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III. Translate, Acts xxi. 34-39:

Beginning, Μη δυναμένου δὲ αὐτοῦ γνῶναι τὸ ἀσφαλὲς, κ.τ.λ.
Ending, Ταρσεύς, τῆς Κιλικίας οὐκ ἀσήμου πόλεως πολίτης.

Supply ellipsis in Ελληνιστί γινώσκεις; Who were οἱ σικαρίοι, and whence their name? In what particular does the account given by Josephus of this tumult differ from the one before us? Derive, and give the different significations of παρεμβολή. Parse γνῶναι, ἠκολούθει.

IV. Translate, Acts xxvii. 15-22:

Beginning, Συναρπασθέντος δὲ τοῦ πλοίου καὶ μὴ, κ.τ.λ.

Ending, γὰρ ψυχῆς οὐδεμία ἔσται ἐξ ὑμῶν πλὴν τοῦ πλοίου. What is the proper meaning of αντοφθαλμεϊν? Explain βοηθείαις ἐχρῶντο, ὑποζωννύντες τὸ πλοῖον, and χαλάσαντες τὸ σκεῦος. What do you understand by ἡ σύρτιs and ἀσιτία in this passage? In περιῃρεῖτο, explain the meaning of the preposition, and of the tense. Parse ἐπιδόντες, ὑποδραμόντες, κερδῆσαι.

V. Translate, Gal. iii. 7-14:

Beginning, Γινώσκετε ἄρα ὅτι οἱ ἐκ πίστεως, οὗτοί, κ.τ.λ.

Ending, ἐπαγγελίαν τοῦ πνεύματος λάβωμεν διὰ τῆς πίστεως. Describe the geographical position of Galatia. Relate the circumstances connected with its name. What language was spoken by its inhabitants, and how long had it been in the condition of a Roman province ?

VI. Translate, 1 Tim. i. 1-9:

Beginning, Παῦλος ἀπόστολος Χριστοῦ Ἰησοῦ κατ', κ.τ.λ.

Ending, χρῆται, εἰδῶς τοῦτο ὅτι δικαίῳ νόμος οὐ κεῖται.

What stay did St Paul make at Ephesus on the occasion referred to? Explain the construction of προσέχειν with dative. What do you understand by γενεαλογίαι ἀπεράντοι, οἰκονομία Θεοῦ, and τῷ νομῷ νομίμως χρῆσθαι? Give the etymology of γνήσιος, (with its Latin equivalent,) ἀπέραντος, ἀστοχέω, ἀνυπόκριτος.

VII. Translate, 2 Tim. iv. 6—12:

Beginning, Εγὼ γὰρ ἤδη σπένδομαι, καὶ ὁ καιρὸς τῆς, κ.τ.λ.
Ending, Τύχικον δὲ ἀπέστειλα εἰς Εφεσον.

From what expressions in this Epistle may we conclude that St Paul was, at the time of his writing it, a prisoner, and at Rome? What is the situation of Dalmatia with respect to Thessalonica? What mention do we find of Tychicus in the Acts of the Apostles? Give some other instances οἱ ἐκείνη ἡ ἡμέρα being used to denote the day of judgment.

SECOND DIVISION.-(B.)

I. TRANSLATE, Acts xvii. 16-18:

Beginning, ̓Εν δὲ ταῖς Ἀθήναις ἐκδεχομένου αὐτοὺς τοῦ, κ.τ.λ.

Ending, ὅτι τὸν Ἰησοῦν καὶ τὴν ἀνάστασιν εὐηγγελίζετο.

Enumerate the different places visited by St Paul in his journey from Troas to Athens. What class of persons were οἱ σεβόμενοι? Give an account of the leading tenets maintained by the Epicureans and Stoics respectively. Derive σπερμολόγος. Supply ellipsis in συνέβαλλον.

II. Translate, Acts xxi. 1-5:

Beginning, Ὡς δὲ ἐγένετο ἀναχθῆναι ἡμᾶς ἀποσπασθέντας, κ.τ.λ. Ending, πάντων σὺν γυναιξὶν καὶ τέκνοις ἕως ἔξω τῆς πόλεως. Distinguish between ἀνάγεσθαι and κατάγεσθαι. Where is Patara? How is it situated with respect to Tyre? What intimation have we in the previous part of this book, of the Gospel having been preached in Phonicia? Parse διαπερῶν, ἀναφανέντες, ἐπεμείναμεν.

III. Translate, Acts xxii. 20—xxiii. 1—5:

Beginning, Τῇ δὲ ἐπαύριον βουλόμενος γνῶναι τὸ ἀσφαλές, κ.τ.λ.
Ending, γέγραπται γὰρ, Ἄρχοντα τοῦ λαοῦ σου οὐκ ἐρεῖς κακῶς.

What was the constitution of the court here called τὸ συνέδριον? Give some of the usual explanations of these words of St Paul, οὐκ ᾔδειν ὅτι ἐστὶν ἀρχιερεύς. What is the proper meaning of πολιτεύομαι? Parse γνῶναι, καταγαγών, ἔστησεν, κάθῃ.

IV. Translate, Acts xxviii. 1-6:

Beginning, Καὶ διασωθέντες τότε ἐπέγνωμεν ὅτι Μελίτη, κ.τ.λ. Ending, αὐτὸν μέλλειν πίμπρασθαι ἢ καταπίπτειν ἄφνω νεκρόν. It has been argued, that because Μελίτη was in the Adriatic sea, it could not have been the modern Malta; shew the invalidity of this argument. From what nation were the inhabitants of Μελίτη descended? Why does St Luke term them βάρβαροι? Parse ἐπέγνωμεν, παρεῖχον, τυχοῦσαν, προσεδόκων.

V. Translate, Gal. i. 13-20:

Beginning, Ηκούσατε γὰρ τὴν ἐμὴν ἀναστροφήν ποτε, κ.τ.λ.

Ending, γράφω ὑμῖν, ἰδοὺ ἐνώπιον τοῦ θεοῦ ὅτι οὐ ψεύδομαι.

What do you understand by παραδόσεις in this passage? What is known and conjectured concerning James, the brother of our Lord? Was he one of the Twelve? What account does St Paul himself give in the Acts of the Apostles of the cause of his leaving Jerusalem after this interview?

VI. Translate, 1 Tim. i. 18-ii. 1-4:

Beginning, Ταύτην τὴν παραγγελίαν παρατίθεμαί σοι, κ.τ.λ.
Ending, θέλει σωθῆναι καὶ εἰς ἐπίγνωσιν ἀληθείας ἐλθεῖν.

Give an instance of the Jews praying for heathen kings to whom they were in subjection. Explain τας προαγούσας ἐπὶ σε προφητείας, and ἐν αὐταῖς. Can you call to mind any other passage in St Paul's Epistles in which the expression παραδοῦναι τῷ Σατανᾷ occurs ? What do you

suppose to be its import? What was one characteristic of Hymenæus's heresy mentioned in II. Timothy?

VII. Translate, 2 Tim. iii. 10-17 :

Beginning, Σὺ δὲ παρηκολούθηκάς μου τῇ διδασκαλίᾳ, κ.τ.λ. Ending, θεοῦ ἄνθρωπος, πρὸς πᾶν ἔργον ἀγαθὸν ἐξηρτισμένος. What are the two different renderings of παρηκολούθηκας which have been proposed by commentators? How has the passage πᾶσα γραφὴ θεόπνευστος been sometimes translated? What account have we of the persecutions at Antioch, Iconium, and Lystra in the Acts of the Apostles? Parse διωχθήσονται, ὑπήνεγκα.

Smith's Prizes.

February 2, 1857.

BY THE REV. JAMES CHALLIS, M.A.

Plumian Professor.

1. WHAT is necessary to constitute an exact definition? In the demonstration of Prop. xv111. of Book V. of Euclid, is it legitimate to assume the converse of the fifth definition of that Book? Does a mathematical definition admit of proof on the principles of the science to which it relates?

2. Taking as the definition of parallel straight lines that they are equally inclined to the same straight line towards the same parts, prove that "being produced ever so far both ways they do not meet.'

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Prove also Euclid's Axiom XII. by means of the same definition.

3. From the equation

H = cos (m + e√√1 − Ho),

obtain by trigonometrical formulæ three terms of the development of H in a series proceeding according to powers of e.

4. Prove that if two roots of an equation f(x)=0 be nearly equal, the mean between them nearly satisfies the equation ƒ'(x) = 0, and more nearly the equation

Bƒ'(x) ƒ'' (x) − f(x)ƒ''' (x)=0,

and that if the mean be a, their difference is very nearly

24f'(
f" (a)

5. A curve is described by setting off on the focal radius-vectors of an ellipse distances inversely proportional to them, and having equal greatest and least values. Find the ratio of the mean of all its radius-vectors to the mean of all the radius-vectors of the ellipse, and the ratio of their areas.

6. Describe the double-image object-glass of a telescope, and the double-image erecting eye-piece, and state generally the principle of double-image combinations of lenses.

7. The centre of oscillation of a pendulum is retarded by a constant force equal to ng: shew that in small oscillations the decrement of the angle of ascent is nearly equal to 2n.

8. In the case supposed in the preceding question, the arc of vibration is maintained at a constant value by impulses, which impress a velocity V on the centre of oscillation when at its lowest point: shew that if a be the length of the simple pendulum, and 2a the angular excursion, the value of V for small oscillations is nearly

√ga {√ a2+2na -√a2 - 2na}.

9. A heavy particle is projected in the interior of a smooth vertical circle at its lowest point, so that it just reaches the highest point: required the velocity of projection.

What kind of path will the particle describe if the velocity of projection carry it higher than the centre of the circle, but not so high as the vertex?

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11. From observations made at an occultation, the times of the coincidences of Jupiter's centre, and of one of his satellites, with the Moon's limb at disappearance and reappearance, are known, and the relative horary apparent motions in Right Ascension and Declination of the Moon and Jupiter, and of Jupiter and his satellite, are given: from these data and the given apparent semi-diameter of the Moon, calculate the difference of the Right Ascensions and Declinations of Jupiter and the satellite at a given time.

12. Required the segment of a sphere the attraction of which on a point at its vertex is half that of the whole sphere on the same point.

Shew that, a being the radius of the sphere, the solution of the question conducts to the cubic equation

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