4. Give a list of the original vowel-sounds, with their normal representation in Greek, Latin, Sanskrit and Teutonic. In what cases does e in Latin take the place of original i, and vice versâ? 5. Give an account of the working of Ablaut in Greek in the "e-roots." Derive inquit, disco, sumus. 6. What consonantal law is exemplified in the correspondence of Sanskrit-antar, English-under? State the law and illustrate it. Write down the Greek and Latin cognates of ten, tooth, tear, widow, guest, quick; and test the consonantal correspondence in each case. 7. State clearly the rule of treatment of the palatal stops in Greek, Latin, Teutonic, and Sanskrit. 8. Discuss the necessity of assuming original j and v. 9. Treat fully the history of ns in Greek, and sr in Latin. 10. To what original sounds does Latin f belong? When does it become b? How far do the other Italic languages agree with Latin herein? 11. Take the following sets of cognate words, and examine the exact phonological relationship between the words in each set:-in, ἐν; πρόφρων, πρόφρασσα; ὃς, suus; ποινή, τίσις; malus, mast; ὄσσε, ὄψομαι; πέμπε, quinque; εἶμι, eg, ἴασι. What is the common element in singulus and μῶνυξ ? 12. Examine the phenomenon of "Compensatory Lengthening." Why is it assumed rather than “Epenthesis” in κτείνω, φθείρω ? Additional for Third Year only. 13. Point out the difficulties of discovering the shape and meaning of original suffixes. 14. Point out and explain any peculiarities in the formation of παντοδαπός, ἀλλήλους, ἐμαυτῷ, ἴφιος, πολλοστός, μητιόεις. 15. Write down the I.-E. numerals, cardinal and ordinal, from 1 to 10, 20, 30, 100, 1000. Explain any peculiarities in their Greek and Latin representatives. 16. Decline an o-noun and an i-noun in I.-E., and shew how far such declension is maintained in Greek and Latin. MIXED MATHEMATICS.-PART I. The Board of Examiners. TO BE USED ALSO AS FIRST HONOUR PAPER. 1. Find the resultant of two parallel forces acting on a rigid body. 2. Shew that for the equilibrium of a rigid body acted on by any forces in a plane it is necessary and sufficient that the sums of the resolved parts of the forces in two directions and the moment of the forces about one point vanish. A heavy disc is free to move about a point A in its plane. A string is attached to the centre of gravity G, and pulled horizontally with a force T. If W be the weight of the disc, shew that the tangent of the angle between A G and the vertical Τ W is 3. Find the centre of gravity of a uniform triangular lamina. An equilateral triangle and a square have a side in common. Find the distance of the centre of gravity of the two from the centre of the square. 4. Give the equations connecting (1) the dynamical measure of the force on a particle with its mass and acceleration; (2) the force in pounds and poundals; (3) the force in foot pound second units, and in centimetre gramme second units. [Take a kilogramme as 2.2 lbs., and a metre as 39 37 inches.] 5. Prove the equation s = vt + ft2 for motion in a straight line under constant acceleration f, v being the velocity at time zero, and s the space passed over. Shew that a stone thrown a height of 200 feet will be within 72 feet of the ground on the way down in 6.4 seconds nearly from the time of its leaving the hand. 6. Prove that the acceleration of a particle moving uniformly in a circle of radius r with velocity v 02 is towards the centre, and equals Hence shew that, apart from the resistance of the air, a particle would revolve around the earth close to its surface in about 1 h. 25 min. [Take 4,000 miles as the radius of the earth and g = 32.] 7. Demonstrate the equation p = gpz for the pressure at the depth z in a liquid of density p. Shew that the pressure on a square foot at a depth of 1 mile below the surface of water is about 147 tons. 8. State and prove Archimedes' theorem relative to the apparent loss of weight of a body immersed in a liquid. A solid mass of 12 lbs. weighs 3 lbs. in one liquid and 4 lbs. in another. Compare the densities of the liquids. 9. Explain carefully the mode of action of the common pump. MIXED MATHEMATICS.-PART II. The Board of Examiners. TO BE USED ALSO AS FIRST HONOUR PAPER. 1. Prove that two couples in the same plane are equivalent if their moments are the same. 2. Investigate the reduction of a system of coplanar forces to two forces ΣΧ, ΣΥ parallel to the rectangular axes x, y, and a couple Σ(yX— x Y). 3. State Coulomb's Laws of Friction. A uniform heavy isosceles triangular lamina ABC is supported on small studs at its corners, and rests on an inclined plane, with its base BC horizontal, the coefficient of friction of the stud A being μ, and of B and C μ2. Shew that slipping takes place when the elevation of the plane is <-1 tan 4. Find the centre of gravity of a tetrahedron. Shew that the centre of gravity of a slice cut off a spherical shell of any thickness by two parallel planes is midway between the planes, provided the slice has a hole through it. 5. Shew that the components of acceleration of a point (x, y) referred to rectangular coordinates are d2x day dt2' dt2 |