2. "Itaque perpaucis adversantibus, omnia quæ ne per populum quidem sine seditione se assequi arbitrabantur, per senatum consecuti sunt: nam et stipendium Cæsari decretum est et decem legati: et ne lege Sempronia succederetur, facile perfectum est." Write a historical note on this pas sage." 3. Describe the relations of the several parties at Rome to Pompey at the time of the mission of Nepos. 4. State the reasons for believing that Cæsar and Crassus were accomplices in Catiline's first conspiracy. 5. Give an account of Cicero's conduct in the affair of Scaptius. 6. Explain the words or phrases :-Cavillatio, conditio, provincias, ornare, prævaricatio, fenus ex triente factum erat bessibus. 7. From a comparison of Greek and Latin, it has been argued that there existed a Helleno-Italic people, which had reached a certain stage of civilization before its separation. Give some account of the argument. 8. Explain and illustrate the relation between the Latin words sequor, silva, virus, decem, and the corresponding Greek words. MR. FERRAR. Translate the following passage into Latin Prose : If it be desired to know the immediate cause of all this free writing and free speaking, there cannot be assigned a truer than your own mild, and free, and humane government; it is the liberty, lords and commons, which your own valorous and happy counsels have purchased us; liberty which is the nurse of all great wits: this is that which hath rarified and enlightened our spirits like the influence of heaven: this is that which hath enfranchised, enlarged, and lifted up our apprehensions degrees above ourselves. Ye cannot now make us less capable, less knowing, less eagerly pursuing of the truth, unless ye first make yourselves, that made us so, less the lovers, less the founders of our true liberty. We can grow ignorant again, brutish, formal, and slavish as ye found us; but ye must then first become that which ye cannot be, oppressive, arbitrary, and tyrannous, as they were from whom you have freed us. MILTON'S Areopagitica. Translate the following passage into Latin Verse : On Linden, when the sun was low, But Linden showed another sight, By torch and trumpet fast arrayed, To join the dreadful revelry. Then shook the hills with thunder riven; But redder yet those fires shall glow 'Tis morn-but scarce yon level sun Shout 'mid their sulphurous canopy. CAMPBELL. · Translate the following passage into Greek Iambics :- In all my miseries, but thou hast forced me, And sleep in dull cold marble, where no mention Still in thy right hand carry gentle peace, To silence envious tongues. Be just, and fear not. Let all the ends thou aim'st at be thy country's, Thy God's and Truth's; then if thou fall'st, O Cromwell, Translate the following passage into Greek Prose : SHAKSPEARE. I come now to speak upon what, indeed, I would gladly have avoided, had I not been particularly pointed at for the part I have in this bill. It has been said by a noble lord on my left hand, that I likewise am running the race of popularity. If the noble lord means, by popularity, that applause bestowed by after ages on good and virtuous actions, I have long been struggling in that race; to what purpose all-trying time can alone determine: but if the noble lord means that mushroom popularity that is raised without merit, and lost without a crime, he is much mistaken in his opinion. I defy the noble lord to point out a single action of my life, where the popularity of the times ever had the smallest influence on my determinations. I thank God I have a more permanent and steady rule for my conduct,-the dictates of my own breast. Extract from a Speech of Lord Mansfield. JUNIOR FRESHMEN. Mathematics. A. MR. W. ROBERTS. 1. Being given the base of a triangle, find the locus of the vertex when the sum of the squares of the bisector of the base, and of half the base, is in a given ratio to the rectangle under the sides. 2. Through the vertex C of an isosceles triangle, draw a line meeting the base AB in a point P, such that if M be the middle point of CP, the square of AP may be equal to twice the difference of the squares of BM and PM. 3. Construct a triangle, being given the base, difference of sides, and the ratio of its area to that of the triangle standing on the same base, and having the centre of the inscribed circle for vertex. 4. Being given two fixed points A, B, let two right-angled triangles ACD, BCD be described having a common hypotenuse CD; if the line CD be parallel to a given line, prove that the difference of the angles CAB, CBA will be given. 5. Being given base, rectangle under sides, and bisector of vertical angle; construct the triangle. 6. Being given base, rectangle under sides, and radius of circumscribing circle; construct the triangle. DR. SHAW. 7. The rectangle under the chords of the sum and difference of two arcs is equal to the difference of the squares of their chords? 8. Describe a circle which shall pass through two given points, and bisect the circumference of a given circle. 9. If the external bisectors of the angles of a triangle be produced to meet the opposite sides, the three points of intersection will lie in a right line? 10. Given in position three points A, B, C; through one of them C draw a right line so that if from the remaining two the perpendiculars AP, BQ be let fall upon it 11. Given two systems of points A, B, C and A', B', C' on a circle; find a point P such that the anharmonic ratio of P, A, B, C and of P′, A′, B′, C′ shall be equal; and show that the problem admits of two solutions. 12. If a system of circles have a pole and polar in common, they will have the same radical axis ? MR. TARLETON. 13. Prove that the square of the distance between the centres of the circles inscribed and circumscribed to a triangle, together with twice the rectangle under their radii, is equal to the square of the radius of the circumscribed circle. 14. Find the complete locus of a point at which the sides of an isosceles triangle subtend equal angles. 15. Given the bases of two triangles, and the sum of their areas; find the locus of their common vertex. 16. If through the point of intersection of two circles a line be drawn making equal angles with the circles, show that the rectangle under the segments intercepted between the point and the circles is greater than that under the segments of any other line drawn through the same point. 17. If from a point 0 outside a circle two tangents be drawn, and through the middle point of the chord of contact any other line be drawn meeting the circle in P and Q, show that OP and OQ are equally inclined to the tangents from 0. 18. If a quadrilateral be circumscribed round a circle, the middle points of the diagonals and the centre of the circle are in one right line? B. MR. W. ROBERTS. 1. The values of the sides a, b, c of a triangle being given by the equations 438.4616175 C = 1140.0002055, required the value of the radius of the circumscribing circle. 3. Two sides of a triangle are represented by 1707.37424 and 1067. 1089, and the angle between them is half the angle of an equilateral triangle; find the area. 4. The sides of a right-angled triangle are .00008654 and .00003602; find the perpendicular from the right angle on the hypotenuse. DR. SHAW. 5. 5 tons of Newcastle coal are worth 7 yards of Genoa velvet, and 13 yards of velvet are worth 22 yards of poplin; if 3 yards of poplin exchange against 23 bushels of oats, and 5 bushels of oats exchange against 1 ton of lead ore, find how much lead ore is worth a ton of Newcastle coal. 6. The estate of a bankrupt, £21,000, is to be divided among four creditors, whose debts are-A's to B's as 2:3, B's to C's as 4:5, C's to D's as 6:7; what must each receive? 7. The sides of a triangle are 8.2, 9.5, and 13.6 feet long; calculate the radii of inscribed and circumscribed circles, also of the three exscribed. 8. Lead is 14.5 as heavy as water, and a cubic foot of water weighs 62.3 lbs. avoirdupois; from these data calculate the weight of a leaden sphere the radius of which is 9 inches. MR. TARLETON. 9. Whether is it better to sell a farm for £1000 payable at present, £1000 payable at the end of five years, and £1000 payable at the end of ten years; or to sell it for £3000, payable at the end of five years, compound interest being allowed at 4 per cent. per annum ? 10. Express 357 in the scale of notation whose radix is 31. 11. Find the cube root of to seven places of decimals. 12. If a person borrow £1100, at 6 per cent. per annum compound interest, and agree to pay both principal and interest in eleven equal annual instalments, how much must each payment be, the first being made at the end of the first year? C. MR. W. ROBERTS. 1. Being given the base of a triangle, and the rectangle under the diameter of its circumscribing circle, and the line joining the feet of perpendiculars let fall on the sides from the extremities of the base; find centre of circumscribing circle. 2. Find the ratio of the line joining the feet of perpendiculars dropped from the extremities of the base of a triangle on the sides to the perpendicular let fall from the middle point of the base on the line joining either of its extremities with the centre of the circumscribing circle. 3. Let I be the centre of the circle inscribed in a triangle ABC; through I draw lines perpendicular to IA, IB, and meeting AB in the points P, Q; it is required to prove the following proportion : IC: AC. BC :: PQ: AB 4. ABC is a triangle in which the rectangle under the sides AC, BC is equal to the square of half the base AB; let M be the middle point of |