7. O is the centre of a spherical surface of radius OA, separating two 11 media of refractive indices μ and μ'; prove the relation

A glass sphere (μ objects in the water sphere to a depth appear inverted.

=

=

3) is half immersed in water (μ ); shew that of viewed directly through the sphere, those below the times the radius appear erect and those at a greater depth

8. Define the focal length of a thin lens and the principal foci; and 12 prove the formula uv = f2, where u, v are the distances of an object and its image from the first and second principal focus respectively, measured in opposite directions.

There are n convergent thin lenses of numerical focal lengths f1, fa ... fñ, such that the distance between the lenses f, and ƒ, + 1 is 2 (fr + fr+1) for all values of r. If u is the distance of an object from the first principal focus of the first lens and vn the distance of the final image behind the second principal focus of the last lens, shew that the magnification produced by the system is

9. Explain what is meant by the equivalent lens of a system of lenses, and find its focal length F for two thin concave lenses of focal lengths f, f', separated by an interval a.

Prove that the focal length of a single lens equivalent to a system of three concave lenses of focal lengths fi, fa, fa separated by intervals a1, ag is given by the equation

10. Describe Cassegrain's telescope, shewing the course of a ray when 10 it is in normal adjustment.

If the focal length of the larger mirror is 360 inches and of the smaller 75, and if a single lens of focal length 8 inches is used for the eye-piece, shew that for normal adjustment when the principal focus of the eye-lens is at the vertex of the large mirror, the distance between the two mirrors is 300 inches, and that the eye-ring is at a distance 17 inch beyond the principal focus of the eye-lens.

MONDAY, 18TH NOVEMBER.

[10 A.M. TO 1 P.M.]

PHYSICS-PAPER I.

1. Distinguish between centripetal and centrifugal force and prove that 10 the centrifugal force is proportional to the square of the velocity and inversely proportional to the radius.

The centrifugal force of the earth at the equator is of the force of gravity. Find the time of one day in case the rotation of the earth was increased to such a degree that the effect of the centrifugal force was equal to that of gravity.

2. Describe Nicholson's hydrometer and explain how the instrument may be used to find the specific gravity of solids and of liquids.

What weights must be placed in the lower pan of a Nicholson's hydrometer to produce the same effect as 20 grams of the same kind of weights in the upper pan? (Specific gravity of the weights

=

9).

3. Prove that the pressure of the atmosphere decreases in a geometrical 10 proportion, when the height increases in an arithmetical proportion, and show how this is used to determine the height of mountains by the barometer. Describe any kind of mercury-barometer which is used for this purpose.

4. Explain "temperament of the musical scale." Why has it been 10 introduced? How many kinds of temperament do you know? What is the difference between the equal temperament and that of Kirnberger?

5. What is interference of sound and how do you demonstrate it experimentally? Explain why compound musical notes are void of all roughness unless the seventh harmonic is audible.

8

6. Explain the dynamical theory of gases and prove that the molecular 10 velocities are inversely as the square roots of the molecular weights.

7. Explain why the balancing of a hot against a cold column of the same liquid eliminates the expansion of the vessel in which the liquid is contained. How has this principle been used to determine the absolute expansion of mercury?

The cold column of a liquid at 0° is 80 cm. high, and the hot at 100° C. is cm. higher. Find the absolute coefficient of expansion of the liquid.

8

8. Describe the calorimeter of Favre and Silbermann. In what is it superior to Bunsen's Ice calorimeter ?

8

9. Describe the radiometer and explain fully its different manners to move under different circumstances.

8

MONDAY, 18TH NOVEMBER.

[2 P.M. TO 5 P.M.]

PHYSICS-PAPER II,

1. How was it first proved that light has a finite velocity?

8

2. Find the vibration frequencies of the following kinds of radiant energy:

3. Explain the construction and use of the collimator tube of a spectro- 10 scope, through which the light to be analysed passes before falling on the prism. How is the slit adjusted with respect to the lens?

4. What are the differences between the ordinary and extraordinary rays in a uniaxial crystal?

5. How can an electrophorus be used to charge a Leyden jar? Is there 10 any limit to the charge that can be obtained by this means?

6. How can the intensity of the magnetic field at different points be 8 compared by the method of oscillations?

7. What is the largest eurrent that can be sent through a resistance of 10 2 ohms by means of 8 cells, the resistance of each of which is 4 ohms, and the E. M. F. 15 volts? How must the cells be arranged?

8. How can the amount of electrical energy converted into heat energy, in a wire of known resistance, in a given time, be calculated (1) when the current is measured, (2) when the difference of potential between the ends of the wire is known?

9. Describe the Bell telephone and explain how speech is transmitted by 10

its means.

SATURDAY, 23RD NOVEMBER.

[10 A. M. TO 1 P.M.]

CHEMISTRY-PAPER I.

N.B.-The two Sections should be kept separate.

All definite chemical changes should be represented by equations.

SECTION I.

1. The volume of a molecule of a compound body in the gaseous state 10 is exactly double that of the atom of hydrogen. Examine the truth of this statement, give the experimental facts on which it is based, and discuss any exceptions to it.

2. Enumerate three oxidising and three reducing agents, explaining 10 their action. To what class does hydrogen peroxide belong? Explain its action on silver oxide and ozone, and state what tests you would apply to detect its presence.

3. How does sulphur dioxide act on aqueous solutions of chlorine, 10 iodine and sulphuretted hydrogen? Contrast its action with that of ehlorine as a bleaching agent.

4. What different gases could be obtained from (1) manganese dioxide, 10 (2) potassium dichromate, and (3) potassium chlorate by the action of hydrochloric and sulphuric acids?

SECTION II.

5. Give all the elements which can be made to combine with hydrogen 10 directly, and in each case explain the conditions under which the combination can be brought about.

6. From what two natural sources and by what processes is iodine 10 isolated ? What is its action on mercury, antimony, phosphorus and hydrogen sulphide, and under what circumstances will the reactions take place?

7. Compare the chlorides of phosphorus, arsenic and antimony with regard 10 to their modes of formation, their chemical properties and their action on

water.

8. When phosphorus and charcoal burn with a limited supply of air the 10 lower oxides of the two elements are formed; point out the difference of the two reactions and explain the properties of the two oxides.

SATURDAY, 23RD NOVEMBER.

[2 P.M. TO 5 P.M.]

CHEMISTRY-PAPER II.

N.B.-The two Sections should be kept separate.

All definite chemical changes should be represented by equations.

SECTION I.

1. What occurs when a solution of ferric chloride is treated with (a) 10 sulphuretted hydrogen, (b) ammonia, (c) ammonium sulphide, (d) potassium iodide, (e) stannous chloride?

2. What is the action on copper of the common acids? How is copper 10 sulphate obtained? What occurs when (1) ammonia and (2) potassium iodide are added to a solution of it, and when it is heated?

3. Mention the elements that form both basic and acidic oxides. Enu- 10 merate these oxides with examples of their compounds to show their nature. Give essential conditions for transforming one class into another.

4. Describe the preparation of mercuric nitrate and mercurous nitrate 10 from the metal. How can each of these salts be converted into the other?

SECTION II.

5. Explain how in the LeBlanc process the sulphuric acid of the 10 sodium sulphate is recovered and why in the Ammonia-Soda process the chlorine of the sodium chloride could hitherto not be recovered. Which of the two processes is in your opinion the more perfect one and why?

6. How is pure chromium trioxide prepared and what are its properties? 10 Why does its solution in water not contain chromic acid ?

7. Explain how aluminium is prepared from bauxite and manganese from 10 its oxide.

8. What is produced when aqua regia acts on platinum? How would 10 you test for the product and why would you not use the ordinary tests for platinum and chlorine? How are platinic tetrachloride and hydroxide prepared from it ?

SATURDAY, 23RD NOVEMBER.

[10 A.M. TO 1 P.M.]

BOTANY-PAPER I.

1. Give a botanical description of the following, and mention whether 10 they are roots or stems :

Onion, Carrot, Beet, Turnip, Ginger, Potato

2. Describe the various terms expressive of the condition of the margins 19 of leaves with examples.

3. What is a mixed inflorescence? Describe the inflorescence of Aroidea 10 and Graminaceæ.

4. Describe the different kinds of regular polypetalous and gamopetalous 10 corollas with examples..

5. Describe the following kinds of fruits with examples:-Carcerule, 10 Amphisarca, Drupe, Syconus, Sorosis, Capsule, Follicle, Siliqua.

6. Describe the various methods by which dehiscent fruits open to let 1) out the seeds.

7. Describe :

(a) The calyx of Compositeæ, Crucifereæ, Solanaceae ;

(b) Pollen of Asclepiadaceae and Orchidacea;

(c) The stigma of Apocynaceae and Asclepiadaces; and

(d) The stamens of Labiate and Aristolochiacea.

10

8. What are Gametes? Describe the gametophyte phases of Sperma- 1) phyta and Pteridophyta.

SATURDAY, 23RD NOVEMBER.
[2 P.M. TO 5 P.M.]

BOTANY-PAPER II.

1. Where and how is starch manufactured? In what parts of plants is it stored up? Describe its composition and chemical characteristics.

2. What is turgescence of a cell? How is it caused, and what part 19 does the protoplasm play in bringing about this condition ?

3. Give an account of the Ground or Fundamental Tissue System, and the 10 of its distribution in the stem and leaf.