47. If any line be drawn from the pole intersecting the circle, tangents at the points of intersection meet on the polar? JOSEPII PATTON. Paper. 1. Prove the principle of indeterminate co-efficients, and apply it to find the log (1 + c). 2. Show that log z = 2 M (==) + (==) + 1(==) and apply this to find the Napierian logarithm of the common base. 3. Prove that the sum of the cubes of n natural numbers is equal to the square of their sum. 4. Prove, without trigonometry, that the area of a triangle is given by the formula, area s ( s − a) ( s —b) (s—c) Where a, b, &c. are the sides, and s = a+b+c 5. Apply this to find the area of the triangle whose sides are 4,352, 7,567 and 5,293 yards. 6. Given base and ratio of sides, construct the triangle when the area is a maximum. 7. Inscribe in a circle a triangle whose sides shall pass through three given points. 8. Given the difference between the diagonal and side of a square, to construct it? 9. Given three lines from a point within a square to the angles, to construct it? 10. If a perpendicular be let fall from the intersection of the diagonals of a quadrilateral inscribed in a circle upon the third diagonal, it will pass through the centre ? 11. Given the segments into which the base of a triangle is divided by straight lines trisecting the vertical angle ? 12. Given the three points in which the sides of a triangle are cut by the perpendiculars from the angles, to construct it? JOSEPH PATTON. 1. 2. 3. 4. WEST AND CLARE SCHOLARS. PHYSICAL GEOGRAPHY. What are the usual proofs that the earth is of a round form? What was his answer to the objection that we do not see the earth to be round? What is the dip of the earth for one mile? What is the correct form of the earth? 5. 6. 8. How was it discovered not to be an exact sphere? 9. How is the pendulum used for that purpose? 10. What is the length of a degree at the equator, and at the pole? 11. What is the mean density of the earth? 12. Explain the method of proving this experimentally? 13. How can this great density be reconciled with known facts respecting the surface of the earth? 14. To what depth have we any knowledge of the earth's strata? 15. How has this knowledge been obtained? 16. How does the temperature vary in descending towards the centre? 17. What is supposed to be the extreme height of the atmosphere? 18. There is a limit beyond which it cannot extend? 19. Of what is it composed? What is the nature of this combination? Mention some of the effects of this. 20. What is the use of the oxygen? 21. What of the carbonic acid? 22. way? Besides supporting life, air is essential to man in another 23. How does vapour differ from gases? 24. Who first discovered atmospheric pressure? 25. Explain the principles of the barometer? 26. If the barometer were filled with water, what would be its length? 27. What is the ordinary pressure of the atmosphere upon a square inch? 28. What variations take place in it during a day? 29. How can the heights of mountains be discovered by the barometer? 30. Why is the air nearest to the sun not the hottest? 31. To what height does the line of perpetual ice ascend at the equator? 32. In the Himalaya what peculiarity is there in the height of the perpetual snow line? 33. How is this accounted for? 34. What is meant by isothermal lines? 35. The existing arrangement of the mountains on the globe is very beneficial? 36. What causes winds? 37. Explain the trade winds. 38. Within what limits do they prevail? 39. Between the Northern and Southern Trades? 40. Why is the belt of variable winds altogether in the Northern Hemisphere ? 41. What becomes of the ascending current of heated air? 42. This has an important effect on the navigation between Europe and America ? 43. Give an explanation of the monsoons ? 44. Over what extent of country do they prevail? 45. Account for the land and sea breezes ? 46. Describe the movement of a hurricane or cyclone? 47. Hence it is easily seen why the wind blows in opposite directions in opposite sides of the centre ? 48. In what direction is the rotation in the Northern and in the Southern hemispheres? With what velocity do they move? 49. Give a simple rule for finding the position of the centre. 50. From the low barometric pressure in the centre, what may be inferred of the state of the sea? 51. Many instances prove this to be the fact,-Coringa? 52. Explain why the origin of a cyclone cannot be observed. 53. By what means can we find the amount of vapour in the air? 54. Explain the deposition of dew. 55. Why is our rainy season during the South West monsoon? 56. How is the fall of rain measured? 57. What is the greatest fall of rain that has been known to take place? 58. Why is the fall of rain in the tropical regions greater than in the Northern? 59. What portion of the earth is covered with water? 60. In which of the hemispheres does it preponderate ? 61. How does Humboldt suppose the channel of the Atlantic to have been hollowed out? 62. Explain how the attraction of the sun or moon produces a tide at the remote side of the earth. 63. Hence explain the phenomena of tides. 64. What causes modify the general laws? 65. Great source of the tides? 66. In some cases there may be no tide? 67. Are there tides in the Mediterranean? 68. In what time does a tide move from Cape Comorin to the Gulf of Cambay? 69. What is the motion of the water, and the motion of the wave? 70. At what temperature does salt water freeze? 71. Two causes which prevent the sea from becoming solid ice at the Poles?. 72. How has the existence of currents been detected? 73. What are the chief causes of currents? 74. State some of their beneficial effects? 75. What is the velocity of the earth at the equator? 76. Enumerate the principal currents in the Atlantic. 77. Describe the path of the equatorial, and its branches. 78. How is the Guyana current affected by the Maranon? 79. What is the temperature and velocity of the Gulf-stream at the Gulf of Florida? 81. The mild temperature of part of Northern Europe is supposed to be due to the Gulf-stream,-how ? 82. In the Bight of Biafra the currents are remarkable? 83. In the Indian Ocean what currents are there? 84. Of what nature are the currents in the Bay of Bengal, Persian Gulf, and Red Sea ? 85. Humboldt's current has a great effect on the climate of a part of Western America? 86. What is meant by the basin of a river? 87. How does the velocity of a river depend upon its depth? 88. What is the largest in Asia? Where does it take its rise? 89. What is meant by the Watershed? 90. This is not necessarily a mountain? Mention an instance in the West of India ;-in America. 91. Describe portage. 92. Hudson's Bay may be connected with the Gulf of Mexico, -how? 93. How has it been proposed to connect the Atlantic and Pacific Oceans? 94. Besides shortening the distance between Europe and China, this route will be particularly favourable to European commerce? 95. What is the direction of the principal mountain chains in the Old and New Worlds? 96. In what direction do the chief rivers of Asia flow? 97. This is true of all the rivers in the world? 98. What consequently is the nature of the land in central Asia ? 99. A similar conclusion may drawn from the direction of the rivers of the Peninsula of Hindoostan ? 100. What is the peculiarity in the mountains which run North and South? 101. In what parallel of latitude is the Altai chain? 102. What renders it probable that the Nile has its origin in a lofty mountain in central Africa? 103. Mention some lakes below the level of the sea. 104. What rivers flow into the Caspian Sea? 105. How much below the level of the Red is the Dead sea? 106. What is the greatest height at which lakes are found? JOSEPH PATTON. 1. WEST SCHOLARS. ANALYTICAL GEOMETRY. (Viva Voce.) What is meant by the locus of a given equation? 2. Prove that a straight line cuts the curve in as many points as it has dimensions. 3. The locus of an equation of the first order is a straight line? 4. In a curve of the nth order how many co-efficients? 5. How many points determine a curve of the second order? |