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24. Three posts, B, C, D, are in a straight line at intervals of 100 yards. An observer at A finds that the angle BAC is 20°, and the angle CAD 30°. Determine the position of A. (Scale 100).

Solid Geometry.

(18.)

25. In a plane inclined at 40° place a line 3" long inclined at 25°, and through this line draw a plane inclined at 70°. (20.) *26. Determine the angle made by the given line AB with the given plane. (22.) 27. The figured plans of six points, ao, bs, Cio, d15 20, 25, taken in order, form a regular hexagon of 1" side. Find the intersection of the plane containing A, C, and F, with the plane containing B, D, and E, and state its inclination. (Unit = 0-1".) (22.) 28. What are the different forms that may be taken by the projection of a circle, and how must the circle be lying in each case? (16.) *29. A right cone is lying on its side upon the horizontal plane, b is its vertex, and ab is the plan of its axis, which is inclined at 25°. The point c is the plan of the centre of a sphere, which also rests upon the horizontal plane, and which is in contact with the cone. Complete the plan. (30.) 30. Draw the plan of an octahedron of 2" edge, one edge being inclined at 30°, and another (on the same face) at 20°. (28.) *31. The figure shows two pieces of wood halved and dovetailed together. Make an isometrical projection of them; separating them so that one will not hide any part of the other. Give an isometric scale. (24.) *32. Taking the figure as the plan of a hexagonal nut 1" deep, which works on a V threaded screw 2" in diameter, of pitch and 1" depth of thread, make a section and elevation on ab. *33. Taking this nut as a solid prism, resting on the horizontal plane, and ab as the plan, r' the elevation of a ray of light, to which the other rays are parallel, show the shadow thrown on the horizontal and vertical planes.

(28.)

(26.)

Honours Examination,

INSTRUCTIONS.

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

Plane Geometry.

41. Describe a circle enclosing and touching three other circles of 0.6", 0.8′′, and 1" radius respectively, each of which touches the other two. (32.) *42. Determine the major and minor axes of the given ellipse, and draw a tangent to it at the point P. (36.)

21. Sketch a simple single riveted lap joint, for 3-inch plates a rivets, and dimension the overlap and pitch of rivets. Sk a 3-inch rivet showing the usual form and proportions of head.

22. Sketch and explain the modes of fixing a wheel or pulley b key, by cone keys, and by staking on.

23. A shaft running at 100 revolutions per minute drives anoth leather belt. Pulley on first shaft 18 inches diameter; pu second shaft 30 inches diameter. Find the speed of the secon Suppose the same belt is to drive the second shaft at 40 revo per minute. Find the diameters of the two pulleys.

24. Sketch a slide valve in mid position to the following dimer Exhaust port 3" wide; bars 1" wide; steamports 2" wide; o lap 1 inches. Sketch also the same valve at the beginning piston stroke with inch lead. The valve need not be drav scale, but may be sketched and the dimensions marked on it.

25. Double-acting Pump. Draw first the vertical section.

Ther

horizontal section. If you have time, draw also the cross seci The valve and seating is not to be drawn separately, but gives s necessary dimensions. Show nuts and bolts fully, where they, required. Complete the sectional shading.

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Honours Examination.

INSTRUCTIONS.

Read the General Instructions on page 6.

You are only permitted to attempt ten questions. You may select these from any part of the paper.

Illustrate your answers by sketches, which may be in pencil, and need not be drawn to scale, but should be in as good proportion as can be judged by the eye. The sketches may be accompanied by such dimensions and remarks in writing as may be necessary. All the sketches should be made on the foolscap paper upon which your answers are

written.

41. Define a factor of safety and give some ordinary values of the factor of safety for iron, timber, and stone structures. State why in some cases it is necessary to adopt large factors of safety.

42. An ordinary crank pin journal is 3 inches in diameter and 6 inches long. Find the safe load on the journal if the stress is not to exceed 9,000 lbs. per square inch. The moment of inertia of a circle of diameter d is 0.0491 d and the modulus of a circular section is then 0.098 d3.

31"

Scale

43. The Americans use in locomotives a combined lap and butt joint as in the sketch. Taking the plates at " thick, rivets 1inch diameter, pitch of rivets in middle row 2 inches, and in outside rows 4 inches, find the resistance of the joint to tearing and shearing. The resistance of the plates to tearing may be taken at 22 tons, and that of the rivets to shearing at 20 tons.

44. A leather belt is required to transmit 2 h.p. from a
shaft running at 80 revolutions per minute to a
shaft running at 160. Find the stresses in the belt,
assuming that the smaller pulley is 12 inches in
diameter, and that the ratio of the tensions in the
tight and slack sides of the belt is 24: 1. Hence

find the width of belt, taking the working stress
at 100 lbs. per inch of width.

45. What circumstances affect the action of a belt when
the speed is high?

46. A toothed spur wheel is 4 inches pitch. Sketch a tooth and mark on it suitable dimensions. Draw

accurately a suitable curve for such a tooth taking

the pitch line straight as in a rack, and using a describing circle of 5 inches radius.

47. Sketch with details as full as possible (1) one form of piston suitable for a quick running high pressure engine with cylinder under 2 feet in diameter; (2) one form of piston suitable for a large stationary or marine engine. Point out any reasons for the arrangements adopted.

48. Sketch and describe shortly the three common forms of link motion.

49. How should the man-hole of a large stationary boiler be constructed? What are the objections to the old form of man-hole with internal plate and external bridge? How can a manhole be strengthened by staying?

50. An engine has ports 4 inches wide. The slide valve has 2 inches outside and inch inside lap. The lead is inch. Radius of eccentric, 5 inches. Find the fractions of the stroke at which steam is cut off and released, by a diagram or otherwise.

51. An engine tender is fitted with a Ramsbottom scoop. What is the limit to the height to which the water can be raised, if the speed is 40 miles per hour?

52. A small crab is wanted to raise half a ton by the power of one man, acting on a winch handle of 15 inches radius and exerting a force of 30 lbs. Sketch the necessary gearing and chain barrel, the pinion having 12 teeth of 14 inches pitch. The chain barrel may be taken 7 inches in diameter. Find the pressure on the wheel teeth due to the load.

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