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III. Translate, Acts xxi. 34–39:

Beginning, Μη δυναμένου δε αυτού γνώναι το ασφαλές, κ.τ.λ.

Ending, Ταρσεύς, της Κιλικίας ουκ ασήμου πόλεως πολίτης. Supply ellipsis in Ελληνιστί γινώσκεις ;-Who were οι σικαρίου, 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 γνώναι, ήκολούθει. IV. Translate, Acts xxvii, 15_22:

Beginning, Συναρπασθέντος δε του πλοίου και μη, κ.τ.λ.

Ending, γαρ ψυχής ουδεμία έσται εξ υμών πλην του πλοίου. What is the proper meaning of αντοφθαλμεϊν? Explain βοηθείαις έχρώντο, υποζωννύντες το πλοίον, and χαλάσαντες το σκεύος. What do you understand by ή σύρτις and ασιτία in this passage? Iη περιηρείτο, explain the meaning of the preposition, and of the tense. Parse επιδόντες, υποδραμόντες, κερδήσαι.

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

Beginning, Γινώσκετε άρα ότι οι εκ πίστεως, ούτοι, κ.τ.λ.

Ending, οπαγγελίας του πνεύματος λάβωμεν δια της πίστεως. Describe the geographical position of Galatia. Relate the circumstances connected with its name. What language was spoken by its inha. bitants, and how long had it been in the condition of a Roman province ?

VI. Translate, 1 Tim. i. 1–9:

Beginning, Παύλος απόστολος Χριστού Ιησού κατ', κ.τ.λ.

Ending, χρηται, ειδως τούτο ότι δικαίω νόμος ου κείται. 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 απεράντου, οικονομία θεού, and τω νομώ νομίμως χρήσθαι ? Give the etymology of γνήσιος, (with its Latin equivalent,) απέραντος, άστοχέω, ανυπόκριτος.

VII. Translate, 2 Tim. iv. 6–12:

Beginning, Εγω γαρ ήδη σπένδομαι, και ο καιρός της, κ.τ.λ.

Ending, Τύχικoν δε απέστειλα εις "Έφεσον. 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 of εκείνη η ημέρα being used to denote the day of judgment.

SECOND DIVISION.-(B.) 1. TRANSLATE, Acts xvii. 16–18:

Beginning, Εν δε ταϊς Αθήναις εκδεχομένου αυτούς του, κ.τ.λ.

Ending, ότι τον Ιησούν και την ανάστασιν ευηγγελίζετο. Enumerate the different places visited by St Paul in his journey from Troas to Athens. What class of persons were oι 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, “Ως δε έγένετο αναχθήναι ημάς αποσπασθέντας, κ.τ.λ.

Ending, πάντων συν γυναιξίν και τέκνοις έως έξω της πόλεως. Distinguish between ανάγεσθαι 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 Phe. nicia ? Parse διαπερών, αναφανέντες, επεμείναμεν. III. Translate, Acts xxii. 20—xxiii. 1–5:

Beginning, δε επαύριον βουλόμενος γνώναισο ασφαλές, κ.τ.λ.

Ending, γέγραπται γαρ, "Άρχοντα του λαού σου ουκ έρείς κακώς. What was the constitution of the court here called το συνέδριον? Give some of the usual explanations of these words of St Paul, ουκ ήδειν ότι έστιν αρχιερεύς. What is the proper meaning of πολιτεύομαι? Parse γνώναι, καταγαγών, έστησεν, κάθη.

IV. Translate, Acts xxviii. 1-6:

Beginning, Και διασωθέντες τότε επέγνωμεν ότι Μελίτη, κ.τ.λ.

Ending, αυτόν μέλλειν πίμπρασθαι ή καταπίπτειν άφνω νεκρόν. It has been argued, that because Melírn 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 επέγνωμεν, παρείχον, τυχούσαν, προσεδόκων. V. Translate, Gal. i. 13–20:

Beginning, Ηκούσατε γαρ την εμήν αναστροφήν ποτε, κ.τ.λ.

Ending, γράφω υμίν, ιδού ενώπιον του θεού ότι ου ψεύδομαι. What do you understand by tapadóceis 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 iuterview ?

VI. Translate, 1 Τim. 1. 18-ii. 1- 4:

Beginning, Ταύτην την παραγγελίαν παρατίθεμαι σοι, κ.τ.λ.

Ending, θέλει σωθήναι και εις επίγνωσιν αληθείας ελθείν. Give an instance of the Jews praying for heathen kings to whom they were in subjection. Explain τας προαγούσας επί σε προφητείας, and εν αυταίς. Can you call to mind any other passage in St Paul's Epistles in which the expression παραδούναι τω Σατανά occurs ?

What do you suppose to be its import? What was one characteristic of Hymenæus's heresy mentioned in II. Timothy? VII. Translate, 2 Τim. iii. 10-17 :

Beginning, Συ δε παρηκολούθηκάς μου τη διδασκαλία, κ.τ.λ.

Ending, θεου άνθρωπος, πρός παν έργον αγαθόν εξηρτισμένος. What are the two different renderings of παρηκολούθηκας which have been proposed by commentators ? How has the passage πάσα γραφή θεόπνευστος been sometimes translated ? What account have we of the persecutions at Antioch, Iconium, and Lystra in the Acts of the Apostles ? Parge διωχθήσονται, υπήνεγκα.

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. XVIII. of Book V. of Euclid, is it legitimate to assume the conyerse 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."

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

3. From the equation

H = cos (m +evi - 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 f'(x)=0, and more nearly the equation

Bf' (*)/"(*)-f(*) "" (*)=0,

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

24f'(a)t
f" (a)

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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

Nga{Va? +2na -Val - 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 ?

10. From the equations

X = r cos 0 + 2r sin (0 – v) sin v sin’w,
y=r sin 0 – 2r sin (0 – v) cos v sinaw,

%= 2r sin (0 – v) sin w cos w,

obtain
and

Ø being any function of x, dx' dy dz

dr dy and z.

do

in terms of do

and do

Il. From observations made at an occultation, the times of the coinci. dences 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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