(b). ENGLISH COMPOSITION. MR. BARLOW. Candidates will please select one subject from each of the following groups, and write two short essays: (a). The rise of new words in the English language. The causes of the existence of synonyms in languages. The principal peculiarities that distinguish the grammar of Chaucer's English from that of the English of the present day. The trial of the Earl of Strafford. "Praise undeserved is satire in disguise." The character of the English Puritan of the seventeenth century. Irish Sizarship. PROFESSOR O'MAHONY. : Translate the following passage from Greek into Irish :- Translate the following passage from English into Irish : : Beginning, It is difficult for us, of these days, Translate the following passages from Irish into English : Luke, vi. 46-49. 1. Give a brief account of the Indo-European languages, especially of that member of the group to which the Irish language more immediately belongs. 2. Write a short essay on the antiquity of letters in Ireland. 3. Name, in chronological order, the principal works on Irish grammar before Dr. O'Donovan's valuable treatise appeared. 4. Give some account of the "Grammatica Celtica" of Zeuss; pointing out what advantages he possessed over native Irish scholars, and what positions in respect to the Irish language may be considered as proved conclusively by him? 5. Besides the modern language and literature, we have monuments of the Irish in two other stages; specify them, and mention some of the works belonging to each stage. 6. The features which seemed to render the Irish a peculiar language have been satisfactorily accounted for? 7. What is the work called the "Annals of the Four Masters"? Where, when, and by whom compiled ? 8. What are O'Donovan's rules for determining the gender of nouns ? 9. Mention the principal changes made by the article in the initials of nouns. 10. How do such nouns as breiċeaṁ, feiċeam, &c., form the genitive singular, and dative plural? II. Decline an aill árd. 12. Give the rules for the formation of the infinitive mood in Irish. 13. Conjugate the assertive verb ir, and give a synopsis of the forms which this verb assumes in synthetic union with personal pronouns and conjunctions. 14. Conjugate the verb pizim. 15. In compound words, which part qualifies or determines the other? 16. Write an abstract of the rules for the government and collocation of pronouns. Translate the following passages into English: I. Ní feiom flata ná firlaic duitsi aisc feiċeaṁnais do tabairt ar mac deigfir da d-ticfad do tabairt a laí baġa le a bunað ceineoil a n-imarġail ard-ċaża. II. Coisteag brog, no Coirteaż adastair, amail indises is na lebruib: ruidles sin do buain a fid comaithcera, aċt na diz tairir. Ma do cuaid tairis imorra, masa corted bo seiched do ben, da banassa ind is fiu letscrepall. Mara corted dam seiched so ben de, da fer assa in-a dire is fiu serepall; ocur ní ráinig tra trian tairdib; ocus dia poised is a riazail re lan-timchell a misaib marbdataiz no re lettimchell, a misaib beodataiz. UNDERGRADUATE HONOR EXAMINATION PAPERS. Michaelmas Term. EXAMINATION FOR THE DEGREE OF BACHELOR OF ARTS. Moderatorships in Mathematics and Mathematical Physics. Examiners. CHARLES GRAVES, D. D. JOHN H. JELLETT, M. A., Professor of Natural Philosophy. MICHAEL ROBERTS, M. A., Professor of Mathematics. DR. GRAVES. 1. Form the intrinsic equation of the common cycloid; and prove from it that the curve is its own evolute. 2. Substitute d " dx d dy, when x=0. and z + for x, y, and z, respectively, in the expression y2-3-x223-3x2y2z +x1z, and operate with the whole upon unity. What will be the result obtained? Its form shows that the proposed expression is a solution of the equation d2u d2u 3. What is the effect of the symbol ep (D) d2u dz2 d dz = 0. operating upon a proposed function of x, D standing for the symbol 4. Find the value of the series + DR. SALMON. 5. Find the condition that the conic lyz+mzx + mxy may be such that the normals at the vertices of the triangle of reference meet in a point. How many such conics can be drawn through any point? 6. A triangle is inscribed in an ellipse whose centre of gravity coincides with the centre of the curve; how are the eccentric angles of its vertices connected? The three normals at the vertices of such a triangle meet in a point; find the locus of that point. 7. A surface of the second degree touches eight planes; what is the locus of its point of contact with any of them? 8. Reduce to a problem in elimination the problem of finding the surface of centres of the paraboloid ax2 + by2+ 2rz=0. 9. Write down the conditions that the surface x2 + y2+ z2 + w2 — 2yz cos L — 2zx cos M-2xy cos N-2xw cos P -2yw cos Q-2zw cos R=0 may touch the planes x, y, z, w; and examine in what case only these conditions can be fulfilled without supposing cos L= cos P, cos M= cos Q, cos N = cos R. satisfies a linear differential equation of the second order. II. Show that the ratio of the definite integrals Stav 1 (1 Jo (1 + gx)p+q+r−1 can be put under the form dx dx, (1 + gx)p can be expressed by means of the transcendant г. xp+q+r−2 ( 1 − x) ̄* 4a2 dx 12. Show that the reducing cubic in Euler's mode of solving the biquadratic equation ax2+4bx3+6cx2 + 4dx+e= 0 H 3 Δ ( y − 17 ) I =0, a2 where H= b2-ac, I= ae − 4bd + 3c2, and ▲ is the discriminant of the derived equation. 13. Point out the connexion between the reducing cubic in Euler's mode of solving a biquadratic and the equation 13-λ(ae - 4bd + 3c2) — which occurs in the theory of the linear transformation of homogeneous functions of two variables of the fourth degree, and express the roots of this latter equation in terms of the roots of the original biquadratic. into one in which 0 is the independent variable, connected with x by the equation ex. 2. Expand 1(x) in powers of x by means of Burmann's theorem. 3. Find the value of 5. Find the maximum value of (x − y) an − ( a − y) xn + (a − x) yn when x=y=a. 4. Find the limiting value when x is infinite of xx {{ }} du ̧-a2x2-fly2_q?z? ̧ (ax+by+cz) e 6. One of the parallel sides of a trapezoid being given, and also the length of the two equal sides which are not parallel, construct it so that its area may be a maximum. Give a complete interpretation of the solution furnished by the differential calculus. 7. Eliminate the arbitrary functions from dx u = xyz. F{ƒ1(x2 + y2 + z2), ƒ1⁄2 (xy +xz+yz)} . if + (ƒ + gx1) u =0 8. Find the envelope of the circles whose diameters are the chords of a given ellipse parallel to its axis minor. 9. Assuming that neither Mx-Ny nor My + N≈=0, prove that the expression Mdx + Ndy may be made an exact differential by means of the factor x2 + y2 Mx-Ny' if My + Nx My+Nx or by means of the factor x2 + y2 My+Nx 10. Form the differential equation of the gauche surfaces whose generatrices are all parallel to the same plane; and show that surfaces of this class are always non-convex at every point. is a function of xy; is a function of (x2 — y2). DR. SALMON. 1. The sides of a triangle touch a conic U, and two vertices move on another conic V; express the locus of the third vertex in terms of the invariants and covariant of the conics. |