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[Logarithmic Tables supplied.]

1. A stream flows for a mile with a total fall of 22 feet in a channel, whose cross-section is nearly enough a parabola, with axis vertical, vertex downwards, 20 feet wide, and 14 feet deep at centre. If for this be substituted an open semicircular channel 7.2 feet diameter of the same length, what will the fall be with the same discharge as that of the stream, taking Chezy's coefficient to be 85 for the original, and 100 for the new channel. The wetted perimeter of the parabola may be taken as nearly enough 20 feet, and its area as substantially equal to that of the semicircle.

2. Find the rate of discharge for a rectangular sluice in a canal dock gate, 2 feet by 15 inches, discharging below water, with a difference of level at opposite sides of 6 feet, the coefficient of discharge being 0.65.

3. A water-main is 1500 yards long, 8 inches bore. What will be the discharge in gallons per minute, with a total loss of head of 25 feet, taking Chezy's coefficient as 100 for feet and seconds.

4. Explain the principle of the Venturi meter, and describe its construction and the observation to be made to find the rate of flow.

5. Sketch and describe the construction and action of (a) a positive, (b) an inferential, water-meter of well-known type.



6. Sketch a front elevation, a back elevation, and a vertical cross-section over the head of a window in a brick wall 18 inches thick, the ope being 3 feet with a straight arch, and figure on dimensions.

7. Sketch a vertical cross-section, a vertical longitudinal section, and a plan of a lead gutter behind a parapet wall. What weight of lead would you adopt?

8. Describe the method of making observations with a theodolite so as to eliminate errors of graduation and eccentricity.

9. Describe the principle of Hadley's Sextant, and show how you would arrange a vernier and a circular arc so that the vernier should read to 10 seconds.

10. In a marine survey, how is the position of a place at which a sounding has been taken, determined, and afterwards plotted on the map or chart?





1. Show that if the moment of a system of coplanar forces about any three points not in a right line vanishes, the forces are in equilibrium. What deduction could be drawn if the moments of the forces about the three points were equal?

2. Forces acting at a point can be represented in magnitude and direction by p.. OA1, P2. O42,... Pn. OA where P1, P2...P, are certain multiples: show that the resultant can be represented in magnitude and direction by (P1+P2+...+ Pn) OA, where A is the centre of gravity of masses proportional to p1, P2 Pa placed respectively at the points A1, A2 . . . A„.

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3. A square is formed of four similar uniform rods freely jointed at the extremities. Two opposite joints are connected by a string equal in length to a side of the square. If the square be suspended from either of these joints, find the tension on the string.

4. An elliptic plate is cut in two along the minor axis: find the centre of mass of one of the parts.

5. A continuous stream of particles moving with velocity V impinges at an angle on a smooth plane. If the coefficient of restitution between the particles and the plane be e, find the pressure on the plane.

6. What is meant by the hodograph of a moving particle ? A particle is moving freely in an ellipse under the influence of a force towards one focus. passing an extremity of the geometric mean between the of the major axis.

Prove that the velocity when minor axis of the orbit is a velocities at the extremities

7. A particle is moving in a right line under the influence of a force which is directed towards a fixed point on the line and which varies as distance of the particle from the point: find the position of the particle at any time.

8. Establish the equations of motion of a rigid body moving under any forces.

9. A compound pendulum is vibrating under the action of gravity: find the time of oscillation and the reaction on the supports.

10. Find the radius of gyration of a solid cone about its axis.



1. A vessel containing liquid is moving vertically downward with acceleration f. What is the pressure at a point at depth h below the surface ? What is the condition for equilibrium of a body floating in the liquid? What happens when ƒ becomes greater than g?

2. A triangle is immersed in a liquid with its plane vertical, its centre of gravity at a given depth and a given side horizontal. Show that the centre of pressure will be at the same depth whether this side is highest or lowest.

3. A spherical shell is just filled with liquid. Find in magnitude and in line of action the stress between two hemispheres of the liquid separated by a vertical plane. 4. Define the metacentre of a ship. Show that the righting moment of a ship heeled over through a given small angle is proportional to the distance between the centre of gravity and the metacentre.

5. A hollow sphere is silvered on the inside. A pencil of light issues from a point on its surface and is reflected back and forward along a diameter. Find the focus after n reflexions.

6. State the conditions for an image being achromatic. In how far can these be realised by means of a combination of two lenses ?

7. A hemisphere of glass (index) has its plane face in contact with water (index): find the focus for a narrow beam of light falling vertically on the hemisphere in air.

8. Explain the effect of atmospheric refraction on the apparent position of the heavenly bodies.

9. The Moon is in her last quarter on the autumnal equinox. What will be, roughly, the sidereal time of her rising ?

10. Explain the principle of Sumner's method for finding position at sea by means of two observations of the Sun's altitude.





[Sketches figs. 4, 5, and 6 accompany this Paper.]

1. Draw the stress diagram for the frame in fig. 4. 2. Draw the diagram of bending moments for the system of loads on a beam shown in fig. 5.

3. Find the reactions at supports for the forces on beam fig. 6, the reactions are both vertical as the given forces have no horizontal resultant.

4. Sketch and describe forms of bridge flooring suitable (a) for a single line railway of moderate span, with plate main girders, (b) for a double line bridge with main side girders about 28 feet centres apart, with bracing in bays of about 15 feet.

5. State the Board of Trade Rules for wind pressure to be provided for in railway bridges.



6. Describe the system now adopted at Exeter for the treatment of sewage, and state the degree of purification which has been attained.

7. Describe the mode of carrying out the thorough drainage of land of a pervious nature, using broken stones, and give particulars of the minor drains and sub-mains.

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