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5. If the notation of the faces of the triakisoctahedron be (1, 1, n); show that the dihedral angles, measured over the longer and shorter edges, are
292 + 1 6. In the dimetric system, the ratio of the unique axis of Idocrase to each of the equal axes is the tangent of 28° 9' ; find the dihedral angles of its primitive octahedron.
7. If the faces of the dihexagonal prism of the Beryl be (1, 4, 0); show how it may be constructed geometrically.
8. Andalusite has been observed to occur in rhombic prisms, having the longitudes of the poles of their faces equal to 45° 22' and 63° 44'; deduce from these data the ratio of two of its parameters.
9. The faces of the trimetric octahedron are represented by (a, b, c); find the dihedral angles they make with each other, and classify them.
10. If, in the monoclinic system, whose angle is o, c denote the parameter at right angles to the plane of the oblique parameters a and b; find in the primitive octahedron the following angle
(a, b, c) (a, b, -c). 11. State the chemical formula of Beryl, and mention the localities in which it has been found in Ireland.
12. What are Rutile, Anatase, and Brookite, and where are they found in the British Islands ?
13. What is the composition of Killinite, and what is its relation to Spodumene ?
14. What are the felspars and micas that have been proved to occur in Irish Granites; and mention the localities in which each species is found
15. What are Kyanite and Scapolite, and where are they found in the British Islands.
1. State the objects and instruments of psychological investigation.
2. Give Locke's account of Abstraction and Generalization. How far are his conclusions adopted by Cousin ?-and what is Cousin's distinction between immediate and comparative Abstraction ?
3. Neither our knowledge of the qualities nor substratum of bodies is a comparative judgment !
(a). Show that this is admitted by Locke. 4. Give Berkeley's argument for the existence of spiritual substance.
5. Locke's theory of the knowledge of real and personal existence involves a paralogism, according to Cousin ?
6. Berkeley's argument against external material existence is not fairly stated by Cousin ; the premises contain more than is necessary for the conclusion ?
(a). Cousin shows that “the principle of substance" is not derived from association ?
7. Locke gives his principal argument on the nature of essences in the form of a Sorites; resolve this Sorites into syllogisms of the first figure.
8. By what propositions does Locke conclude against an “à priori" knowledge of the properties of substances ?
(a). We may derive legitimate conjecture even beyond experience ? (6). Give Locke's examples of this.
9. In discussing the origin of our Ideas, what is Locke's proposition concerning Relations ?-and give the general argument by which he proposes to establish it.
10. Show by what steps Archbishop Whately, in the analytical outline, comes to the Dictum of Aristotle.
Translate the following passages into English :1. Beginning, ώς δ' ότ' ανήρ οχετηγός από κρήνης μελανύδρου, κ. τ.λ. Ending, λάβρος, ύπαιθα ρέων, κονίην δ' υπερεπτε ποδοιϊν.
HOMER, Iliad, xxi. 257-271. 2. Beginning, αυτάρ επήν μνηστήρας ενί μεγάροισι τεοίσιν, κ. τ.λ. Ending, όλβιοι έσσονται τάδε τοι νημερτέα είρω.
HOMER, Odyssey, xi. 119-136, 3. Beginning, τόδε θαύμ' έχει με, κ. τ.λ. Ending, ανύσειε γαστρί φορβάν.
SOPHOCLES, Philoctetes, 687-712. 4. Beginning, και πρώτα μεν δείλαιος, ίλεω φρενί, κ. τ. λ. Ending, κρατός διασπαρέντος, αίματός θ' ομού.
SOPHOCLES, Trachinie, 765-784. 5. Beginning, ώ ψάμαθοι πολιήτιδος ακτάς, κ. τ.λ. Ending, πέμπετε τώνδ' απ’ οίκων;
EURIPIDES, Hippolytus Coronifer, 1124–1145. 6. Beginning, ώ πολύξεινος, και ελεύθερος, κ. τ.λ. Ending, χαίρουσ' εύφρονι μολπά.
EURIPIDES, Alcestis, 585-603.
Translate the following passages into English :1. Beginning, Προς τούτοις τοίνυν τηλικούτοις ουσιν, κ. τ.λ. Ending, σφαλερωτέραν αυτή πεποίηκε.
DEMOSTHENES, In Epistolam Philippi. 2. Beginning, Έκ τούτου δή έχοντο επί τας σκηνάς, κ. τ.λ. Ending, Και ο Κύρος μεν δή ούτω περί τούτων εγίγνωσκεν.
XENOPHON, Cyropædia, lib. v. 3. Beginning, Και η μεν γνώμη κοινωνείτω, κ. τ.λ. Ending, ως μη απολείποιτο της φοράς.
LUCIAN, De Conscr. Hist. 4. Beginning, Μάλιστα δε κατόπτρω έoικυίαν παρασχέσθω, κ. τ.λ. Ending, και έρρύθμιζον, και επήνθιζον το χρυσω.
Translate the following passage into Greek Prose :Beginning, And now, on the news respecting Eubea reaching the Athe
nians, Ending, contested against them with the greatest success.
Translation of Thucydides.
GREEK VERSE COMPOSITION.
Translate the following passage into Greek Trimeter Iambics :Beginning, Pylades. Where is she? that my words with speed may tell.... Ending, The precious burden !
Miss SWANWICK, from GOETHE.
Translate the following passages into English :1. Beginning, Ac velut, effusa si quando grandine nimbi... Ending, Per medium Æneas juvenem ; totumque recondit.
VIRGIL, Æneid, lib. x. 803-816. 2. Beginning, Nec pingues unam in faciem nascuntur olivæ.. Ending, Tmolus et assurgit quibus et rex ipse Phanæus.
VIRGIL, Georg., lib. ii. 85-98. 3. Beginning, Geta. Hem! A. Quid egisti ? G. Emunxi argento senes.... Ending, Quin male narrando possit depravarier.
TERENCE, Phormio, act iv. sc. 4.
4. Beginning, Pi. Multi more isto atque exemplo vivunt, quos quom Ending, Facere, et in me inconciliare copias omnes meas.
PLAUTUS, Bacch., act iii. sc. 6. 5. Beginning, An magis oblectant animum jactata petauro. Ending, In pelago.
JUVENAL, Sat. xiv. 265-277. 6. Beginning, Solis natalibus est qui... Ending, Seu ceraso peccent casiæ, nescire paratus.
PERSIUS, Sat. vi. 19-36.
Translate accurately the following passages : 1. Beginning, Redeo ad altercationem. Surgit pulchellus puer: Ending, śmionuaoias sine ulla pastoricia fistula auferebamus.
CICERO, Ep. ad Att., i. 16. 2. Beginning, Si quid in te peccavi, ac potius quoniam peccavi,... Ending, nocere omnino nobis non potuisset.
CICERO, Ep. ad Att., iii. 15. 3. Beginning, At enim solidum id est ut me Siculi maxime velint:.... Ending, se in judiciis diutius dominari non posse.
CICERO, in Verr. Divin. 4. Beginning, Teneo, teneo, inquam, in mediis vectigalibus.. Ending, exspectatum existimationis tuæ judicium : non facis.
CICERO, in Verr. 5. Beginning, Ac ne bello quidem Italico, mox civili omissum, Ending, plerique legis nexus modicum in præsens levamentum fuere.
TACITUS, Ann., iii. 28.
Translate the following passage into Latin Prose :Beginning, To touch but for a moment on one other subject.... Ending, we may hope that the dawn of the morning is but the nearer.
BROWNE, Aids to Faith—Inspiration.
Translate the following passage into Latin Elegiacs :Beginning, And is there care in Heaven? And is there love.... Ending, 0, why should heavenly God to men have such regard
SPENSER, Faery Queen, book ii. canto 8.
GRECIAN AND ROMAN HISTORY.
DR. INGRAM. 1. Some writers have regarded the Lycurgean system as representing the common type of Dorian institutions. Do you consider this view a correct one ?
2. In what respects did the Periclean constitution at Athens differ from that of Cleisthenes ?
3. Write a note on the distinguishing characters of Grecian, Roman, and modern colonization.
4. In what transactions of Grecian political history do the names of these eminent writers appear :-Hecatæus, Polybius, Sophocles, Thucydides, Tyrtæus ? 5. Describe briefly and accurately the condition of the several states of Greece when Philip of Macedon ascended the throne.
6. State the essential facts of Roman history during the Regal period, as (it is supposed) they may be elicited from the legends.
7. What were the principal enactments, of a progressive character, contained in the Decemviral Code?
8. What were the several changes successively made in the constitution of the Roman judicia?
9. When, and how, did the following countries become Roman provinces :—Spain, Sicily, Sardinia, Cilicia, Syria, Numidia ?
10. Write short notices of-a. Spurius Cassius; 6. C. Flaminius; c. C. Quinctius Flamininus; d. L. Æmilius Paullus the Younger.
11. Give a full account of the family of Augustus.
12. Write down the ancient names from which the following are derived :-Amiens, Auvergne, Bourges, Fréjus, Grenoble, Nismes, Treves, Utrecht. Also the modern names of the places known in ancient times as Avaricum, Bibracte, Genabum, Hispalis, Interamna, Præneste, Saguntum, Tusculum.
1. In comparing Homer and Virgil, state the influences which had af. fected the subject matter and the form of epic poetry in the interval between them, and point out the bearing of these upon the comparison.
2. Mr. Conington disposes of many of the disparaging criticisms on the Æneid by stating what he conceives to be the true relation between Homer and Virgil ?
3. Analyze the character of Turnus in its connexion with the leading idea of the epic of Virgil.
4. Compare the female characters of the Iliad and the Æneid, and account for the difference of type observable in them. 5. “Eumenidum veluti demens videt agmina Pentheus
Et solem geminum et duplicis se ostendere Thebas
Aut Agamemnonius scænis agitatus Orestes." The reference to the stage in these lines has been made a subject of objection; discuss it.