*3. Construct a square of 4" side, bisect the sides, and join the adjacent points of bisection, thus obtaining a second square (see diagram), bisect the sides of this second square, and obtain a third square. Continue the process till five squares have been drawn. (7.)

4. Draw any irregular four-sided figure, no side less than 11⁄4". Construct a similar figure whose sides are 11⁄2 times those of the first figure.

Solid Geometry.

5. The tops of two vertical poles are 85' 0" apart. 40' o" apart, and the height of one pole is 12' o". height of the other pole. Scale 1" to 1o o".

(7.)

The poles are Determine the (9.)

6. Explain clearly what is meant by the terms ground line, projector, elevation of a point, plan of a line, trace of a plane.

7. Represent-a. A line in the horizontal plane.

b. A line in the vertical plane.

(9.)

c. A pair of equal parallel lines, not parallel to either plane of projection.

8. Under what conditions is the plan of a square

a. An equal square.

b. A straight line.

c. A rectangle.

d. A parallelogram.

(9.)

(10.)

9. Construct a triangle o a b (oa = 24", ob = 334′′, ab = 41⁄2"), a and b are the horizontal traces of the lines oa, ob, meeting at a point of which is the plan. The height of o above the horizontal plane is 11⁄2". Obtain the real angle contained by the lines. (12.) *10. Cut off a real length of 3" anywhere along the given line a'b', ab. (11.) *II. The traces ao, ob of a plane are given; vt is the vertical trace of a plane perpendicular to the vertical plane of projection. Determine the intersection of the two planes. (14.) *12. abcd represents a black board on which an equilateral triangle is drawn as shown. Draw the plan of the board and the triangle when the plane of the former is inclined at 45° and its long edges (ad, bc) are horizontal. (12.)

*13. The plan and elevation of a cottage are given. Draw an elevation of the latter on the line zz.

(15.)

*14. Make a section of the cottage (Q 13) on A B.

(15.)

Second Stage or Advanced Examination.

INSTRUCTIONS.

Read the General Instructions at the head of the Elementary

Subject 1 1879. ELEMENTARY PAPER.

Diagrams Nos 10, 11,12,13, are to be pricked off or accurately copied on to the drawing paper.

No 3

*22. The figure represents a window of the decorated English style. The construction is sufficiently shown and dimensions are given, Draw the window to scale of 2" to 1'o".

(18.) 23. The sum of the diagonal and one side of a square is 6". Construct the square. (14.) *24. The triangle abc moves so that the sides ab, bc always pass through the fixed points p, 9 respectively. Draw the curve traced by the point 6 in moving from pto g. What is this curve?

Solid Geometry.

(16.)

25. Represent a. A line passing through the ground line and making 45° with both planes of projection.

b. A plane whose traces include a real angle of 45°.

(18.) 26. Determine the projections of a line 3'5′′ long, its extremities to be in the planes of projection, and its inclination to the horizontal and vertical plane 25° and 40° respectively. (18.) 27. 'If a line is perpendicular to a plane its projections are respectively perpendicular to the traces of the plane.' Prove this statement.

(20.)

*28. Determine the angle contained between the two given planes.

(22.) 29. Draw three lines meeting at a point and making angles of 120°, 130°, 110°, with each other. These lines are the plans of the edges of a cube of 3" edge. Complete the plan of the cube and draw its elevation on any plane parallel to no side or diagonal.

(22.) 30. Three spheres of o85", o'5", and 1′25′′, radius touch each other and the horizontal plane. Draw their plans. (22.) *31. Sections of a sphere by planes containing its centre are termed "great circles." Draw the plans and elevations of four great circles of the given sphere passing through the point p, and dividing the spherical surface into four equal parts. Invisible portions of the circles to be dotted.

(24.) *32. A vertical triangular slot is cut through a sphere. The plan of the sphere and slot is given. Draw an elevation of the sphere. (26.) *33. The plan and elevation of a Norman gable cross are given. Draw an elevation of the cross on zz.

(28.)

#34. Make a section of the given cross on AB.

(28.)

*35. Make an isometric view of the cross. The outer circular portion may be supposed removed so that the cross is altered as shewn by the dotted lines. An isometric scale is not to be used.

(28.)

Honours Examination.

INSTRUCTIONS.

Read the General Instructions at the head of the Elementary paper. Only eight questions are to be attempted.

Plane Geometry.

*41. In what sense can a line be said to represent an area? Represent the given figures A, B, C, by lines proportional to their areas.

(30.)

(30.)

42. Construct a hexagon equal to an octagon of 1" side. 43. Describe any mechanical methods of drawing the ellipse, parabola, and hyperbola. (30.)

44. AB, BC are two bars linked at B. The bar BC rotates about a fixed centre C; the point A is free to move in a straight line passing through C. The arrangement is therefore that of a crank and connecting rod. Trace the complete curve described by a

point on AB distant 3⁄44" from B (AB = 31⁄4" ; BC = 11⁄2".)

Solid Geometry.

(30.)

(45.)

*45. The triangle aob is the plan of one of the eight equal isosceles triangles which make up an octagon; o is the plan of the centre of the octagon. Complete the plan of the latter. *46. Determine a plane bisecting the angle contained between the given planes.

(40.)

*47. Determine the angle made by the given line with the given plane. (Unit o'r".)

(35.)

*48. Determine the plan of the circumscribing circle of the given triangle. (Unit o'1".)

(35.)

*49. A vertical right prism and an oblique pyramid stand on the horizontal plane. The bases of both are given, and vu' is the vertex of the latter solid. Draw the elevation of the solids on xy, shewing their interpenetration. Invisible edges to be dotted. (50.) *50. The elevation of a "solid of revolution" with a vertical axis is given; p is the plan of that axis. Determine

The elevation on ry of the section by the plane voh. (50.) N.B.-The dotted lines show the radii with which the curved portions of the outline are struck.

*51. Determine either

The shadow cast by the given solid on the horizontal plane,

or,

The outline of the shaded portion of the solid.

(50.)

(50.)

N.B.-The rays in either case to be parallel. Their direction is given in plan and elevation.

*52. Two lines are given by their figured plans ab, cd. A surface is generated by a line moving parallel to the horizontal plane and always meeting both the given lines. Determine the true form of the section of this surface by a vertical plane AB The section to be carried up to a height of 3" above the ground. What is this surface termed, and can it be developed? (50.) *53. Make an isometric view of the Anglo-Saxon window of which the plan and elevation are given. An isometric scale is not to be used.

(50.) *54. Make a perspective view of the given window. The conditions laid down as to the picture plane, horizon, etc., are to be strictly adhered to.

(55.)

N.B.-By proper managements the vanishing points fall easily within the paper. If the latter is crowded the construction lines may be rubbed out, or they may be drawn through the other figures.