3. If a sphere rolling on a horizontal plane impinge against a vertical wall which is inelastic and rough, determine the motion of the sphere after the shock. 4. Two equal rods connected by a hinge are laid on a smooth horizontal plane so as to form one right line; one of the rods receives a blow at its free extremity in a direction perpendicular to its length : a. Determine the initial motion; b. Show that the angle between the two rods varies uniformly. 5. A cylinder is laid on a rough horizontal plane, and in contact with a rough vertical wall, the coefficients of friction being equal; a string coiled round it passes over a pulley, and supports a weight, which is gradually increased till the equilibrium is broken; what is the nature of the initial motion? 6. A spherical shell is filled with a fluid of the same density, which is gradually solidifying without changing its density; if the sphere be placed on a rough inclined plane and allowed to roll down, and if the law of its velocity be known, determine the rate of solidification. N. B.-The fluid is supposed to solidify in shells commencing from the outside. 7. A prismatic vessel, having any number of sides which are connected with each other by smooth hinges, is filled with water; what is its figure of equilibrium? Moderatorships in Classics. Examiners. THOMAS LUBY, D. D. THOMAS STACK, M. A., Regius Professor of Greek. GEORGE LONGFIELD, M. A. JOHN K. INGRAM, LL. D., Professor of English Literature. MR. STACK. Translate the following passages accurately into English I. Beginning, πρῶτον μὲν δὴ τῶν τεττάρων τὰ τρία διελόμενοι, κ. τ. λ. Ending, τὸ θερμότερον καὶ τοὐναντίον ἅμα. PLATO, Philebus, 12. 2. Beginning, τοῦ μεν οὖν περιττοῦ γένεσιν οὔ φασιν, κ. τ. λ. Ending, ἡ μὲν οὖν ἀποριά αὕτη, ποτέρως δεῖ λέγειν. ARISTOTLE, Metaphys., xiv. 9. 3. Beginning, τίς δ' ἀρίστη πολιτεία καὶ τίς ἄριστος, κ. τ. λ. Ending, ἄρχειν δὲ δεσποτικὴν ἀρχήν. Ibid., Politic., vi. 11. 4. Beginning, τῇ δὲ αὐτῷ ἰδέᾳ ἐκεῖνά τε ἔσχον καὶ τὰ ἐνθάδε, κ. τ. λ. Ending, μηδὲν ἐνδώσομεν, φαίνεσθαι. MR. LONGFIELD. THUCYDIDES, Vi. 76–77. Translate the following passages 1. Beginning, "Ω γέρον, οὐκ ἀδαημονίη σ' ἔχει ἀμφιπολεύειν, κ. τ. λ. Ending, ἢ ἤδη τέθνηκε καὶ εἶν ̓Αίδαο δόμοισιν, HOMER, Odyss., xxiv. 244–264. 2. Beginning, Η μὲν ἄρα προφυγοῦσα πέτρας εἰς ἕν ξυνιούσας, κ. τ. λ. Ending, "Ακρων δέρμα λέοντος ἀφημμένον ἐκ ποδιώνων. THEOCRITUS, Idyl., xxii. 27-52. 3. Beginning, φαντὶ δ ̓ ἀνθρώπων παλαίαὶ, κ. τ. λ. Ending, ἀστέων μοῖραν, κέκληνται δέ σφιν ἕδραι. 4. Beginning, οὗτοι προδώσει Λοξίου μεγασθενὴς, κ. τ. λ. Ending, χαλκηλάτῳ πλάστιγγι λυμανθὲν δέμας. PINDAR, Olymp., viii. 54–76. ESCHYLUS, Choeph., 261-282. SOPHOCLES, Trach., 823-842. 5. Beginning, "Ιδ' οἶον, ὦ παῖδες, προσέμιξεν ἄφαρ, κ. τ. λ. Ending, ἐπιζέσαντα. 6. Beginning, φεῦ τῆς βροτείας, ποῖ προβήσεται, φρενός; κ. τ. λ. Ending, βάκχευε, πολλῶν γραμμάτων τιμῶν καπνούς· EURIPIDES, Hippolytus, 936-954. 7. Beginning, ΧΟ. ὦ Διὸς ἐννέα παρθένοι ἁγναὶ, κ. τ. λ. Ending, ἐμπεσόντα συσκεδᾶν πολλὰς ἀλινδηθρας ἐπῶν. ARISTOPHANES, Ranæ, 875-904. DR. LUBY. Translate the following passages into English Prose : I. Beginning, Hunc rerum cursum, quanquam nulla verborum... TACITUS, Agricola, 39, 40. 2. Beginning, Crebro per eos dies apud Domitianum absens accusatus, . Ending, simul vitiis aliorum in ipsam gloriam præceps agebatur. 3. Beginning, Consules, diversis itineribus profecti ab urbe,.. Ending, intra paucos dies castra cum altero juncturum.” Ibid., 41. Livr, lib. xxvii. c. 40. 4. Beginning, Tot igitur annos versatus in foro sine suspicione,. Ending, pugnantibus naturæ studiis cupiditatibusque conflatum. CICERO, Pro M. Cælio, c. 5. Translate the following passages into English : 1. Beginning, Postquam mihi responsum est, abeo ab illo mastus ad forum,. Ending, Tu tabellas consignato; hic ministrabit; ego edam. 2. Beginning, Pavit et Admeti tauros formosus Apollo;. TIBULLUS, lib. II. Eleg. iii. 11-32. 3. Beginning, Si proprium est, quod quis libra mercatur et ære, Ending, Permutet dominos et cedat in altera jura. HORACE, Epist., lib. 1. ii. 158-174. 4. Beginning, Dic igitur, quid causidicis civilia præstent... Ending, Et strepitu et facie majoris vivere census. JUVENAL, Sat. vii. 106-137. 5. Beginning, Vix miseris serum, tanto lassata periclo,...... Ending, Ultima castrorum medicatus circuit ignis. LUCAN, Pharsalia, ix. 890-915. MR. STACK. Translate the following passage into Greek Prose :— It may very easily have happened that from some of us proverbs have never attracted the notice which I am persuaded they deserve; and therefore that, when summoned to bestow even a brief attention on them, we are in some doubt whether they will repay our pains. We think of them but as sayings on the lips of the multitude; not a few of them have been familiar to us as far back as we can remember; often employed by ourselves, or in our hearing, on slight and trivial occasions; and thus from these and other causes it may very well be, that, however sometimes one may have taken our fancy, we shall yet have remained blind in the main to the wit, wisdom, and imagination, of which they are full; and very little conscious of the amusement, instruction, insight, which they are capable of yielding. Unless, too, we have devoted a certain attention to the subject, we may not be at all aware how little those more familiar ones, which are frequent on the lips of men, exhaust the treasure of our native proverbs; how many and what excellent ones remain behind, having now for the most part fallen out of sight; or what riches in like kind other nations possess. We may little guess how many aspects of interest there are in which our own by themselves, or our own compared with those of other people, may be regarded. And yet there is much to induce us to reconsider our judgment, should we be thus tempted to slight them, and to count them not merely trite, but trivial and unworthy of a serious attention. The fact that they please the people, and have pleased them for ages, that they possess so vigorous a principle of life, as to have maintained their ground, ever new and ever young, through all the cen turies of a nation's existence,-nay, that many of them have pleased not one nation only, but many, so that they have made themselves an home in the most different lands,-and further, that they have, not a few of them, come down to us from remotest antiquity, borne safely upon the waters of that great stream of time, which has swallowed so much beneath its waves,-all this, I think, may well make us pause should we be tempted to turn away from them with anything of indifference or disdain.-TRENCH on Poverbs. MR. LONGFIELD. Translate the following passage into Greek Tragic Trimeters :- In harbour, then, old man? Well! I am not. The unconquered spirit drives me o'er life's billows; Nor in the furrows of my hand. Who dares COLERIDGE, from SCHILLER. DR. LUBY. Translate the following passage into Latin Prose : The strongest and fiercest of man's fellow-creatures, --the whale, the elephant, the eagle, and the tiger,- -are slaughtered by him to supply his most capricious wants, or tamed to do him service, or imprisoned to make him sport. The spoils of all nature are in daily requisition for his most common uses, yielded with more or less readiness, or wrested with reluctance, from the mine, the forest, the ocean, and the air. Such are the first fruits of reason. Were they the only or the principal ones, were the mere acquisition of power over the materials, and the less gifted animals which surround us, and the consequent increase of our external comforts, and our means of preservation and sensual enjoyment, the sum of the pri vileges which the possession of this faculty conferred, we should after all have little to plume ourselves upon. But this is so far from being the case, that every one who passes his life in tolerable ease and comfort, or rather whose whole time is not anxiously consumed in providing the absolute necessaries of existence, is conscious of wants and cravings in which the senses have no part, of a series of pains and pleasures totally distinct in kind from any which the infliction of bodily misery or the gratification of bodily appetites has ever afforded him; and if he has experienced these pleasures and these pains in any degree of intensity, he will readily admit them to hold a much higher rank, and to deserve much more attention, than the former class. Independent of the pleasures of fancy and imagination, and social converse, man is constituted a speculative being; he contemplates the world, and the objects around him, not with a passive, indifferent gaze, as a set of phenomena in which he has no further interest than as they affect his immediate situation, and can be rendered subservient to his comfort, but as a system disposed with order and design. He approves and feels the highest admiration for the harmony of its parts, the skill and efficiency of its contrivances. Some of these which he can best trace and understand he attempts to imitate, and finds that to a certain extent, though rudely and imperfectly, he can succeed,-in others, that although he can comprehend the nature of the contrivance, he is totally destitute of all means of imitation;—while in others, again, and those evidently the most important, though he sees the effect produced, yet the means by which it is done are alike beyond his knowledge and his control. Thus he is led to the conception of a Power and an Intelligence superior to his own, and adequate to the production and maintenance of all that he sees in nature,-a Power and Intelligence to which he may well apply the term infinite, since he not only sees no actual limit to the instances in which they are manifested, but finds, on the contrary, that the farther he inquires, and the wider his sphere of observation extends, they continually open upon him in increasing abundance; and that, as the study of one prepares him to understand and appreciate another, refinement follows on refinement, wonder on wonder, till his faculties become bewildered in admiration, and his intellect falls back on itself in utter hopelessness of arriving at an end.-HERSCHEL. DR. INGRAM. Translate the following passage into Latin Verse: To strew fresh laurels, let the task be mine, |