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8. Prove that when a ray of light is refracted from one medium into another, the deviation increases as the angle of incidence increases, whether refraction be from a denser into a

medium or vice versâ.

rarer

Hence show that the axis of a pencil of rays which passes through a prism in a principal plane is turned from, or towards, the edge of the prism, according as the prism is denser or rarer than the surrounding medium.

9. Find the geometrical focus of a pencil of rays after direct refraction through a lens the thickness of which is neglected. Hence show that in any lens whatever the position of the principal focus is the same whichever side be turned towards the incident light.

If Q, q, be conjugate foci and the lens be concave, trace the change in position of q as Q moves from a great distance on one side to a great distance on the other.

10. Describe Galileo's telescope, giving a diagram of the path of rays from a distant point to the eye. What is the best place for the eye in using this telescope?

Define the "magnifying power" of a telescope, and prove that in this telescope the magnifying power is the ratio of the focal length of the object-glass to the focal length of the eye-glass.

GEODESY.

Examiner-CAPT. W. H. JOHNSTONE, R. E. ASSOC. INST. C. E.

1. Describe the method of observing horizontal angles with a theodolite. If not pressed for time how could you improve the accuracy of your observed angles?

2. You are required to carry a triangulation over a piece of country comprising about 30 square miles. Only horizontal distances are required, not vertical heights. You will be supplied with a 6-inch Everest theodolite and whatever chains, staves, &c. you may require. Describe how you would proceed, indicating the successive steps of the process. Give a diagram of your triangulation and mention the length of your base.

3. Describe fully how you would test the correct adjustment of an Everest theodolite (whose antecedents were unknown to you) before commencing the above triangulation.

4. Describe how you would set out a right angle in the ground :(1.) With a 100-feet chain.

(2.) With a piece of rope, the length of which you have no means of measuring.

5. What is meant by the "line of Collimation" of the telescope of a theodolite or level? Describe how you would "collimate" a Dumpy level. How is it that defective collimation produces no errors as long as the distances observed are equal?

6. Describe the process of "traversing" with a theodolite. Under what circumstances would you employ this method of survey. ing, and what are its advantages?

7. "I set up a levelling staff upon a point A and turning my level upon the staff, I read 2:23 feet, I now send the staffman forward, in the direction in which I wish to level, and halt him at a convenient point B about 200 feet off. Directing the level upon the staff at B I read 7.89. I now take up my level and carry it forward to a convenient distance beyond the staff. Having set up the level I read 3'11 upon the staff at B But I now see, away to the right, a Bench mark, the reduced level of which I know to be 153 07 feet. I therefore send the staff to it and read 5:36. Again sending the staff forward to C, I read 473. Shifting the level as before I read 6:04 back upon C and 3.12 forward upon D."

Enter the above flying levels in a suitable form of level book and deduce the reduced level of the points A, B, C and D. Mention the difference in level between the points A and D.

8. You are standing on the sea-shore which is unobstructed and practically level. Show how you would find your distance to a buoy which is moored a short distanco out to sea :

(1.) When provided with only a 100-feet tape and a ball of string. (2.) When provided with a 100-feet tape and a pocket sextant. (3.) When provided with a 100-feet tape and an optical square or cross staff.

N. B. You are supposed to have pencil and note book but no logarithmic or trigonometrical tables.

9. Explain clearly the principle of the Vernier. You have a scale of inches divided into tenths,-what will be the length of a Vernier scale which will enable you read to the eightieth part of an inch?

10. What is the best and most accurate method of finding the variation of the compass with a theodolite? Give a detailed explanation of the successive steps of the process.

CARPENTRY AND MECHANISM.

Examiner-MAJOR ECKFORD, R. E.

1. Give one or two methods of fixing the end of the rafter to the tie beam, also of attaching an iron king rod and two wooden struts to a wooden tie beam.

2.

What is the relative thickness of the tongue and the cheeks of a mortise.

3. Give two examples of scarfs for lengthening timber. (2), When the beam is not required to be of the same dimensions throughout, describe an easy way to join two pieces of timber together.

4. Give a sketch of a trussed beam. And of a truss for a roof of 50 feet span, using queen posts and struts to support the rafter.

5. How is the centering for a bridge over a stream (which can be diverted or which is only full during the rains) usually supported in India? Describe the method of lowering the centres by sand cylinders.

6. Sketch a centering for a bridge a single arch, sixty feet span, an arc of 60°, using the abutments of the arch; to take the thrust of the centering and not supporting the centering underneath. 7. In a compound wheel and axle, Fig. (1) length of handle = a diameter of greater axle (b) diameter of smaller do. c, what is the velocity ratio of P to W? 8. Insert a train of wheels between the hour wheel of a clock revolving once in twelve hours, and a wheel which revolves once in 24 days and twelve hours.

=

=

9. Give the velocity ratio of P to W in a rack and pinion where the handle of the pinion is 18" long, the number of teeth on pinion 7, and the distance from tooth to tooth 2′′ on pitch line.

10. In a compound screw, Fig. (2) let the distance between the threads of the large screw be 1" and the distance in the smaller screw "what will be the velocity ratio of P and W, when the length of the handle is three feet?

11. Required the velocity ratio of P and W Fig. (3), in the endless screw attached to a toothed wheel and axle, when the number of teeth in the whole circumference of wheel is 40; diameter of axle 10" and length of handle of screw, is l′ 6′′.

HYDRAULICS.

Examiner-MAJOR ECKFORD, R. E.

1. What is the least velocity you should give running water to prevent the growth of weeds? What velocity of water was fixed in the Sone Cauals? What is a velocity rod?

2. What is meant by Hydraulic mean depth, and what section gives the greatest area of water for a given wetted border ?

3. Give a section of the weir (dam) used at Dehra on the Sone? How does this differ from the dam for the Agra Canal across the Jumna at Okola? Give a section of the Lower Ganges Canal weir. 4. Where does damage commence from the action of floods on these weirs? and how would you repair this damage?

5. Give cross sections of the Sone Canal at head, the Agra Canal at head and Lower Ganges Canal at head.

6. How many acres will one cubic foot per second irrigate in the cold season and how many in the khurreif harvest? Deduce from this the number of cubic feet which should be allowed per 1000 acres, making allowance for fallow and uncultivated land.

7. Where are weir sluices particularly placed and where are they placed in the Sone Canal weir? What would be the effect of there being no sluices ?

8. Where are regulating bridges placed? and where would you place Escapes? What is the use of an Escape on a running Canal ? 9. Give a section of an ogee fall, a perpendicular fall, and of a fall provided with gratings. Which is the best kind? What is the defect of an ogee fall?

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