RETURN to an Address of the Honourable The House of Commons, "RETURNS specifying the Names of the EXAMINERS appointed to examine the CANDIDATES who presented themselves since last Return, for Admission to the ENGINEER'S ESTABLISHMENT and PUBLIC WORKS DEPARTMENT of India:" "Of the Names of the SUCCESSFUL CANDIDATES in Order of Merit, their respective Ages, Places of Education, and the Names of the CIVIL ENGINEERS to whom any of such Candidates have been Articled Pupils :" "And, of the MARKS assigned on each Subject to every Candidate; and of the EXAMINATION PAPERS on each Subject (in continuation of Parliamentary Paper, No. 76, of Session 1863)." India Office, 1 17 July 1863. W. T. THORNTON, Secretary, Public Works Department. (Mr. Adam.) Ordered, by The House of Commons, to be Printed, PUBLIC WORKS DEPARTMENT-INDIA. CIVIL ENGINEER ESTABLISHMENT. EXAMINATION PAPERS for June 1863. 2 June 1863. EUCLID.-Rev. J. Cape. 1. DEFINE scalene triangle, acute angled triangle, rhombus, segment of a circle, and similar segments. 2. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides, which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity. 3. 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 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. 4. Through a given point, to draw a straight line which shall make equal angles with two given straight lines. 5. In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. If the obtuse angle C be a third part of four right angles, then AB2 AC2 + BC2 + AC × BC. = 6. If two circles touch each other externally, the straight line which joins their centres shall pass through the point of contact. 7. If a straight line touches a circle, and from the point of contact a straight line be drawn cutting the circle; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle. If two circles touch each other externally, and through the point of contact any two straight lines be drawn meeting both the circumferences, the chords of the two intercepted arcs will be parallel. 8. To inscribe an equilateral and equiangular hexagon in a given circle. Compare the sides of an equilateral triangle, and an equilateral hexagon inscribed in a circle. 9. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle. 10. In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle. 11. If the four sides of a trapezium be bisected, the lines joining the points of bisection shall form a parallelogram, whose area equals half the area of the trapezium. 12. If two straight lines meeting one another be parallel to two other straight lines which meet one another, but are not in the same plane with the first two; the plane which passes through these is parallel to the plane passing through the others. 2 June 1863. ARITHMETIC, TRIGONOMETRY, AND MENSURATION.-Rev. J. Cape. 2. Divide 234.375 by 0375; and also 0375 by 234 375. 3. What are the vulgar fractions which can be reduced to finite decimals; and what are those which produce recurring decimals? Find the vulgar fraction equivalent to the recurring decimal ·1272727. 4. Find the value of 75 of a guinea + of 5 s. + 0'6 of 7 s. 6 d. of 2 d. 5. If 11 cwt. can be carried 15 miles for a sovereign, how far can 23 cwt. 14 lbs. be carried for 9 l. 5 s.? 6. What is the difference between discount and interest? Required the true discount on a bill of 612 l. 15 s. due 6 months hence, at 4 per cent. per annum. 7. Define complement of an arc, sine, cotangent, and secant of an arc. 8. In any plane triangle, the sides are to one another as the sines of the opposite angles. 9. Find from the tables the following quantities: (a.) Logarithm of 123-456. (6.) Number corresponding to logarithm 3:456789, to six places of significant figures. (7.) Log sine of 123° 34′ 50′′. (8.) Log cotangent of 55° 40′ 40′′. (.) Arc to log cosine 9.345678, to the nearest second. = 10. In the triangle ABC whose sides are AB 2569 2 links, AC = 4900 4 links, and BC= 5024'6 links: to find the angle A to the nearest second. 11. Explain the ambiguous case in plane triangles. When may the ambiguity be removed? 12. Wishing to know the height of a tower on the top of a hill, I took the angle of elevation of the top of the tower 51°, and of its bottom 40°; then measuring on a horizontal plane in a line directly from my first station to the distance of 250 feet further, I found the angle of elevation of the top of the tower to be 33° 45'. Required the height of the tower. 13. Find the area of the triangle given in the 10th Question, in acres, roods, and perches. 14. Find the area of the segment of a circle whose chord is 150 feet, and the arc contains 112° 30'. 15. The perambulator is so made as to turn twice in the length of 1 pole; required its diameter. 16. Find the whole superficies and the solid content of the frustum of a square pyramid, each side of the greater end being 20 feet, and each side of the lesser end 8 feet; also the perpendicular height being 8 feet. 17. What 17. What quantity of canvas is necessary for a conical tent, whose perpendicular height is 8 feet, and the diameter at the bottom 13 feet? 18. Required the number of cubic yards in an embankment, the transverse sections perpendicular to the axis being trapezoids, whose dimensions were as follows: Horizontal lines at top, 22; 219; 216; 216; 218; 216; 22 feet. 4. From a certain sum I took away a third part, and put in its stead £.50. Again, from the sum thus augmented I took away one-fourth, and put in its stead £.70; I then found that I had £.120. What was the original sum? 6. A and B engage together in play. In the first game A wins as much as he had, and 4s. more, and finds he has twice as much as B. In the second game, B wins half as much as he had at first, and I s. more, and then it appears he has three times as much as A. What sum had each at first? 8. A vintner sold 7 dozen of sherry and 12 dozen of claret for £.50. He sold three dozen more of sherry for £.10 than he did of claret for £.6. Required the price of each. 9. If 4 quantities, a, b, c, d be proportionals, they are also proportionals by composition, and division; that is, 10. The distance between two towns is 159 miles. The first day a person travels from one town towards the other 16 miles, the second day 15, the third day 15, and so on. In what time will the journey be performed? |