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5. A small pencil of converging rays is incident directly upon a spherical reflector; shew that the distance of the centre of the sphere from the principal focus is a mean proportional between the distances of the conjugate foci from the same point. Trace the changes in the position and appearance of the image as an object approaches the reflector from a considerable distance.
6. Describe the eye. What sort of lens is used by a longsighted person ? Explain by a figure the course of the rays through the lens.
7. Define a prism. Shew that no ray of light will pass through a prism, if the sine of half the angle of the prism is equal to the reciprocal of the index of refraction. Give a brief description of Newton's investigations upon the nature of light by means of a prism, and the results he arrived at.
8. Distinguish between a Telescope and a Microscope. Give figures of Newton's Telescope, and of a compound Refracting Microscope, shewing the path of a pencil through each. In Newton's Telescope, if the radius of the mirror be four feet, and the focal length of the eye-lens an inch, find the magnifying power.
9. Distinguish between a mean solar and a sidereal day. When the Sun is in Libra, which is the fastest, the clock or the sun-dial?
A certain eclipse was observed to begin at half-past three in the afternoon of the first of January. The Sun's Right Ascension at apparent noon was 18h. 46'. 52", and the equation of time was 3'.50” mean solar time, which may be supposed constant for a short time; find the time by the sidereal clock at which the eclipse began.
10. Give an explanation of the causes of the seasons. What difference would there be in the seasons if the eccentricity of the Earth's orbit was very much increased and the obliquity of the ecliptic decreased.
11. Bradley, when sailing on the Thames, was led to discover aberration by observing a vane on the top of the mast which appeared to alter its direction whenever the vessel changed its
course, the wind meanwhile blowing always in one direction. Explain this, and by other examples illustrate aberration.
If the Sun be at a solstice, shew that the time of rising or setting of all stars on the horizon at midnight is unaffected by aberration. Find the position of that star whose point of rising also is unaffected by aberration.
12. Describe the Transit Instrument.
If there be a small error of deviation of the east end of the axis towards the south, and an equal error of level so that the west end is too high, find the declination of the star whose time of transit at a given place is unaffected by these errors.
13. What observations are necessary to determine the rate at which a signal travels along the wires of the Electric Telegraph? 14. Define course steered, and lee-way.
Explain what is meant by plane sailing and great circle sailing. Describe some practical method of finding the longitude at sea.
TUESDAY, Dec. 14, 1858. 6 to 8 P.M.
II. E. 1.
Chemistry. 1. What is meant by an element in chemistry? How do we know that diamonds and charcoal are the same substance?
2. Describe and explain a mode of preparing chlorine. Give an account of the most striking qualities of that substance; and explain why a candle burns in it with a smoky flame.
3. State the law which regulates the different chemical combinations of the same two elements. Give examples.
4. Describe and explain the method of manufacturing carbonate of soda from common salt.
5. Explain the use of fluxes in smelting. What are the most common fluxes?
6. What are bibasic and polybasic acids ? Give instances. How is Tartaric acid shewn to be bibasic? What is the common source of that acid, and how is it prepared ?
7. What is a compound radicle and a basyl? State the constitution of ether. Shew, by an appeal to its derivatives, the general nature of its chemical relations and analogies.
8. What is the general constitution of fats ? Explain how soap is made from them; and to what the cleansing action of
soap is due.
9. Describe a method of accurately determining the quantity of carbonic acid contained in any carbonate.
10. The analysis of 100 parts of a certain mineral gave 44.4 parts of Silica, 35.9 of Alumina, 15.6 of Lime and 4.1 of Magnesia. Construct a formula for the mineral, pointing out the principles on which you proceed; the equivalent of Silica being taken as 30-2, of Alumina 51.4, of Lime 28, and of Magnesia 20.
N. B. The Examination in Practical Chemistry will take place on WEDNESDAY, Dec. 22nd, at 10 A.M., but the Examination Room will be open at HALF-PAST NINE, in order that Candidates may get their apparatus ready before the Examination begins.
WEDNESDAY, Dec. 22, 1858. 10 to 12.
II. E. I. Practical Chemistry *.
Candidates must state every experiment or test tried, the result of it, and the conclusion drawn from it; and finally the conclusion drawn from the whole.]
1. THE substances marked G and H each contain but one acid and one base, which you are required to find.
2. The substance marked K contains no bases other than Alumin'a, Oxides of Iron and Manganese, Lime, Magnesia, and Potash. You are required to find which of these it contains. It does not contain Phosphoric Acid.
3. The substance marked L contains one acid, which you are required to find.
4. Examine the substance marked M with the blowpipe.
* The Notice to Candidates was the same as that given above, p. 54.
SATURDAY, Dec. 18, 1858. 6 to 8 P.M. II. E. 2. Heat, Electricity, and Magnetism. 1. What is meant by the temperature of a body? and on what principle are instruments for measuring it constructed ? If the temperature indicated by a centigrade thermometer be 10o.32, what will it be according to Fahrenheit's scale?
2. What is meant by the specific heat of bodies? and what is meant by latent heat? If a solid at temperature T, and whose weight is W, be placed in a quantity of distilled water whose temperature is zero, and whose weight is w, find the common temperature at which the water and body will ultimately arrive, the specific heat of the body being half that of the water, and no heat being lost or gained by the influence of extraneous bodies.
3. If a heated body be placed in air, what is the Newtonian law according to which the body will cool? What has been shewn to be the accurate law of radiation from the surface of the body when it is placed in a vacuum ? According to what law does the intensity of radiation from any point of a heated surface vary with the direction in which the radiation takes place?
4. Assuming the luminous heated solar rays to have the property of traversing the earth's atmosphere with little loss of heat, while the heat ascending from the heated surface of the earth has not that property, account for the decrease of temperature in ascending from the lower to the higher regions of the atmosphere.
5. Give Joule's proposition respecting the equivalence of heat and vis viva, and describe, in general terms, the experiment by which he proved the proposition in the case of producing an increased temperature in water by stirring it. To how many foot-pounds is a degree of heat equivalent ?
6. How does it appear that the states of electrical excitement of which bodies are capable are of two kinds ? Describe some instrument by which the electrical state of any body may be tested. If glass and silk be rubbed together, what will be the electric state of the silk?
7. What is inductive electric action? Illustrate by an appeal to experiment. Explain the action of a Leyden jar.
8. Describe the Thermo-electrometer, and explain its action.
9. Describe Grove's nitric acid battery, and explain its advantages. What regulates the tension in such a battery ?
10. What is the relation between currents of electricity and magnetism? Explain how an electric current can be obtained from a magnet.
11. What are secondary poles in a magnet, and how may they be detected ?
12. Describe the phenomena of diamagnetism.
TUESDAY, Dec. 21, 1858. 9 to 11 A.M.
9 II. E. 3. Acoustics, and Physical Optics. 1. In what state must a body be when it becomes sonorous ? How is it proved experimentally that sound cannot be propagated through a vacuum ? When propagated through the atmosphere, how are our organs of hearing affected by it? What is the difference between a noise and a musical note with respect to the vibrations which produce them respectively?
2. How has the velocity of sound in air been experimentally determined? Does it vary with the density of the atmosphere if the temperature be constant, or with the temperature if the density be constant ?
3. If a loud report were produced by the firing of cannon on board a vessel at sea, would the sound be first heard on board another vessel at a distance, by aerial vibrations, or by those propagated in another manner?
4. Explain the action of the Stethescope. Is the tube necessarily hollow?
5. What causes the difference in the pitch of musical notes? To what is this analogous in light, according to the Undulatory theory?