DEPARTMENT OF SCIENCE AND ART OF THE COMMITTEE OF COUNCIL ON EDUCATION, LONDON, S.W. (Telegraphic Address: "SCIENCE ART, LONDON.") SCIENCE EXAMINATION PAPERS, 1897, Including the Papers set at the Evening Examinations in April and May, and at the Day Examinations in June. PRINTED FOR HER MAJESTY'S STATIONERY OFFICE, BY WYMAN AND SONS, LIMITED, FETTER LANE, E.C. And to be purchased, either directly or through any Bookseller, from EYRE & SPOTTIS WOODE, EAST HARDING STREET, FLEET STREET, E.C.; or JOHN MENZIES & Co., 12, HANOVER STREET, EDINBURGH, and 90, WEST NILE STREET, GLASGOW; or HODGES, FIGGIS, & Co., Limited, 104, GRAFTON STREET, DUBLIN. Price Sixpence. (For Papers set at the Day Examinations, SUBJECT I. PRACTICAL PLANE AND SOLID GEOMETRY. EXAMINERS, PROFESSOR T. F. PIGOT, C.E., M.I.M.E., AND MAJOR W. D. CONNER, R.E. GENERAL INSTRUCTIONS. If the rules are not attended to, the paper will be cancelled. You may take the Elementary, or the Advanced, or the Honours paper, but you must confine yourself to one of them. All figures must be drawn on the single sheet of paper supplied, for no second sheet will be allowed. The constructions may be left in pencil, provided they are distinct and neat, and that the construction lines are shown. They must be strictly geometrical and not the result of calculation or trial. In the absence of those lines which are essential to a correct solution no marks will be awarded, however correct the result may appear. Lines parallel or perpendicular to others may be drawn mechanically without showing any construction. Lines may be bisected by trial. A single accent (') signifies feet; a double accent (") inches. H.P. and V.P. represent the horizontal and vertical planes of projection respectively. Put the number of the question before your answer. You are to confine your answers strictly to the questions proposed. Questions marked (*) have accompanying diagrams. The value attached to each question is shown in brackets after the question. Your name is not given to the Examiners, and you are forbidden to write to them about your answers. The examination in this subject lasts for four hours. 414. Wt. 10052. 2500.-11/97. Wy. & S. A 2 First Stage or Elementary Examination. Read the General Instructions on page 1. Only eight questions are to be attempted. Plane Geometry. 1. Construct a scale to read yards. It must be long enough to measure 150 yards. Representative fraction, (10:) *2. Draw a regular six pointed star, similar to that shown in the diagram, but using the dimensions printed on it. (No marks will be given for reproducing the diagram the same size.) (12.) 3. Draw a triangle ABC. AB = BC = 3" ; AC = 1′′. With centre C describe a circle touching the line AB. Then draw another smaller circle which will touch the first circle, and the line AB, its centre to be on the line BC. Solid Geometry. (10.) *4. Ascertain and write down the inclination to the horizontal plane of the line AB, of which the projections ab, a'b', are given. (10.) *5. Draw a plane such that any point on it shall be equidistant from the points A and B. *6. A rope is stretched from a point (See Q. 4.) (14.) A, on the top of a wall, to a point B, on the ground. Front and side elevations are given. Determine the length of the rope. (12.) *7. Find the intersection of the line ab ab' with the plane VOH. (12.) 8. Each of the horizontal and vertical traces of a plane makes an angle of 45° with the xy line. A point (P) in the plane is 2" above the horizontal plane, and its plan is " from the xy line. Draw the projections of a line passing through P, lying in the plane, and inclined to the horizontal plane at the same inclination as the plane is. (10.) 9. The plan of an isosceles triangle ABC, of which the base AB rests on the horizontal plane, is an equilateral triangle of 2" side. Given that the vertex C is 2" above the horizontal plane, find the inclination of the plane containing the triangle, and the true length of the sides AC and BC. (10.) *10. The projections of a right cone are given. A right cylinder (3" long) lies on the ground, its axis being horizontal, and the diameter of its circular section 2". Its curved surface touches the cone at a point which is equidistant from each end of the cylinder, and is on the line AV, the projections of which are given. Draw the plan of the solids, indicating the point of contact. (10.) *11. On a vertical plane, the horizontal trace of which is pq, draw the elevation (1) of a solid of which the square (A) is the plan, and the triangle (B) the elevation on xy, and (2) of a solid of which (B) is the plan, and A the elevation on mn. (14.) 12. A regular tetrahedron rests with one edge (2" long) in the horizontal plane, whilst a face containing that edge is inclined at 40° to the horizontal plane. Show in plan the section of it made by a horizontal plane 1" above the horizontal plane of projection. Also draw an elevation of the tetrahedron on an ry line parallel to the edge lying in the horizontal plane. Graphic Arithmetic. ALTERNATIVE AND OPTIONAL. 13. If a line 4" long represent 7 units, draw a line = (16.) √5. (10.) *14. If A be the unit, represent graphically B+ C (10.) Second Stage or Advanced Examination. INSTRUCTIONS. Read the General Instructions on page 1. Only eight questions are to be attempted. Plane Geometry. 21. Two lines meet at an angle of 60°. Find the locus of points in the interior of the angle such that the sum of their distances from the two given lines is constant, and equal to 23". (18.) |