distance of the object from the mirror, andr the radius of the mirror. 8. What is meant by the critical angle ? If a ray of light be refracted through a prism, the angle of incidence being given, prove from the law of refraction that the deviation increases with the angle of the prism. What is the limit of the angle of the prism (1) if μ 7 1, (2) if μ <1? 9. Find the geometrical focus of a pencil of rays after direct refraction through a thin lens. If the second surface of the thin lens is silvered, prove that the geometrical focus, after two direct refractions at the first surface and one reflection at the second, is determined by the equation 1 1 μ +1=2 น where u and v are the distances of the foci from the lens, and r and s the radii of the first and second surfaces respectively. 10. In what respects is the vision of distant objects aided by telescopes? Point out how the eye-glass contributes to the desired results, by comparing the image of the object as seen through the eye-glass with that formed by the object-glass and viewed by the naked eye. What are the principal points of contrast between the Astronomical and Galileo's telescope? GEODESY. Examiner-MR. S. F. DOWNING, B.A, C.E., A.I.C.E. 1. On a map it is found that 100 acres are represented by 359.48 square inches, but the scale not being attached it is required to calculate what it is. In the answer give the representative fraction, and also express the scale as so many feet, or decimals of a foot per mile. 2. A curve of 28 statute chains radius is set out by offsets at the chain end; compute the length of the offset in links. If the same curve be set out by the theodolite, compute the angle which is required, and describe the method of proceeding in both cases. = 3. Compute the tangent length, secant point, and the length of the curve with the following data. Radius 3935.25 feet, angle of intersection 144° 26'. Answers to be in feet. 4. The points best suited for the entrances to a tunnel having been selected, describe the method by which the centre line (above ground) between them may be laid out in the first instance with some degree of accuracy, the intervening ground being of a rugged character, and the tunnel having considerable length. 5. Enunciate the "universal theorem," and prove it in the case of the meridian lying altogether without the Polygon. 6. With a level in perfect adjustment, a distinct point, known to be 3 miles 5 furlongs distant, appears to intersect the cross-wires. Taking refraction into account what is its true relative position with respect to the eye? Prove the formula you employ. 7. Describe the contour line: and explain by a sketch the method of making a section in any direction by means of a contoured map. What do you understand from the following extract in reference to the Madras Harbour works-"the effect of the north pier and surf bank has been to push the three-fathom contour line slightly out to sea"? 8. No level ground being available for the base line required at the commencement of a trigonometrical survey, describe how, in such a case, the base line should be measured. 9. Mention the general order of operations in the geodesy of engineering works such as roads, railways, and canals. 10. Describe the various methods of determining on ground with an irregular transverse slope the width to the right and left of the centre line. 1. PRACTICE OF BUILDING.-No. 1. How would you ascertain the nature of the subsoil on which it is proposed to build? After the foundation has been excavated, what precaution should be taken before the building is commenced ? 2. Give a cross-section, with dimensions, of the foundations and footings of a building 20 feet square exterior dimensions, and 20 feet high. The foundation to be of concrete, weight 120 lbs per cubic foot. Walls of brick work weight 112 lbs per cubic foot. Roof flat, weight 100 lbs per superficial foot. Pressure on soil not to exceed 1 ton per superficial foot. What are the common sizes of bricks used in India? Describe the process of pugging-Why should clay with kunkur in it be avoided for brick-making? How should firing a kiln be regulated? When the firing is completed, what precautions should be taken to retain the heat ? 4. What are the tests of a good brick? What tools are used by the bricklayer? Why should bricks be wet before being laid down? What precautions should be taken to prevent uneven settlement of a building in course of construction? 5. Enumerate the limes found in Northern India. Specify those which are hydraulic, and state any peculiarity in slaking which distinguishes hydraulic from fat limes. With which sort should soorkee be used instead of sand, and why? 6. Describe lime-burning in the Deyra Dhoon, and sketch the kiln used. 7. Give the materials of concrete and their proportions, and describe the processes of mixing and laying. 8. In selecting timber what defects should be looked for, and what appearances indicate sound wood? What woods are used for carpentry and joinery in Northern India? What do you understand by seasoned timber? What precautions should be taken for the preservation of timber buried in walls or in the ground? 9. What materials are in use for roof-coverings? In what localities are the different descriptions used? 10. For what engineering purposes are cast-iron and wroughtiron respectively adapted? In what sections is wrought-iron gener ally obtainable in the market? PRACTICE OF BUILDING.—No. 2. Examiner-MAJOR J. H. CROWDY, R.E. 1. What is meant by bond? Give a sketch of two successive courses of the corner of a brick-building in English bond. 2. What different sorts of masonry are used in building? What special precautions should be taken to ensure the stability of rubble walls? Give a specification for coursed stonework. In what bond is ashlar masonry laid? What are quoins, and what points should be observed in their selection and laying? 3. Under what circumstances are discharging and inverted arches used? What is the direction of the coursing joints in an oblique arch, and how would you mark them on the centreing? Describe the method of laying out the heading joints of a semi. elliptical arch, 4. What is the use of buttresses in enclosure walls, and what proportion of the wall should be so disposed? 5. What points should be observed in the construction of fire places and chimneys? What section and area would you give to flues in ordinary cases? 6. What is the usual pitch for tiled roofs? What point should be specially observed in disposing main roofing timbers on the walls of a building? Describe double Allahabad tile roofing. 7. Give a plan and section with dimensions of a revetment wall 25 feet high, with counterforts and perpendicular back, to retain a bank of earth mixed with large gravel. 8. Give a plan and elevation of a masonry bridge of two spans and mark thereon-abutment-pier-arch-spandril-wing wallparapet and blocking course. 9. In what soils are well foundations applicable? Describe their construction and the precautions necessary to preserve them from scour. 10. Give a sketch of a lattice-girder. Why is it advantageous to use cast iron in the upper flange and wrought iron in the lower flange of a girder? Sketch a chain riveted joint in the web of a plate girder. ROADS AND RAILROADS. Examiner-MR. S. F. DOWNING, B.A., C.E., A.I.C.E. 1. Give a cross-section and full dimensions of a main road leading into a large town: including the side drains, and one of the main transverse drains in brickwork. 2. Exemplify the importance of maintaining the surface of a road in good order, by comparing the resistance of friction with the total resistance on an inclination, according as the road is in good or bad order. 3. Describe fully the earth-work tables given in your text book, and the manner in which they may be applied so as to give the area of the side slopes. 4. State what materials are generally used for ballast, its use, and the depth to which it is ordinarily laid. 5. On a railway whose gauge is 5 feet 6 inches, what must be the super-elevation of the outer rail on a curve of 30 statute chains radius, the weight of a train being one hundred tons, and its velocity thirty miles per hour? Prove the formula you employ. 6. What are the ruling points which serve to guide the Engineer in drawing the gradient lines upon the longitudinal section of a railway ? 7. Compare the Indian gauge with the metre gauge proposed for the future extensions and branches in this country, on the several grounds of economy in first cost of works, rolling stock, etc., and in subsequent working expenses and salaries: stating some of the argu. ments for and against its adoption. 8. What is the object of the coning of the wheels in railway rolling stock? State the amount of this coning at the present time and at an earlier period, and the reason for the alteration. 9. This coning of the wheels necessitates a certain detail of construction in the straight portion of the line. State this, and give a correct sketch of the transverse section of a line of way. 10. On a railway incline at the rate of one in eighty, we have the total resistance of a train weighing 110 tons equal to 3960 lbs. Compute the friction in lbs. per ton. If the train be descending this incline, what will be the total downward force? and at what inclination is the resistance on the descent equal to zero? STRENGTH OF MATERIALS. Examiner-MR. S. F. DOWNING, B. A., C. E., A. I. C. E, 1. What is the weight of a wrought-iron girder 80 feet in length, properly proportioned, having to sustain a uniform load of 1.75 tons per running foot? Prove each successive step of the rule you employ. 2. Two plates 18" wide and 3-8" thick are to be united for resistance to a tensile force: Compare the several arrangements which may be adopted, and trace out the relative strength in differ. ent transverse lines. With a limit of 4-5 tons per square inch, what is the greatest force which can be applied when the plates are joined in the best manner possible? 3. The span of a suspension bridge is 420 feet, and the dip is 1-14th of the span. The total load is 15 tons per lineal foot of span. Calculate the transverse area of the chains at the highest point, and at the centre, the limiting strain being 45 tons per square inch. 4. Two pillars of cast-iron, each being 60 5" long, and having diameters 0·51′′ and 1′′ respectively, were broken with the following weights: 0.2174 ton for that 051" diam. and 3 0491 tons for that 1" diam. Compute from these experimental results the index of the power of the diameter to which the ultimate strength is proportional. 5. A cast-iron girder 28 feet in clear span has to sustain a uniform load of 9 cwt. per foot run; give a design for it, with cross sections at the centre, and at a point 1-4th of the span. If at a point 9 feet from either abutment the whole of the above were concentrated, what would now be your design, and cross sections? The depth in each case to be constant, and = 6. Prove, as shown to you at lectures, that for a solid rectan gular girder, M= in the equation. bd3f 7. In a segmental arch 76' span, and 19' rise, the depth of keystone is 2'6", and the breadth from face to face 34 ft., compute the horizontal thrust in tons, the weight of the masonry being 14 cube feet to a ton. Prove the formula you employ. 8. Prove the formula for the thickness of a vertical rectangular retaining wall, viz, Thickness = Height x 0.578 × tan(90° — 0) W in which of repose, w = weight of cube foot of earth W W=weight of cube foot of wall. This expression merely gives equili brium, with a coefficient of stability of 2. How would you modify the formula? 9. A wrought-iron girder of uniform strength having a depth of 8', and clear span of 96′ is loaded so as to produce a strain in the upper flange of 3 85 tons per square inch, and in the lower of 4-25 tons per sq. in. Compute the deflection at the centre, and prove the several steps of the investigation. |