4. The six coordinates of a ray satisfy identically one equation of the second degree. If further they satisfy one linear equation, what must be the "locus" of the ray? Investigate this, and discuss also the "locus" if two linear equations be satisfied, or three or four.

MR. W. R. ROBERTS.

1. Find the condition that the line whose coordinates are a, b, c, f, g, h should touch the surface

be determined as the intersection with it of the confocal surfaces

determine, in terms of p and q, the differential equation of the lines on the quadric.

3. Express in terms of p and q the angle between the curves p = constant, q=constant, which lie on the surface of centres represented by the system of equations

4. Show that the lines of curvature of the surface

xm yn zp = a

lie on the surface obtained by forming the discriminant with regard to λ of the following equation:

5. Find the equation of the surface which has the twisted cubic, given

6. Determine the double lines on the surface

√ x + √ ÿ + √ z + √ w = 0.

BERKELEY MEDAL EXAMINATION.

MR. PALMER.

I.

Translate the following passages:—

Beginning, ή δ' Ὀδυσῆ ἐλέησεν ἀλώμενον, ἄλγε ̓ ἔχοντα, κ. τ. λ.
Ending, οὐδέ τί τοι παθέειν δέος οὐδ ̓ ἀπολέσθαι.

HOMER, Od., v. 336-347.

2. Beginning, Πεντήκοντα δέ οἱ δμωαὶ κατὰ δῶμα γυναῖκες, κ. τ. λ. Ending, ἄνθος ἀφιεῖσαι, ἕτεραι δ ̓ ὑποπερκάζουσιν.

Ibid., vii. 103-126.

3. Beginning, ταρσοὶ μὲν τυρῶν βρῖθον, στείνοντο δὲ σηκοὶ, κ. τ. λ. Ending, ἥμισυ δ ̓ αὖτ ̓ ἔστησεν ἐν ἄγγεσιν.

Ibid., ix. 219-223.

4. Beginning, ἀλλ ̓ ὅτε δὴ τάχ' ὁ μοχλὸς ἐλάϊνος, κ. τ. λ. Ending, ὣς τοῦ σίζ ̓ ὀφθαλμὸς ἐλαϊνέῳ περὶ μοχλῷ.

.240–248.

Ibid., ix. 378-394.

5. Beginning, ὡς εἰπὼν ἀπέπεμπε δόμων βαρέα στενάχοντα. κ. τ. λ. Ending, ἐν στόματι προύχουσιν, ἀραιὴ δ ̓ εἴσοδός ἐστιν.

Ibid., x. 76-90.

6. Beginning, οὐδὸς δ ̓ ἀμφοτέρους ὅδε χείσεται, κ. τ. λ. Ending, μαρναμένους· πῶς δ ̓ ἂν σὺ νεωτέρῳ ἀνδρὶ μάχοιο.

Ibid., xviii. 17-31.

7. Beginning, οἱ μὲν ἔπειτα δόμονδε θοῶς κίον, κ.τ.λ. Ending, στὰς ἄρ ̓ ὑπὸ βλωθρὴν ὄγχνην κατὰ δάκρυον εἶβεν. Ibid., xxiv. 220-234.

1. Translate and explain :

(a).

(b).

πόλλ ̓ ἄλγεα δυσμενέεσσιν

χάρματα δ' εὐμενετῃσι· μάλιστα δέ τ ̓ ἔκλυον αὐτοί.
ἀκταὶ ἀπορρῶγες λιμένος ποτιπεπτηυίαι.

(c). ἀλλ ̓ ἔμπης καλάμην γέ σ' δΐομαι εἰσορόωντα

γιγνώσκειν.

2. Give the meaning and the derivation, where possible, of the following:—θῆσθαι, νάσσα, ἀβάκησαν, νέποδες, δήω, δέατο, νῆϊς, εἴρερος, θέμωσε, ἀθηρηλοιγός, δέρτρον, διδέντων, ἀρνευτήρ, τιθαιβώσσω, ἰονθάς, ἀμφουδὶς.

3. "I must have offended the gods."

Translate that into the language of the Odyssey.

4. What phrases occur for "abounding in wealth," "she laughed idly"?

5. "The day is far spent." How is this expressed?

6. Write a note on the use of roîos in the Odyssey.

7. Write a note on the peculiar construction of xpǹ, Xpeíw.

8. tok is used in different senses?

9. Kelwv is found in two different senses ?

10. A word denoting "viatica" appears in three different forms in the Odyssey?

II. In what senses are åpeτáw and ȧpéσкw used?

12. Mark the quantities of the following words, stating their meaning :—πλημμυρίς, στίβη, λάρος, λαρός, κώρυκος.

13. Several uncommon words, meaning "to sleep," "go to sleep," are found in the Odyssey?

14. The penult. of the perf. in -aσt is found short in Odyssey?

15. Which of his adventures did Ulysses call otkriσtov?

16. A part of σrvyéw is used in a causal sense?

17. What parts of a peculiar form for xeipwv are found in Odyssey?

18. Distinguish between aros and ȧáaros. With what context is the latter formed?

19. What dative plural of ăvaş is found?

20. éviάoμai: what is the meaning and derivation of this word? what compounds of it are found?

21. What rare formations from the perfect of máσxw are found in Odyssey?

22. Explain the word used for xaîpe in the last book.

23. vew is only used once with a singular subject in Homer?

24. páσσate: from what verb is this? Give the perfect pass. third plural used in Odyssey?

25. What different verbs meaning "to forebode" are found in Odyssey?

26. What lines in the Odyssey are quoted by Herodotus?

27. What are the most famous quotations from the Odyssey?

28. What parts of the Agamemnon of Æschylus vividly recall the Odyssey?

29. The effect produced by procumbit humi bos is also produced by e line in the Odyssey?

30. Who were Lampetie, Arete, Phemius, Pisistratus, Theocly menus?

Where were Temese, Ephyre, The Taphians, Alybas? In what connexion are they mentioned in the Odyssey?

31. Who are called τρώκται ?

32. With whom does Mure identify the Phaeacians?

MR. TYRRELL.

I. Beginning, εἰ γὰρ νῦν παρὰ νηυσὶ λεγοίμεθα πάντες ἄριστοι, κ.τ.λ. Ending, πρόσσω ἱεμένοιο, μετὰ προμάχων ὀαριστύν.

HOMER, Iliad, xiii. 276–291.

2. Beginning, βῆ δ ̓ ἴμεν ἐς θάλαμον, τόν οἱ φίλος υἱὸς ἔτευξεν, κ. τ. λ. Ending, καλῷ, νηγατέφ ̇ λευκὸν δ ̓ ἦν, ἠέλιος ὥς.

Ibid., xiv. 166-185.

3. Beginning, ἀλλ ̓ οὐ λῆθε Διὸς πυκινὸν νόον, κ.τ.λ. Ending, πρώτον, ὄφρ ̓ ἀνέχοιτο θαμὰ θρώσκοντας ὀϊστούς.

:

1. Translate, with a short note on each :-
(α) ἔκλαγξαν δ ̓ ἄρ ̓ ὀϊστοὶ ἐπ ̓ ὤμων χωομένοιο,
αὐτοῦ κινηθέντος

Ibid., xv. 461-470.

(6) ̓Ατρείδη, νῦν ἄμμε παλιμπλαγχθέντας οΐω
ἂψ ἀπονοστήσειν, εἴ κεν θάνατόν γε φύγοιμεν,
εἰ δὴ ὁμοῦ πόλεμός τε δαμᾷ καὶ λοιμὸς Αχαιούς.
(ε)
οὐδέ σ' οΐω

ἐνθάδ' ἄτιμος ἐὼν ἄφενος καὶ πλοῦτον ἀφύξειν.
(α) δαιμόνι', οὔ σε ἔοικε, κακὸν ὣς, δειδίσσεσθαι.

ἀλλ ̓ αὐτός τε κάθησο, καὶ ἄλλους ἵδρυε λαούς.
(ε) αἴθ ̓ ὄφελες ἄγονός τ ̓ ἔμεναι, ἄγαμός τ' ἀπολέσθαι.
(f) τὸν δ ̓ οὔτ ̓ ἄρ τε γέφυραι ἐεργμέναι ἰσχανόωσιν.
(9) καί νύ κεν ἔνθ ̓ ἀπόλοιτο ἄναξ ἀνδρῶν Αἰνείας.
(h) ̓Ανδρομάχη, θυγάτηρ μεγαλήτορος Ηετίωνος,
Ηετίων, ὃς ἔναιεν ὑπὸ Πλάκῳ ὕληέσσῃ,
(i) καὶ τὰ μὲν ἐν χρυσέῃ φιάλῃ καὶ δίπλακι δημῷ
θείομεν, εἰσόκεν αὐτὸς ἐγὼν ̓́Αϊδι κεύθωμαι.
(;) καί οἱ ὑπὸ σκήπτρῳ λιπαρὰς τελέουσι θέμιστας.
(*) αἰψά τε φυλόπιδος πέλεται κόρος ἀνθρώποισιν·

ἧστε πλείστην μὲν καλάμην χθονὶ χαλκὸς ἔχευεν·
ἄμητος δ ̓ ὀλίγιστος, ἐπὴν κλίνῃσι τάλαντα
Ζεύς.

(a)

κὰδ δέ μιν αὐτὸν

εἰλύσω ψαμάθοισιν ἅλις χέραδος περιχεύας
μυρίον.

(m) ἡ δὲ μολυβδαίνῃ ἐκέλη ἐς βυσσὸν ὄρουσεν,
ἥτε κατ ̓ ἀγραύλοιο βοὸς κέρας ἐμβεβανία,
ἔρχεται ὠμηστῇσιν ἐπ ̓ ἰχθύσι Κῆρα φέρουσα.
2. What is the note of interpolation in these passages ?-
ἐκ δὲ τρήρωνα πέλειαν
λεπτῇ μηρίνθῳ δῆσεν ποδός, ἧς ἄρ ̓ ἀνώγει
τοξεύειν. ὃς μέν κε βάλῃ τρήρωνα πέλειαν,
πάντας ἀειράμενος πελέκεας, οἶκόνδε φερέσθω.
(δ) ληΐδα δ ̓ ἐκ πεδίου συνελάσσαμεν ἤλιθα πολλήν.
(c) ἀμφίσταντο δὴ ἄστυ διαπραθέειν μεμαῶτες.

(α) καί νύ κεν ̓Ακτορίωνε Μολίονε παῖδ ̓ ἀλάπαξα.

3. What is objectionable in the following readings, and what remedy should be applied?

4.

(α) ὅππως οἱ παρὰ νηυσὶ σόοι μαχέοιντο ̓Αχαιοί

(6) ἀλλα σύ, εἰ δύνασαί γε, περίσχεο παιδὸς ἐῆος.

(c) ὃς πολέμου ἔραται ἐπιδημίου ὀκρυόεντος.

(α) δέγμενος Αἰακίδην ὅπότε λήξειεν ἀείδων.

(f) Ιλίου προπάροιθεν ἐμῇς ἐν χερσὶ βάλῃσιν.

(α) What is the difference between σφωε (enclitic) and σφῶι; οὐτάμενος, βεβλημένος, and βεβολημένος; τέμνειν and μιστύλλειν ; λυτο and λύτο ?

(6) Why should we prefer ἔδεισαν to ἔδδεισαν; ἐπι ἦρα to ἐπίηρα; ξάων to ἐάων ?

5. Parse πέρθαι, ὀρωρέχαται, ἔρχαται, ἀπόνητο, πεφήσεται, δειδέχατο, ἕωμεν.

6. What peculiarity is there in the Homeric use of these words :βλάπτειν, φράζειν, ὅρκος, ἐρωεῖν, κῆρυξ, θερ'πων, ἱερός, βέλος, ἐπεστέψαντο, φόβος ?

7. Give instances of adjectives which have the comparative or superlative formed from substantives or adverbs.

8. Quote passages in which divine and human language are contrasted. (α) Write a note on Homer's use of the subjunctive.

9.

(6) Give instances of pres. and imperf. in place of perf. and pluperf.

(c) Of ǎv and key with the future indicative.

(α) What anomalous use of μέτα do we find in Homer ?

10. (α) Under what conditions is a trochaic caesura allowed in the fourth foot ?

(6) What remarkable metrical feature is presented by this verse : ἔργων τοιούτων· ἐμὲ δὲ χρὴ γήραϊ λυγρῷ ?

(c) What is a rhopalistic verse ?