10. In a common mercurial barometer, investigate the change in the height of the mercury arising from a small change in the pressure of the atmosphere. 11. For a given day and place, investigate the difference in the lengths of morning and evening arising from the Sun's change of declination in the interval between his rising and setting. 12. Given the lengths of two measured degrees of the terrestrial meridian, with the latitudes of their middle points; determine the lengths of the equatoreal and polar radii of the Earth. MR. LESLIE. 13. A body is projected vertically in a medium whose resistance is as the square of the velocity; write down the equations which determine its motion, and show that they can be integrated. 14. A particle moves under the action of a central force; given the orbit described, show how to determine the law of force, and apply the method to the case of a focal ellipse. 15. Prove the formula for determining heights by means of the barometer, and show how this formula is to be modified if the difference of heights be considerable. 16. A bar of metal, half a square inch in section, can support a weight of 1000 lbs.; what is the greatest fluid pressure which a cylindrical tube of this metal can sustain, its diameter being ten inches, and its thickness one-eighth of an inch ? 17. Prove Brinkley's formula for the atmospherical refraction. 18. Prove that the principal focus of a sphere of glass is distant from it by half the radius. B. MR. STUBBS. 1. In determining the dispersion of a ray produced through two prisms placed in any manner with respect to each other, prove that (where Ap and Ap" are the incident and emergent dispersions)— Apx product of cosines of the four angles of incidence = 2. Explain the phenomena of the primary and secondary rainbows, and prove the optical formula which you use. 3. Deduce the change of altitude of the Sun or star when near the meridian in a given time. 4. A particle acted on by gravity is projected with a given velocity from a given point along a horizontal line towards a fixed point; find the curve along which it must be constrained to move that it may approach the fixed point uniformly, the tangent to the required curve at the point of starting being horizontal. MR. TOWNSEND. 5. At the last athletic games in the College Park, a cricket ball, weight 5 oz., was thrown to the maximum distance of 91 yds.; neglecting the resistance of the atmosphere, calculate in foot pounds the entire work accumulated in it at the instant of projection. 6. A fluid sphere, composed of any number of concentric strata of uniform but different densities, is held in equilibrium by the attraction of the entire mass; determine the pressure at its centre. 7. A homogeneous cylinder, floating in water in the position of equilibrium in which its parallel faces are horizontal, receives a small vertical displacement; show that it will oscillate in the same time as a pendulum of the length of its portion originally immersed in the water. 8. In vision through a coaxal system of any number of thin lenses, some convex and some concave, separated by any intervals, exhibit approximately by a figure the course of the pencil by which any point of the object is seen by the observer. MR. LESLIE. 9. The times of descent down chords of a vertical circle drawn from the highest point are equal; state and prove the analogous property when friction is taken into account; and hence construct the line of quickest descent from a point to a circle when friction is considered. 10. A particle moves under the action of a fixed centre whose attraction is expressed by the formula a b find the nature of the orbit described. 11. A square board floats with its plane vertical, and one angle only below the surface of the liquid; find its positions of equilibrium. F ; 12. When two planets P and P' are stationary with respect to each other, prove that cos PSP'=(TT')} T and T being their periodic times. {T} + T'}} " Experimental Physics. ELECTRICITY. MR. GALBRAITH. 1. State the Franklinian hypothesis, or single-fluid theory of electricity, and point out its defect. 2. State the double-fluid theory of electricity. How does it differ from the theory of Boreal and Austral fluids in Magnetism. 3. How should a sewing needle be inserted in a left-handed helix, through which a current of electricity passes, in order that the point should be a north end? 4. What was Ampère's theory as to the constitution of a magnet? On this hypothesis, explain the mutual action of the poles of two magnets on each other. 5. Give Faraday's view of the electrolysis of water. 6. Explain and illustrate by a diagram Groves' gas-battery. 7. Explain the nature and principle of Faraday's voltameter. 8. If 150 cubic centimeters of the mixed gases be collected over water, if the pressure be 750 millimeters, and the temperature 15° C., calculate the weight of water decomposed. 9. Calculate the charges of electricity on each of Richmann's plates after a series of alternate touches. 10. Give an expression for the intensity of the current in the interpolar, taking into account the size of the plates, their distance, and the nature of the exciting fluid. DR. HAUGHTON. 1. Describe the observations on the velocity of Sound made near Paris, in 1822, by the Board of Longitude. What was the resulting velocity, reduced to the temperature of freezing water? 2. State the proportions of the numbers of vibration, in a given time, of the notes of the gamut. 3. Describe the Siren of Cagniard de la Tour, and the Toothed-wheel of Savart; and the use of these instruments. 4. State the usual limits of the male and female human voice. 5. Express the number of vibrations of a stretched cord in terms of its length, weight, and tension. 6. Describe Newton's experiments to illustrate the bands formed by thin plates; and give his Laws. 7. Investigate the formula for thin plate bands, on the Undulatory theory. State the difficulty that occurs in reconciling it with observation; and give Young's explanation. 8. Describe Newton's experiment to show the bands produced by thick plates. 9. Investigate the formula for thick plate bands, on the Undulatory theory. 10. Prove Snell's law of refraction on the mechanical principles of the Emission and Undulatory theories; and show the important difference in the results of the two theories. HEAT. DR. APJOHN. 1. What, in the case of a weight thermometer, is the expression for the coefficient of apparent expansion, e, in terms of W, the weight of mercury which fills the thermometer at o° Centigrade, and wt, the weight of mercury expelled from such thermometer when its temperature is raised by t degrees? 2. In connexion with the preceding question, deduce an expression for t in which the coefficient of expansion does not appear. 3. If two metallic bars have, at 50° Centigrade, the same length, and at 400° a difference of length equal to d, what is the common length of the bars at 50°; e being the coefficient of expansion of the most expansible metal, and e' that of the other? 4. Explain Regnault's air pyrometer, and give the expression by which temperatures are deduced from its indications. 5. v and v' representing the volumes of same mass of any gas at temv a + t peratures t and t, if = a being a constant, what will be the cov' a +t" efficient of expansion of the gas? 6. An iron tube whose length was 10, and internal diameter 1.5 inches, was placed in a furnace, and, when it had acquired a maximum heat, its air was displaced by a stream of dry hydrogen. The hydrogen was then made to pass over red hot oxide of copper, by which it was converted into water, and this, when collected in a chloride of calcium tube, was found to weigh 0.36 grains. What was the temperature of the furnace in degrees Fahrenheit, the temperature of the air being 60°, and its pressure 30? 7. Should (see previous question) the pressure at the time of the experiment be p, and the temperature t, a correction must be made in preceding calculation; what is it? 8. What is the principle on which the determination of specific heats by the method of mixtures, is based? 9. If W lbs. of melted metal at temperature T be dropped into A lbs. of water at t, and that the mean temperature is found to be 0, what is the value of its latent heat, T" being its melting point, c its specific heat in the liquid, and c' in the solid state? 10. If air at 60° be heated until its volume is doubled, and then suddenly compressed into its original bulk, what will its temperature become? Classics. ESCHYLUS. MR. LONGFIELD. Translate the following passages:— 1. Beginnig, κύριός εἰμι θροεῖν ὅδιον κράτος αἴσιον ἀνδρῶν, κ. τ. λ. Ending, αἴλινον, αἴλινον εἰπὲ, τὸ δ ̓ εὖ νικάτο. Agamemnon, 104-120. 2. Beginning, ἰδοὺ δ' Απόλλων αὐτὸς ἐκδύων ἐμὲ, κ. τ. λ. Ending, ἀποῤῥυέντων, ὄμμα συμβάλω τόδε. Ibid., 1240-1265. 3. Beginning, φεῦ τοῦ ξυναλλάσσοντος ὄρνιθος βροτοῖς, κ. τ. λ. Ending, Διὸς θέλοντος ξυγκαθελκυσθήσεται. Septem contra Thebas, 593-610. 4. Beginning, καὶ μὴν παρ ̓ ἡμῶν Περσίδος γλώσσης ῥόθος, κ. τ. λ. Ending, πλῆθος τοσουτάριθμον ἀνθρώπων θανεῖν. Persæ, 408-434. 5. Beginning, ἰὼ θεοὶ νεώτεροι, παλαιοὺς νόμους, κ. τ. λ. Ending, Νυκτός ἀτιμοπενθεῖς. Eumenides, 775-787. 1. Give some account of the Medicean MS. of Eschylus. 2. What is the statement in the Life of Eschylus in this MS. as to the number of his plays, and of his dramatic victories? What plays are referred to in it by name? 3. On what authorities do the statements rest (a) that Eschylus fought at Salamis; (b) that he was accused of impiety before the Areopagus; (c) that his plays continued to be acted after his death? 4. "Veniat Eschylus non poeta solum sed etiam Pythagoreus" (Cicero, Tusc. Disp., ii. 9). What traces of the Pythagorean philosophy have been found in his writings? 5. Write a note on his conception of the kingly character. 6. How has he departed from the Hesiodic representation of the myth of Prometheus? 7. Schlegel compares the epochs of Greek Tragic Art with those of Sculpture? 8. Write a note on the uses of the negative combination μn our. 9. Explain the use of owc and wg with the Future Indicative. 10. And the use of iva, wc, and onwç with the Historic Indicative. |