2. How are relations of time expressed by the three cases, respectively 3. What is the true account of the accusatives said to depend on kata understood ? 4. Why is it generally erroneous to suppose cases to depend on prepositions understood : 5. Explain what is meant by the subjective, objective, passive, and material genitives. 6. State accurately the nature of the relation between the Greek and Latin languages, and of both to Sanscrit. 7. When either language is said to be older than the other, what is the meaning of the expression? 8. Give some account of the life of Iphicrates. 9. Explain the nature and object of Ostracism, according to Grote. 10. Why was Delos chosen as the centre of the Athenian Confederacy? 11. The proceedings of Pisistratus with respect to Delos illustrate its importance ? 12. Give an account of the history of Polycrates, his views and mea sures. CICERO. MR. GRAY. 'Translate the following passages into English :1. Beginning, Esto: ipse nihil est, nihil potest.. Ending, ut tibi hospes aliquis sit recipiendus. In Q. Cæcilium Divinatio, c. 15. 2. Beginning, At ut videatur tamen res agi et non eripi pupillo : Ending, angustiis temporis excluduntur omnes. In Verrem, Act. 11. lib. i. c. 56. 3. Beginning, Primo mirantur omnes improbitatem calumniæ : Ending, ab jure omnium Siculorum ne recedatur. Ibid., Act 11. lib. ii. c. 15. 4. Beginning, In scriptura Siciliæ pro magistro est quidam ..... Ending, litteris dicere in istum et proferre possemus. Ibid., Act 11. lib. ii. c. 70. 1. Explain the following: “ Cognitor, præjudicium, quadruplatores, intus canere, peculium, compromissum, testamentum inofficiosum, demortuus, hereditas commissa, præs litis et vindiciarum." 2. Trace the origin of the “Quæstio perpetua de pecuniis repetundis;" and describe the form of procedure. 3. Explain the phrases, "perpetuum edictum" and "edictum translatitium." 4. Cæsar's policy was essentially different from that of his predecessors in provincial administration ? 5. What explanation has been given of the apparent pusillanimity of Pompey in abandoning Italy? 6. Cæsar's imperial authority was a combination of the prerogatives of several republican offices; in what way did they severally contribute to his power? 7. Mention, in their order, the principal military events from the crossing of the Rubicon to Cæsar's last battle. 8. Draw a map of Sicily, marking the principal towns on the coast, and giving, where you can, the modern names. 9. Describe the condition of Sicily, as a Roman province, in the time of Cicero. 10. State the general rules, and the principle on which they depend, for the use of the different tenses of the subjunctive mood in conditional propositions, and in expressing a wish. 11. Reduce the following sentence to the “oratio obliqua :" “Quid hoc rei est, inquit, tribuni? Ap. Herdonii ductu rempublicam eversuri estis ! Tam felix vobis corrumpendis fuit, qui servitia vestra non commovit auctor ? Quum hostes supra caput sint discedi ab armis legesque ferri placet ?” 12. Conjugate the following: “torreo, torqueo, strepo, tero, verro fodio, sarcio, ordior.” MR. FERRAR. Translate the following passage into Greek Verse:Beginning, I know you all, and will awhile uphold... Ending, Redeeming time when men think least I will. SHAKSPEARE. Translate the following passage into Greek Prose :Beginning, Let none of you, O Athenians, imagine that I am here ...... Ending, her really sure and effectual means of protecting the Chersonese. Transi. of Demosthenes, Translate the following passage into Latin Verse :- TENNYSON. Translate the following passage into Latin Prose :Beginning, The sum of the whole is plainly this....... Ending, are equally so to both by the same actions. BUTLER, Sermon 1. FELLOWSHIP EXAMINATION. Examiners. Mathematics, Pure and Applied. DR. HART. day doc2 day (1–22) dit 1. Integrate the equation, dy dx - 3y +aya = ca. 2. Integrate dy dx 3. Integrate n+1 dy + + (n +4 (n— 4) y=o. dx 4. Investigate the form of V, that SS V dy dx may be capable of a first integration ; V being a function of X, Y, Z, P, q, r, s, t. 5. Find the general equation of the surface which contains a maximum volume within a given area; and show that if it be a closed surface of revolution it must be a sphere. 6. If this surface is bounded by given curves, how are the tangent planes along these bounding curves determined ? 7. Prove that every multiple point on a curve is also a multiple point on its Hessian, and find its order. 8. If several curves of the same degree intersect in the same points, prove that a double point on one of them has the same polar with respect to all the others. 9. Find the equation of three right lines which pass through the points of inflexion of the curve ax3 + by3 + cz3 + 6dxyz=o. 10. Show how to compute the coefficients of the corresponding equation, when the curve is represented by the general equation of the third degree. PROFESSOR ROBERTS. 1. Prove that all homogeneous binary forms of the fifth degree can be reduced by linear transformations to the form ax5 + bys + cz, when x+y+z=0. 2. Express the cubic invariant of the form +(ce - d2) y, as a function of the invariants of the form ax4 + 4bxy3 + 6cx2y2 + 4dwy3 + eye. 3. If a, ß, y are the roots, ax3 + 36x2 + 3cx + d=0, find the equation whose roots are 2a - B-y 2B-a 2y-a-B r (a-B) + Bla-y)' a(-y)+y (B-a)' aly-B) +B(y-a) 4. Deduce from the properties of the Eulerian integrals the following relations : 2m (i km-1 doc n dx = 2 1 - 2007 2p zp-1 dz 2n-2p-'(1 – 2n) n dx Jo vitan 5. Express by circular functions the ratio of the following definite integrals : am-1 dx zm-i dz I + zn 6. Prove that (T})3 = 26 337 F (cos 15° 01), V 3-1 when cos e ✓ 3+1 0 = 1. If the general equation of the second degree, ax2 + by2 + cz2 + 2lyz + 2mxz + 2nxy + 2px + 294 +2rz+d=0, represents an hyperboloid, the origin being situated on the asymptotic cone; find the relation existing among the coefficients, and determine in this case the value of the discriminant. 2. If the centre of the surface, A' (« – a)2 + B' (y - 3)2 + C' (2- y)2 = 1, which is inscribed in a self-conjugate tetrahedron with respect to Ax2 + By2 + Cz2 = 1, lie on this latter surface; find the relation between A, B, C, A', B', C'. 3. If a', a", a" are the primary semiaxes of the three confocal surfaces passing through a point, determine in rectangular co-ordinates the equation of its locus when a' + a" + a'" = constant; and investigate the nature of its traces on the co-ordinate planes. 4. If the general equation of the second degree, ax2 + by2 + cz2 + zlyz + 2mx2 + 2nxy + 2px +297 + 27.+ d=0, represents a paraboloid, determine the form it assumes when the variables are transformed by the following substitutions : x = { + y, y=n+y's, x=y"}, where ay+ny' + my" = 0, ny+by' +ly" = 0, my + ly' +cy" =0; and deduce by means of these transformations the remarkable form of the discriminant in this case. FK 2 FK 5. If a is the amplitude of and if ß is the amplitude of 3' , prove 3 that the product of the imaginary roots of the equation which determines the trisection of Fk is 1 - cos %a cos 28 cosaß + kk sin "a sin 2ß' Ik A(k,p)-(1 – k') sino cosø 2k' 4k A(K, P)+(1- k') sino coso where k2 + k2=1. 7. If p denotes any odd number, and mFk am = am P prove that the equation connecting the amplitudes in Jacobi's transformation can be written under the form 4 tan 1 (a1-0) tan } (az+o). tan} (ap-2+0) 7 tan F when BF (ko) = F(hy); and determine accurately the cases where the upper or lower signs are to be used. 8. Retaining the notation of the last question, let rFk Mbey = am 2P I log tan (6 - ) = 2 prove that (Vith+V1-h) sin pli sin 13.. sin p2p_1=sin?aj sin?az.. sin?ap-2 9. Given the base of a spherical triangle, and the product of the tangents of the halves of the sides equal to the square of the tangent of one |