9. A particle initially at rest is acted on by a constant tangential retarding force and by another force R, initially tangential, the direction of which turns round twice as fast as the tangent to the orbit. The resolved part of R along the tangent is constant. Find the orbit, and shew that, for a certain value of R, it will be a cycloid with its vertex at the initial position of the particle.

10. A heavy rod of length a, which can freely move about one end, is set rotating horizontally with a given angular velocity w. If 2 aw2 = 99, shew that the least angle which the rod in its subsequent motion will make with the vertical is.

11. A perfectly smooth square board, each edge of which is 2a in length, hangs by its upper edge, which is horizontal and at a distance 2 a, above a rough horizontal plane.

A heavy inelastic sphere of radius a rolls with velocity V on the plane and impinges perpendicularly on the board at its middle point. What will be the common velocity of the point of contact immediately afterwards, and what is the least value of V, that the sphere may just push completely past the board?

FRIDAY, JUNE 8, from 2.30 to 5.30 P.M.

SECTION V. Ancient History. (Greek History 1.)

1. In what respects, and to what extent, was early Greek civilisation affected by foreign influences?

2. The migrations of the Greeks, as distinct from their colonising movements, and the evidence by which the several migrations are supported.

3. The ethnic affinities of the non-Hellenic races with which the Hellenes came into contact in Europe.

4. To what causes would you attribute the rise of Athens to greatness, and her marked pre-eminence over all the other Grecian states? In what fields was her pre-eminence most marked?

5. The part played by Sparta in the great struggle between Greece and Persia from its commencement to its termination through the victories of Alexander the Great.

6. What Grecian states were Confederacies, and in which of them were the true principles of Federal Union best carried out?

7. Give some account of Greek naval tactics, and of the progress of Naval Architecture in Greece from the earliest times to the death of Demosthenes.

8. The commercial rivalry of Greece and Carthage, and its results. To what collisions did it lead, and how did it affect the course of Greek colonisation?

9. The physical geography of Greece, and its effects upon the Greek race (1) politically; (2) morally.

10. Explain and illustrate the rise and fall of the Greek despotisms. How do you account for the general disappearance of monarchy in the Greek states?

THURSDAY, JUNE 7, from 2.30 to 5.30 P.M.

SECTION V. Ancient History. (Greek History II.)

1. Give some account of the foreign history of Athens from the battle of Mantinea till the beginning of Philip's operations against Olynthus (362–349 B.C.).

2. Account for the transference of military power from Sparta to Thebes in the first half of the fourth century B.C.

3. Give a summary of the history of Olynthus from the close of the Peloponnesian war to its destruction by Philip.

4. What causes led to a decline of Sparta after the peace of Antalcidas (387 B.C.)?

5. How far was the failure of Athenian resistance to Philip due to mistakes of the Athenians?

6. Describe the practical working of the Athenian constitution in the time of Demosthenes.

7. Give some account of Dercyllidas, Evagoras, Iphicrates, Ismenias, Leosthenes, Lycomedes, Mentor of Rhodes.

8. What were the most important events in Persian history during the fifty years preceding the landing of Alexander in 334 B.C.?

9. Describe the course of events in Greece during Alexander's campaigns in Asia.

10. Describe the influence of philosophy on political life in Greece.

THURSDAY, JUNE 7, from 9.30 A.M. to 12.30.

SECTION V. Ancient History. (HERODOTUS, &c.) 1. Translate into English:

(1) Τὰ δ ̓ ἐς πόλεμον ἔχοντα ὧδέ σφι διακέεται. Επεὰν τὸν πρῶτον ἄνδρα καταβάλῃ ἀνὴρ Σκύθης, τοῦ αἵματος ἐμπίνει. ὅσους δ ̓ ἂν φονεύσῃ ἐν τῇ μάχῃ, τούτων τὰς κεφαλὰς ἀποφέρει τῷ βασιλέϊ· ἀπενείκας μὲν γὰρ κεφαλὴν, τῆς ληΐης μεταλαμβάνει τὴν ἂν λάβωσι· μὴ ἐνείκας δὲ, οὔ. ἀποδείρει δὲ αὐτὴν τρόπῳ τοιῷδε. περιταμὼν κύκλῳ περὶ τὰ ὦτα, καὶ λαβόμενος τῆς κεφαλῆς ἐκσείει· μετὰ δὲ, σαρκίσας βοὸς πλευρῇ, δέψει τῇσι χερσί· ὀργήσας δὲ αὐτὸ, ἅτε χειρόμακτρον ἔκτηται· ἐκ δὲ τῶν χαλινῶν τοῦ ἵππου τὸν αὐτὸς ἐλαύνει, ἐκ τούτου ἐξάπτει, καὶ ἀγάλλεται. ὃς γὰρ ἂν πλεῖστα δέρματα χειρόμακτρα ἔχῃ, ἀνὴρ ἄριστος οὗτος κέκριται. πολλοὶ δὲ αὐτῶν ἐκ τῶν ἀποδερμάτων καὶ χλαίνας ἐπείνυσθαι ποιεῦσι, συρράπτοντες κατάπερ βαίτας. πολλοὶ δὲ ἀνδρῶν ἐχθρῶν τὰς δεξιὰς χέρας, νεκρῶν ἐόντων, ἀποδείραντες αὐτοῖσι ὄνυξι, καλύπτρας τῶν φαρετρέων ποιεῦνται. δέρμα δὲ ἀνθρώπου, καὶ παχὺ καὶ λαμπρὸν, ἦν ἄρα σχεδὸν δερμάτων πάντων λαμπρότατον λευκότητι. πολλοὶ δὲ καὶ ὅλους ἄνδρας ἐκδείραντες, καὶ διατείναντες ἐπὶ ξύλων, ἐπ ̓ ἵππων περιφέρουσι.

(2) Οἱ μὲν ταῦτα ἔλεγον. Γέλων δὲ πολλὸς ἐνέκειτο λέγων τοιάδε “Ανδρες Ελληνες, λόγον ἔχοντες πλεονέκτην, ἐτολμήσατε ἐμὲ σύμμαχον ἐπὶ τὸν βάρβαρον παρακαλέοντες ἐλθεῖν. αὐτοὶ δὲ, ἐμεῦ πρότεροι δεηθέντος βαρβαρικοῦ στρατοῦ συνεπάψασθαι, ὅτε μοι πρὸς Καρχηδονίους νεῖκος συνῆπτο, ἐπισκήπτοντός τε τὸν Δωρ:έος τοῦ ̓Αναξανδρίδεω πρὸς Εγεσταίων φόνον ἐκπρήξασθαι, ὑποτείνοντός τε τὰ ἐμπόρια συνελευθεροῦν, ἀπ ̓ ὧν ὑμῖν μεγάλαι ὠφελίαι τε καὶ ἐπαυρέσιες γεγόνασι, οὔτε ἐμεῦ εἵνεκα ἤλθετε βοηθήσοντες, οὔτε τὸν Δωριέος φόνον ἐκπρηξόμενοι· τὸ δὲ κατ' ὑμέας, τάδε ἅπαντα ὑπὸ βαρβάροισι νέμεται. ἀλλὰ εὖ γὰρ ἡμῖν καὶ ἐπὶ τὸ ἄμεινον κατέστη· νῦν δὲ, ἐπειδὴ περιελήλυθε ὁ πόλεμος καὶ ἀπῖκται ἐς ὑμέας, οὕτω δὴ Γέλωνος μνῆστις γέγονε. Ατιμίης δὲ πρὸς ὑμέων κυρήσας, οὐκ ὁμοιώσομαι ὑμῖν, ἀλλ ̓ ἑτοιμός εἰμι βοηθέειν.”

2. Translate and explain with reference to the context :— (1) Διέδεξαν, ἐπεί σφεας ἔδει πρὸς τοὺς ἀψευδέως ἀρίστους ἀνθρώπων μάχῃ διακριθῆναι, ὅτι οὐδένες ἄρα ἐόντες οὐδαμοῖσι ἐοῦσι Ἕλλησι ἐναπεδεικνύατο.

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(2) Επεὰν δὲ διαμιστύλας κατὰ μέρεα τὸ ἱρήϊον ἑψήσῃ τὰ κρέα, ὑποπάσας ποίην ὡς ἁπαλωτάτην, μάλιστα δὲ τὸ τρίφυλλον, ἐπὶ ταύτης ἔθηκε ὧν πάντα τὰ κρέα.

(3) Ως δὲ κατὰ τοὺς φυλάσσοντας ἦν τὸν κρεμάμενον νέκυν, ἐπισπάσαντα τῶν ἀσκῶν δύο ἢ τρεῖς ποδεῶνας αὐτὸν λύειν ἀπαμμένους· ὡς δὲ ἔρρεε ὁ οἶνος, τὴν κεφαλήν μιν κόπτεσθαι μεγάλα βοῶντα, ὡς οὐκ ἔχοντα πρὸς ὁκοῖον τῶν ὄνων πρῶτον τράπηται.

(4) Κατέρρηξαν δὲ τοῦδε εἵνεκα τὴν ἐποίησαν γέφυραν, ἵνα ἐμε πεδορκέοιεν ταμόντες τοῖσι Βαρκαίοισι χρόνον μένειν αἰεὶ τὸ ὅρκιον ὅσον ἂν ἡ γῆ μένῃ κατὰ τὰ τότε εἶχε καταρρήξασι δὲ οὐκέτι ἔμενε τὸ ὅρκιον κατὰ χώρην.

(5) Ἐσβὰς δὲ ἐς ἄρουραν ἐσπαρμένην, ἅμα τε διεξήϊε τὸ λήϊον, ἐπειρωτῶν τε καὶ ἀναποδίζων τὸν κήρυκα κατὰ τὴν ἀπὸ Κορίνθου ἄπιξιν, καὶ ἐκόλουε αἰεὶ ὅκως τινὰ ἴδοι τῶν ἀσταχύων ὑπερέχοντα.

3. The sources of the History of Herodotus, as indicated by himself. Estimate their relative value.

4. The order and extent of the Persian conquests anterior to the expedition of Xerxes.

5. Greek Oracles—their influence (1) in Greece itself; (2) among foreign nations. Illustrate from Herodotus.

6. The religious systems of Egypt, Persia, Scythia, as stated by Herodotus. Correct or supplement his views from recent researches and discoveries.

7. What can you gather from Herodotus concerning the constitutions of Athens and Sparta ?

FRIDAY, JUNE 8, from 9.30 A.M. to 12.30.

Section V. Ancient History. (THUCYDIDES.) 1. Translate into English:

(1) Ἐν οὖν ταῖς πόλεσι πολλῶν θανάτου ζημία πρόκειται, καὶ οὐκ ἴσων τῷδε ἀλλ ̓ ἐλασσόνων ἁμαρτημάτων· ὅμως δὲ τῇ ἐλπίδι ἐπαιρόμενοι κινδυνεύουσι, καὶ οὐδείς πω καταγνοὺς ἑαυτοῦ μὴ περιέσεσθαι τῷ ἐπιβουλεύματι ἦλθεν ἐς τὸ δεινόν. πόλις τε ἀφισταμένη τίς πω ἥσσω τῇ δοκήσει ἔχουσα τὴν παρασκευήν ἢ οἰκείαν ἢ ἄλλων ξυμμαχίᾳ τούτῳ ἐπεχείρησε; πεφύκασί τε ἅπαντες καὶ ἰδίᾳ καὶ δημοσίᾳ ἁμαρτάνειν, καὶ οὐκ ἔστι νόμος ὅστις ἀπείρξει τούτου, ἐπεὶ διεξεληλύθασί γε διὰ πασῶν τῶν ζημιῶν οἱ ἄνθρωποι προστιθέντες, εἴ πως ἧσσον ἀδικοῦντο ὑπὸ τῶν κακούργων. καὶ εἰκὸς τὸ πάλαι τῶν μεγίστων ἀδικημάτων μαλακωτέρας κεῖσθαι

αὐτάς, παραβαινομένων δὲ τῷ χρόνῳ ἐς τὸν θάνατον αἱ πολλαὶ ἀνήκουσιν· καὶ τοῦτο ὅμως παραβαίνεται. ἢ τοίνυν δεινότερόν τι τούτου δέος εὑρετέον ἐστίν, ἢ τόδε γε οὐδὲν ἐπίσχει, ἀλλ ̓ ἡ μὲν πενία ἀνάγκῃ τὴν τόλμαν παρέχουσα, ἡ δ ̓ ἐξουσία ὕβρει τὴν πλεονεξίαν καὶ φρονήματι, αἱ δ ̓ ἄλλαι ξυντυχίαι ὀργῇ τῶν ἀνθρώπων, ὡς ἑκάστη τις κατέχεται ὑπ ̓ ἀνηκέστου τινὸς κρείττονος, ἐξάγουσιν ἐς τοὺς κινδύνους. ἥ τε ἐλπὶς καὶ ὁ ἔρως ἐπὶ παντί, ὁ μὲν ἡγούμενος, ἡ δ ̓ ἐφεπομένη, καὶ ὁ μὲν τὴν ἐπιβολὴν ἐκφροντίζων, ἡ δὲ τὴν εὐπορίαν τῆς τύχης ὑποτιθεῖσα, πλεῖστα βλάπτουσι, καὶ ὄντα ἀφανῆ κρείσσω ἐστὶ τῶν ὁρωμένων δεινῶν.

(2) Ο τε ἐκ τῆς γῆς πεζὸς ἀμφοτέρων ισοῤῥόπου τῆς ναυμαχίας καθεστηκυίας πολὺν τὸν ἀγῶνα καὶ ξύστασιν τῆς γνώμης εἶχε, φιλονεικῶν μὲν ὁ αὐτόθεν περὶ τοῦ πλείονος ἤδη καλοῦ, δεδιότες δὲ οἱ ἐπελθόντες μὴ τῶν παρόντων ἔτι χείρω πράξωσιν. πάντων γὰρ δὴ ἀνακειμένων τοῖς ̓Αθηναίοις ἐς τὰς ναῦς, ὅ τε φόβος ἦν ὑπὲρ τοῦ μέλλοντος οὐδενὶ ἐοικώς, καὶ διὰ τὸ ἀνώμαλον καὶ τὴν ἔποψιν τῆς ναυμαχίας ἐκ τῆς γῆς ἠναγκάζοντο ἔχειν. δι' ὀλίγου γὰρ οὔσης τῆς θέας καὶ οὐ πάντων ἅμα ἐς τὸ αὐτὸ σκοπούντων, εἰ μέν τινες ἴδοιέν πῃ τοὺς σφετέρους ἐπικρατοῦντας, ἀνεθάρσησάν τε ἂν καὶ πρὸς ἀνάκλησιν θεῶν, μὴ στερῆσαι σφᾶς τῆς σωτηρίας, ἐτρέποντο· οἱ δ ̓ ἐπὶ τὸ ἡσσώμενον βλέψαντες ολοφυρμῷ τε ἅμα μετὰ βοῆς ἐχρῶντο, καὶ ἀπὸ τῶν δρωμένων τῆς ὄψεως καὶ τὴν γνώμην μᾶλλον τῶν ἐν τῷ ἔργῳ ἐδουλοῦντο. ἄλλοι δὲ καὶ πρὸς ἀντίπαλόν τι τῆς ναυμαχίας ἀπιδόντες, διὰ τὸ ἀκρίτως ξυνεχὲς τῆς ἁμίλλης, καὶ τοῖς σώμασιν αὐτοῖς ἴσα τῇ δόξῃ περιδεῶς ξυναπονεύ οντες, ἐν τοῖς χαλεπώτατα διήγον· ἀεὶ γὰρ παρ ̓ ὀλίγον ἢ διέφευγον ἢ ἀπώλλυντο. ἦν τε ἐν τῷ αὐτῷ στρατεύματι τῶν ̓Αθηναίων, ἕως ἀγχώμαλα εναυμάχουν, πάντα ὁμοῦ ἀκοῦσαι, ὀλοφυρμός, βοή, νικῶντες, κρατούμενοι, ἄλλα ὅσα ἐν μεγάλῳ κινδύνῳ μέγα στρατόπεδον πολυειδῆ ἀναγκάζοιτο φθέγγεσθαι. παραπλήσια δὲ καὶ οἱ ἐπὶ τῶν νεῶν αὐτοῖς ἔπασχον.

2. Translate and explain :

(1) Ἔνι τε τοῖς αὐτοῖς οἰκείων ἅμα καὶ πολιτικῶν ἐπιμέλεια, καὶ ἑτέροις πρὸς ἔργα τετραμμένοις τὰ πολιτικὰ μὴ ἐνδεῶς γνῶναι· μόνοι γὰρ τόν τε μηδὲν τῶνδε μετέχοντα οὐκ ἀπράγμονα ἀλλ ̓ ἀχρεῖον νομίζομεν.

(2) Καὶ πλεῖστον δὴ χρόνον αὕτη ὑπ' ἐλαχίστων γενομένη ἐκ στάσεως μετάστασις ξυνέμεινεν.

(3) Καὶ αὐτοὶ εἰ μὲν ἐπὶ πλέον δυνηθῆναι τῆς ἐκείνων κρατ τῆσαι, τοῦτ ̓ ἂν ἔχειν· νῦν δέ, ἐν ᾧ μέρει εἰσίν, ἑκόντες εἶναι ὡς ἐκ σφετέρου οὐκ ἀπιέναι. ὕδωρ τε ἐν τῇ ἀνάγκῃ κινῆσαι, ἣν οὐκ αὐτοὶ ὕβρει προσθέσθαι, ἀλλ ̓ ἐκείνους προτέρους ἐπὶ τὴν σφετέραν ἐλθόντας ἀμυνόμενοι βιάζεσθαι χρῆσθαι.