LAW OF EVIDENCE. PROFESSOR BAXTER; MR. DOYLE. 1. Mention the chief presumptiones juris et de jure with regard to infants. 2. What is meant by a fact being part of the res gestae'? Give examples. 3. Is general evidence of the good or bad character of either party ever, and if ever, when, admissible (a) in a civil action, (b) on a criminal trial? 4. What are the general rules governing the production of secondary evidence? Apply these rules particularly to documentary evidence. 5. What matters are not provable by the unsupported evidence of a single witness? 6. What is an estoppel in pais? How far is a tenant estopped from denying his landlord's title? 7. How far is a witness entitled to refuse to produce a document on the ground that he has a lien upon it? 8. In what cases is evidence: (a) of parol declarations by the writer of an instrument, as to its subject-matter; (b) of parol declarations of intention by a testator; admissible to interpret the instrument or will in question ? 9. State briefly what classes of communications are protected from disclosure on grounds of privilege. 10. Within what limits is a confession made by the accused in a criminal case admissible as evidence against him of the facts stated in such confession? EXAMINATION IN THE SCHOOL OF CIVIL ENGINEERING. SUMMER, 1902. PASS EXAMINATIONS. FIRST PROFESSIONAL EXAMINATION. MATHEMATICS. FIRST PAPER. PLANE GEOMETRY AND TRIGONOMETRY. PROFESSOR GIBNEY. 1. ABC is a triangle and P, Q are two given points in AB, AC, respectively, show how to find a point R in the base BC so that the triangles APR, AQR shall be equal in area. 2. Prove that the difference of the squares on two lines is equal to the rectangle contained by the sum and the difference of the two lines. 3. Show how to describe a circle to touch the five sides of a regular pentagon. 4. Show how to divide a given straight line into two segments that shall be in the ratio of two given straight lines. Show also how to divide the first line so that its segments shall be in the ratio of the squares on the other two given straight lines. 5. Prove that arcs of the same circle are proportional to the angles they subtend at the centre of the circle. 6. The two ends of a piece of inextensible string are fastened to two points in a beam, and a wheel is held in different positions resting on the string and keeping it tightly stretched. Prove that the amount of the area bounded by the string and the two straight lines joining the centre of the wheel to the extremities of the string is the same no matter what part of the string is in contact with the wheel. 7. Prove that if A and B be positive acute angles cos (AB) = cos A cos B + sin A sin B. 8. Find the values of sin 18°, cos 105°. 9. The three sides of a triangle are find its area to the nearest square inch and its least angle to the nearest minute. 2. Find x, y, z from the conditions Y z: z − x x + y :: 4 : 7 : 5, xyz = 12. 3. Prove that the arithmetic, geometric, and harmonic means between two positive quantities are in descending order of magnitude. If n means of each kind are inserted show that the r arithmetic mean is greater than the harmonic mean. 4. Calculate (1.005)7° correct to five places of decimals by the binomial theorem. 5. Find the number of ways in which the position of a cube can be changed without altering the space it occupies. 1. I 6. Calculate, by means of the tables, the value of (3.527) × (·02563) ÷ (876·2). 7. Two planes are perpendicular to a third. Prove that their intersection is also perpendicular to this third plane. 8. A line joining variable points on two fixed straight lines is divided in a constant ratio. Find the locus of the point of division. 9. Find the locus of the centres of the sections of a sphere made by parallel planes. 10. Find the volume of the segment of a sphere cut off by a plane, the radius of the plane base being 9 ft. and the height 3 ft. EXPERIMENTAL PHYSICS. PROFESSOR BERGIN. 1. What is meant by Young's modulus of elasticity? Explain how it may be measured. 2. Describe a force pump for water. 3. The weight of a litre of air at 0° C. and 76 cm. pressure is 1.293 grammes: find the volume of a gramme of air at 10° C. and 75 cm. pressure. 4. Explain some method of determining the coefficient of expansion of a solid. 5. How would you find the latent heat of fusion of ice? 6. What circumstances determine the loudness of a sound? 7. Represent diagrammatically the action of a refracting telescope, and describe some method of determining its magnifying power. 8. Describe a spectroscope and explain fully how to adjust it. 9. What is the effect of polarisation in an electric cell? Describe any method of preventing it. 10. Explain how to measure the strength of an electric current by means of a voltameter. PRACTICAL PHYSICS. 1. Plot the time of swing of a pendulum against its length. 2. Find the diameter of the given wire. 3. Measure the given resistance. FIRST PAPER. DRAWING AND DESCRIPTIVE GEOMETRY. SECTION A. DRAWING. PROFESSOR FITZ GERALD. [Lithographic sketches, figs. 1, 2, and 3, accompany this Paper.] 1. Make an isometric drawing of the object shown in plan and elevation fig. 1 (which is not drawn to scale) using a scale of 1-inch to a foot. 2. Make an isometric drawing of a rectangle, whose sides are 1 inch and 24 inches long, lying on the ground, one corner lies at a distance of 2 inches from the origin, on a line drawn through the origin at an angle of 30° with the right-hand axis, and the longer side of the rectangle lies on this line produced. 3. Make a perspective drawing of the object shown in fig. 2 (which is not drawn to scale) from the data there given, on a scale of 10 feet to an inch. 4. Given the distance 20 feet, height of eye 5 feet, scale 4-inch to a foot, find the vanishing point of lines, inclined upwards from the spectator, at 45°, whose plans make an angle of 60° with the horizontal trace of the picture plane. 5. Find by measuring points, with the same scale distance and height, as in question 4, the perspective view of a point on the ground, lying 8 feet to the right of the perpendicular from the eye on the picture plane, and 10 feet behind the picture plane. |