SATURDAY, October 4, 1884. 9-11.

TRIGONOMETRY.

(B)

1. WHAT is meant by the circular measure of an angle? If one-third of a right angle were taken as the unit, what would be the measure of an angle of 75°, and of the unit of circular measure?

2. Define the cosine and cotangent of an angle, and find an expression for each in terms of the other.

5.

=tan 24.

Three angles are in Arithmetical Progression, the common difference being 120°. Prove that the sum of their sines is zero.

6. Prove that 2 cos 4+1 + sin 24 ± √1 - sin 24, and determine the proper signs for the roots when A=2245o.

Hence find the sines of the angles of a triangle whose sides are 9, 10 and

SATURDAY, October 4, 1884. 1-31.

MECHANICS.

1. DEFINE Force. Give examples of different kinds of forces.

(A)

A heavy chain has weights of 10 lbs. and 16 lbs. attached to its ends, and is hung in equilibrium over a smooth pulley; if the greatest tension of the chain is 20 lbs., find the weight of the chain.

2. Assuming the truth of the parallelogram of forces for the direction of the resultant of two commensurable forces extend it to the case of incommensurable forces. If two forces be incommensurable can their resultant be commensurable with either of them? or with neither? Give examples.

3. If three forces acting at a point are in equilibrium they can be represented by the sides of a triangle taken in order.

Give a geometrical construction for resolving a force into two others, one of which is given in magnitude and the other in direction.

4. Find the magnitude and line of action of the resultant of two parallel forces acting in the same direction.

5. Find a formula for the position of the centre of gravity of any number of heavy particles situated in one plane.

A hole of given size is punched out of a uniform circular plate; shew that the centre of gravity of the remainder must lie within a certain circle.

6. If a heavy body be suspended from a fixed point the centre of gravity will be vertically below the point of suspension.

7. State the conditions of equilibrium on a lever, and prove them in the case of a bent lever with the forces not parallel.

If the forces be 13 lbs. and 14 lbs. and their directions make an angle whose cosine is, find the pressure on the fulcrum.

13

8. Explain the construction and graduation of the common steelyard.

A uniform rod being divided into 20 equal parts by graduations, the fulcrum is placed at the first graduation. The greatest and least weights which the instrument can weigh are 2 lbs. and 20 lbs.; find its weight.

9. Find the relation between the power and weight on a smooth inclined plane when the power acts parallel to the plane.

If the plane be turned over so that its height becomes its base the power required to support a given weight will be greater if the original height was less than the base.

SATURDAY, October 4, 1884. 1-31.

MECHANICS.

1. STATE and illustrate the principle of Transmission of Force.

(B)

A heavy chain has weights of 10 lbs. and 16 lbs. attached to its ends and is hung in equilibrium over a smooth pulley: if the lengths of the chain on either side be as 3 2, find the weight of the chain.

2. Assuming the truth of the parallelogram of forces for the direction of the resultant of two forces, prove it for its magnitude.

Find the resultant of two forces of 13 lbs. and 14 lbs. acting at an obtuse angle whose sine is 13.

3. If three forces acting at a point can be represented by the sides of a triangle taken in order they shall be in equilibrium.

Give a geometrical construction for resolving a force into two others inclined at a given angle, one of which is to be of given magnitude.

4. Find the magnitude and line of action of the resultant of two parallel forces acting in opposite directions.

5. Find the centre of gravity of a uniform heavy triangular lamina.

If a given weight be placed anywhere on the lamina, the centre of gravity of the whole will lie within a certain triangle.

6. If a body rest on a horizontal plane the vertical through the centre of gravity must fall within the base.

7. State the conditions of equilibrium on a lever, and prove them in the case of a straight lever with the forces parallel to each other.

If the pressure on the fulcrum be equal to ten times the difference of the forces, find the ratio of the arms.

8. Explain the construction and graduation of the Danish steelyard.

The distance between the zero of graduation and the end of the instrument is divided into 20 equal parts and the greatest weight which can be weighed is 3 lbs. 9 oz.; find the weight of the instrument.

9. Find the conditions of equilibrium on a smooth inclined plane when the power acts horizontally.

If the plane be turned over so that its height becomes its base the power required to support a given weight will be greater if the original base exceeded the height.

N.B. Candidates are required to satisfy the Examiners in the questions as well as in translation. 1. TRANSLATE the following passages and answer the questions upon them: (α) (11) Καὶ ἐξῆλθον οἱ Φαρισαῖοι καὶ ἤρξαντο συνζητεῖν αὐτῷ, ζητοῦντες παρ ̓ αὐτοῦ σημεῖον ἀπὸ τοῦ οὐρανοῦ, πειράζοντες αὐτόν. (12) καὶ ἀναστενάξας τῷ πνεύματι αὐτοῦ λέγει Τί ἡ γενεὰ αὕτη ζητεῖ σημεῖον; ἀμὴν λέγω, εἰ δοθήσεται τῇ γενεᾷ ταύτῃ σημεῖον. καὶ ἀφεὶς αὐτοὺς πάλιν ἐμβὰς ἀπῆλθεν εἰς τὸ πέραν. καὶ ἐπελάθοντο λαβεῖν ἄρτους, καὶ εἰ μὴ ἕνα ἄρτον οὐκ εἶχον μεθ ̓ ἑαυτῶν ἐν τῷ πλοίῳ. καὶ διεστέλλετο αὐτοῖς λέγων Ὁρᾶτε, βλέπετε ἀπὸ τῆς ζύμης τῶν Φαρισαίων καὶ τῆς ζύμης Ἡρῴδου.

4

Explain the demand made in v. 11. With what addition does St Matthew record the answer? Parse πέραν. Explain the use of εἰ in εἰ δοθήσεται.

(6) Οὐδὲ τὴν γραφὴν ταύτην ἀνέγνωτε Λίθον ὃν ἀπεδοκίμασαν οἱ οἰκοδομοῦντες, οὗτος ἐγενήθη εἰς κεφαλὴν γωνίας· παρὰ Κυρίου ἐγένετο αὕτη, καὶ ἔστιν θαυμαστὴ ἐν ὀφθαλμοῖς ἡμῶν; καὶ ἐζήτουν αὐτὸν κρατῆσαι, καὶ ἐφοβήθησαν τὸν ὄχλον.

From what Book is this passage quoted? What is its original sense, and how is it applied here? Parse λίθον, αἴτη.

(c) Καὶ παραπορευόμενοι πρωὶ εἶδον τὴν συκῆν ἐξηραμμένην ἐκ ριζών. καὶ ἀναμνησθεὶς ὁ Πέτρος λέγει αὐτῷ Ῥαββεί, ἴδε ἡ συκῆ ἣν κατηράσω ἐξήρανται. καὶ ἀποκριθεὶς ὁ Ἰησοῦς λέγει αὐτοῖς Ἔχετε πίστιν θεοῦ· ἀμὴν λέγω ὑμῖν ὅτι ὃς ἂν εἴπῃ τῷ ὄρει τούτῳ ̓́Αρθητι καὶ βλήθητι εἰς τὴν θάλασσαν, καὶ μὴ διακριθῇ ἐν τῇ καρδίᾳ αὐτοῦ ἀλλὰ πιστεύῃ ὅτι ὃ λαλεῖ γίνεται, ἔσται αὐτῷ.

αν

Parse ἐξηραμμένην, κατηράσω, ἄρθητι, διακριθῇ.

What parable is recorded elsewhere similar to the incident here referred to?

2. Translate and explain:

(α) καθεύδετε τὸ λοιπὸν καὶ ἀναπαύεσθε· ἀπέχει.

(b)

βουλόμενος τῷ ὄχλῳ τὸ ἱκανὸν ποιῆσαι.

(c) ὁ καταλύων τὸν ναὸν καὶ οἰκοδομῶν ἐν τρισὶν ἡμέραις, σῶσον σεαυτόν. (α) θεωρεῖ θόρυβον καὶ κλαίοντας καὶ ἀλαλάζοντας πολλά.

(ε) διὰ τοῦτο ἐνεργοῦσιν αἱ δυνάμεις ἐν αὐτῷ.

3. Give the meaning, and, where known, the situation and modern name of Καφαρναούμ, Σιδών, Ιεριχώ ; and explain κατάλυμα, ἐπιγραφή, τῇ ὥρᾳ τῇ ἐννάτῃ.

4. What evidence does this Gospel furnish as to the language usually spoken at the time and place to which the history belongs?

MONDAY, October 6, 1954. 15.

ST MARK'S GOSPEL

(B)

N.B. Candidates are required to satisfy the Examiners in the questions as well as in translation 1. TRANSLATE the following passages and answer the questions upon them: (a) Καὶ ἐξῆλθεν ὁ Ἰησοῦς καὶ οἱ μαθηταὶ αὐτοῦ εἰς τὰς κώμας Καισαρίας της Φιλίππου· καὶ ἐν τῇ ὁδῷ ἐπηρώτα τοὺς μαθητὲς αὐτοῦ λέγων αὐτοῖς Τίνα με λέγουσιν οἱ ἄνθρωποι εἶναι; (25) οἱ δὲ εἶπαν αὐτῷ λέγοντες ὅτι Ιωάνην τὸν βαπτιστήν, καὶ ἄλλοι Ἠλίαν, ἄλλοι δὲ ὅτι εἰς τῶν προφητῶν. (29) καὶ αὐτὸς ἐπηρώτα αὐτοὺς Ὑμεῖς δὲ τίνα με λέγετε εἶναι; ἀποκριθεὶς ὁ Πέτρος λέγει αὐτῷ Σὺ εἶ ὁ χριστός.

οι

Explain the opinions mentioned in r. 28. With what addition des St Matthew record this incident? Parse Ἠλίαν. Explain the use of ὅτι in ὅτι εἶς....

(b) Καὶ τότε ὄψονται τὸν υἱὸν τοῦ ἀνθρώπου ἐρχόμενον ἐν νεφέλαις μετὰ δυνάμεως πολλῆς καὶ δόξης· καὶ τότε ἀποστελεῖ τοὺς ἀγγέλους καὶ ἐπισυνάξει τοὺς ἐκλεκτοὺς αὐτοῦ ἐκ τῶν τεσσάρων ἀνέμων ἀπ ̓ ἄκρου γῆς ἕως ἄκρου οὐρανοῦ.

What prophetic passage is here referred to? Give its context. Parse ἄκρου, ὄψονται. (c) Καὶ προσκαλεσάμενος τὸν κεντυρίωνα ἐπηρώτησεν αὐτὸν εἰ ἤδη ἀπέθανεν· καὶ γνοὺς ἀπὸ τοῦ κεντυρίωνος ἐδωρήσατο τὸ πτῶμα τῷ Ἰωσήφ. καὶ ἀγοράσας σινδόνα καθελὼν αὐτὸν ἐνείλησεν τῇ σινδόνι καὶ ἔθηκεν αὐτὸν ἐν μνήματι ὁ ἦν λελατομημένον ἐκ πέτρας, καὶ προσεκίλισεν λίθον ἐπὶ τὴν θύραν τοῦ μνημείου. Ἡ δὲ Μαρία ἡ Μαγδαληνὴ καὶ Μαρία ἡ Ἰωσῆτος ἐθεώρουν που τέθειται.

Parse ἐνείλησε, λελατομημένον, προσεκύλισε, τέθειται.

How is the μvnμeîov further described elsewhere?

3. Give the meaning, and, where known, the situation and modern name of Βηθσαϊδα, Καισαρία τοῦ Φιλίππου, Βηθανία ; and explain ανώγεων, εἰκών, τῇ μια τῶν σαββάτων.

4. What features in this Gospel point to the impression produced upon an eye-witness ?