THURSDAY, July 3.-Morning, 10 to 1. GEOMETRY. Examiner, G. B. JERRARD, Esq. Di 1. What is meant by a point, an angle, a circle? stinguish between an axiom and a postulate. Do the truths of Geometry, as a portion of human science, rest ultimately on the evidence of the senses? 2. From the greater of two given straight lines to cut off a part equal to the less. 3. Show that if two triangles have two sides of the one equal to two sides of the other, each to each; and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases, or third sides, equal; and the two triangles shall be equal; and their other angles shall be equal each to each, viz. those to which the equal sides are opposite. 4. To draw a straight line perpendicular to a given straight line of unlimited length, from a given point without it. 5. If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. 6. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. 7. Show that if from the right angle of a right-angled triangle two straight lines be drawn, one perpendicular to the base, and the other bisecting it, they will contain an angle equal to the difference of the two acute angles of the triangle. 8. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given recti lineal angle; and thence prove that the perimeter of an isosceles triangle is greater than that of an equal rectangle of the same altitude. 9. In any right-angled triangle the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. 10. Any two parallelograms having been described upon two sides of a given triangle, show how to apply to the third side a parallelogram equal to their sum. THURSDAY, July 3.-Afternoon, 3 to 6. NATURAL PHILOSOPHY. Examiners, G. B. JERRARD, Esq., and Rev. Prof. HEAVISIDE. 1. Can a single force always be found equivalent to two given forces acting at a point in given directions? Show how to find this single force. Given a single force; can it always be resolved equivalently into two forces in given directions ? Two forces of 30 lbs. each press upon a fixed point, their directions being inclined at an angle of 120°; find the magnitude and direction of the resultant pressure. Find 2. Give instances in which systems of pulleys have been arranged so as to obtain a mechanical advantage. the ratio of P to W in any one such system of three pulleys. Is there any mechanical advantage in a single fixed pulley ? Will the mechanical advantage be greater or less in a system of movable pulleys if the strings be inclined instead of being parallel? 3. When there is equilibrium on a given inclined plane, find the ratio of the power to the weight. In what direction will the power act at the greatest advantage? Find the force acting in this direction that will just support 1000 lbs. on a plane inclined at an angle of 45°. What 4. State and illustrate the third law of motion. do you understand by moving force? how is it estimated ? Express the relation between moving force and accelerating force. 5. A body falls from rest in vacuo by the action of gravity; find the velocity acquired (1) when it falls for a given time, (2) when it falls through a given space. Ex. Find the velocity (1) when the body falls for 5 seconds, (2) after it has fallen through 3220 feet. 6. A vessel is filled with water; show how the pressure at any point may be found; how is this pressure estimated? If the water be at rest in an open vessel, how is the pressure at any point affected by the atmosphere? A cubic foot of water weighs 1000 ounces; find the pressure on a square yard of surface immersed horizontally in water at a depth of 60 feet. 7. Define specific gravity, and show how the specific gravity of a solid may be found. A substance weighs 350 grains in air, and 280 in water; find its specific gravity. State any argu 8. Describe the common barometer. ments in favour of the assumption that the mercury in the tube is supported by the pressure of the atmosphere on the mercury in the basin. Describe also the common suction-pump. Will it increase or diminish the column of water that can be raised by it, to transfer the pump from a lower to a higher level? 9. Explain the formation of images by simple lenses. How do you distinguish between converging and diverging rays? What lenses will cause parallel rays to converge ? 10. State the laws of the refraction of light. In what way is the apparent position of an object at the bottom of a clear pool affected by refraction relatively to the eye of a person looking at it from the side of the pool? FRIDAY, July 4.-Morning, 10 to 1. ROMAN CLASSIC AND HISTORY. Examiner, T. B. BURCHAM, Esq. Translate into English: VIRGIL. GEORGICS, Book I. (A.) Vere novo, gelidus canis quum montibus humor At prius, ignotum ferro quam scindimus æquor, Cura sit, ac patrios cultusque habitusque locorum; Arborei fetus alibi, atque injussa virescunt Gramina. Nonne vides, croceos ut Tmolus odores, Alternis idem tonsas cessare novales, Sed tamen alternis facilis labor: arida tantum (B.) Idcirco certis dimensum partibus orbem Per duodena regit mundi Sol aureus astra. 1852. h |