2. State accurately the nature of a mutuum. Distinguish it from pignus, mandatum, and donatio inter vivos.

3. Distinguish between 'culpa' and 'dolus.' What are the liabilities of the depositarius, negotiorum gestor, caupo?

4. Give a detailed account of the origin and effects of Noxal Actions.

5. What are the three senses in which 'injuria' is used in Roman law? What are 'convicium' and 'dissimulatio?"

6. How far did the 'litterarum obligatio' still survive in the time of Justinian? What was the 'exceptio non numeratae pecuniae?'

7. Sketch the state of the judicial system under Justinian, and explain the precise signification of an 'exceptio.'

8. What were the provisions of the-Lex Furia, Lex Cornelia de falsis, Lex Hostilia, Lex Plaetoria, Lex Petronia, Lex Publilia?

9. Explain the following terms:-actio in factum concepta, für improbus, actio communi dividundo, stipulationes conventionales, demonstratio, furtum oblatum, actio familiae erciscundae.

10. What are the rights and obligations which arise in the following cases? Give your reasons in each case.

(1) Stichus stipulates to give Maevius 100 aurei today if a certain ship arrives from Massilia to-morrow. The ship does not arrive.

(2) Seius borrows some plate from Titius, intending to give a supper party, but forgets to return it and carries it away to his villa.

(3) Maevius and Titius are neighbours; they agree to lend each the other his ox for ten days. The ox of Maevius dies while in the possession of Titius.

(4) Seius gives a 'mandatum' to Stichus, who executes it in ignorance of the fact that Seius had died before the mandate had been executed.

Pass School. Group C.

Elements of Geometry. I.

1. Define a parallelogram, a gnomon, a sector of a circle, a polygon.

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When is a straight line said to be placed in a circle'?

2. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.

3. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

4. The straight line drawn at right angles to the diameter of a circle from the extremity of it falls without the circle; and no straight line can be drawn from the extremity, between that straight line and the circumference, so as not to cut the circle.

5. Describe an isosceles triangle, having each of the angles at the base double of the third angle.

6. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle.

7. When is the first of four magnitudes said to have the same ratio to the second which the third has to the fourth?

Define proportion, proportionals, ratio, and compound ratio; and explain the terms ex aequali, alternando.

[Turn over.

8. Parallelograms on equal bases, and between the same parallels, are equal to one another.

9. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by the side on which, when produced, the perpendicular falls and the straight line intercepted without the triangle between the perpendicular and the obtuse angle.

10. From a given circle cut off a segment containing an angle equal to a given rectilineal angle.

11. Describe a circle about a given equilateral and equiangular pentagon.

12. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.

Elements of Geometry. II.

1. Define the terms-degree, grade, unit of circular

measure.

Reduce 94o 50' to degrees and minutes; and find the circular measure of this angle.

2. Define the sine, cosine, and tangent of an angle. If the cosine is, find the sine and tangent.

=

3. Prove that sin 45° and find the secants and cosecants of 135°, 225°, 1125°.

4. Prove that

(1) sec2 4-cot2 A+ cosec2 A-tan2 A = 2;

(2) cot A = tan A+ 2 cot 2 A;

(3) (1+sin 4) (sin B+ sin C) = cos A (cos B+cos C), if A+B+C 90°.

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6. Find the sine and cosine of an angle of 60°.

ABCDEF is an equilateral and equiangular hexagon; each side of which is 10 feet long: find the lengths of AC and BE, and the area of the triangle ABC.

7. Prove that in any triangle ABC, of which the sides are a, b, c.

(2) (b−c) sin A+ (c−a) sin B+(a—b) sin C = 0.

[Turn over.

(2) The value of (1.01)27, to three places of decimals ;

(3) The base of a right-angled triangle, in which the perpendicular is 127 and the hypotenuse 325.

9. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers themselves.

Find A, when 10 tan A = 7 sin 15° 30′.

10. In the triangle ABC, if B = 57° 45′, C = 105° 15′, and a = 227, find A and b.

11. The angle of elevation of the top of a cliff is observed from a boat to be 45°, the boat is rowed 100 yards in a direct line from the cliff, and the angle of elevation is then found to be 22° 30'. Find the height of the cliff.