MONDAY, November 26, 1883. 9-12.

THE ACTS OF THE APOSTLES.

(Β)

1. Give a short account, illustrating by references to this Book, of the controversy among the first Christians as to the limits of the Church.

2. What was the extent of the influence of Hellenism in Judæa at the time?

3. Give your view of the character of Gallio. Compare him with Pilate.

4. Translate:

(α) ἦσαν δὲ προσκαρτεροῦντες τῇ διδαχῇ τῶν ἀποστόλων καὶ τῇ κοινωνίᾳ, τῇ κλάσει τοῦ ἄρτου καὶ ταῖς προσευχαῖς. Ἐγίνετο δὲ πάση ψυχῇ φόβος, πολλὰ δὲ τέρατα καὶ σημεῖα διὰ τῶν ἀποστόλων ἐγίνετο. πάντες δὲ οἱ πιστεύ σαντες ἐπὶ τὸ αὐτὸ εἶχον ἅπαντα κοινά, καὶ τὰ κτήματα καὶ τὰς ὑπάρξεις ἐπίσ πρασκον καὶ διεμέριζον αὐτὰ πᾶσιν καθότι ἄν τις χρείαν είχεν.

εἶχον ἅπαντα κοινά. To what extent does this seem to have been advocated by the Apostles?

(3) Ἡρῴδης δὲ ἐπιζητήσας αὐτὸν καὶ μὴ εὑρὼν ἀνακρίνας τοὺς φύλακας ἐκέλευσεν ἀπαχθῆναι, καὶ κατελθὼν ἀπὸ τῆς Ἰουδαίας εἰς Καισαρίαν διέτριβεν. Ἐν δὲ θυμομαχῶν Τυρίοις καὶ Σιδωνίοις· ὁμοθυμαδὸν δὲ παρῆσαν πρὸς αὐτόν, καὶ πείσαντες Βλάστον τὸν ἐπὶ τοῦ κοιτῶνος τοῦ βασιλέως ᾐτοῦντο εἰρήνην διὰ τὸ τρέφεσθαι αὐτῶν τὴν χώραν ἀπὸ τῆς βασιλικῆς.

Explain ἀπαχθῆναι and κατελθών.

(c) ἐγὼ οἶδα ὅτι εἰσελεύσονται μετὰ τὴν ἄφιξίν μου λύκοι βαρεῖς εἰς ὑμᾶς μὴ φειδόμενοι τοῦ ποιμνίου, καὶ ἐξ ὑμῶν ἀναστήσονται ἄνδρες λαλοῦντες διεστραμμένα τοῦ ἀποσπᾷν τοὺς μαθητὰς ὀπίσω ἑαυτῶν· διὸ γρηγορεῖτε, μνημονεύοντες ὅτι τριετίαν νύκτα καὶ ἡμέραν οὐκ ἐπαυσάμην μετὰ δακρύων νουθετῶν ἕνα ἕκαστον.

τριετίαν. At what period of his ministry ?

(d) περιπεσόντες δὲ εἰς τόπον διθάλασσον ἐπέκειλαν τὴν ναῦν, καὶ ἡ μὲν πρώρα ερείσασα ἔμεινεν ἀσάλευτος, ἡ δὲ πρύμνα ἐλύετο ὑπὸ τῆς βίας. Τῶν δὲ στρατιωτῶν βουλὴ ἐγένετο ἵνα τοὺς δεσμώτας ἀποκτείνωσιν, μή τις ἐκκολυμβήσας διαφύγῃ.

τῶν δὲ στρατιωτῶν—ἀποκτείνωσιν.

How was this prevented?

5. Translate and explain: ὁ κλῆρος τῆς διακονίας—ἀστεῖος τῷ Θεῷχαλάσαντες ἐν σπυρίδι—ἀκοῇ ἀκούσετε, καὶ οὐ μὴ συνῆτε.

1. DEFINE force, and prove that forces can be completely represented by straight lines.

A man is letting a barrel down an unplaned board, barrel down an unplaned board, from the level of the ground to a wine-cellar, by means of a rope wound round the barrel. If he keep the barrel for a short time in one position upon the board, what forces will then be acting upon the barrel?

2. Explain the principle of the transmissibility of force, and adduce any arguments you can for believing it to be true.

3. Prove that the parallelogram of forces is true as regards the direction of the resultant of two commensurable forces.

Two forces of 5 lbs. and 6 lbs. respectively, acting at a point 0, are represented by straight lines OA, OB whose lengths are 5 inches and 6 inches. If the length of the line joining A and B be 8 inches, find the magnitude of the resultant of the forces.

4. What is meant by resolving a force? A force acts at a point A and is represented by a straight line AB, show how to resolve this force along any two straight lines AC, AD passing through the point A and lying on opposite sides of AB.

On the opposite sides of a straight line AB two equilateral triangles ABC, ABD are described, and a force P acts along AB. Resolve this force along the directions AC and AD.

5. Define the centre of parallel forces.

Six parallel forces, of 1 lb., 2 lbs., 3 lbs., 4 lbs., 5 lbs., and 6 lbs., respectively, are applied at points which all lie in the same straight line, and which are distant respectively 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, 6 inches from one end of the line. Find the centre of the forces.

6. Define the moment of a force about a given point.

Two forces act at the same point. Find the algebraic sum of their moments about a point situated in the direction of their resultant.

7. Find the centre of gravity of a uniform triangular plate.

A square board weighing 20 lbs. is made into a table by inserting four equal legs into it, one at the middle point of each side. Three equal weights are placed at three of the corners of this table as it stands upon a horizontal floor, each weight being equal to that of the board. Find the greatest weight which can be placed upon the fourth corner without overturning the table, the weight of the legs of the table not being taken into consideration.

8. How can the centre of gravity of a body be practically determined by suspending it by a string?

9. Enumerate the Mechanical Powers.

Find the ratio of the power to the weight in the case of a lever of inconsiderable weight, acted on by two parallel forces.

10. Define a pulley.

Find the condition of equilibrium for a system of pulleys, round each of which a separate string passes; the strings being all parallel, and one end of each string being attached to a beam above the system.

If in such a system there be three moveable pulleys and if their weights be 1 lb., 2 lbs., 3 lbs. respectively; find the greatest weight and the least weight which can be kept in equilibrium on this combination by a power of 7 lbs., it being understood that the moveable pulleys may be arranged in any order that is preferred.

1. WHAT are the three properties of a force which have to be known in order that the force may be completely determined? Prove that a straight line can represent a force in each of these particulars.

A man is rolling a barrel up an unplaned board from the ground to a door upon a higher level. If he keeps the barrel for a short time in one position on the board, what forces will then be acting upon the barrel ?

2. Enunciate any propositions with regard to forces which are usually assumed as axioms.

3. If the parallelogram of forces be true as regards the direction of the resultant of two forces acting at the same point, prove that it is also true as regards the magnitude of that resultant.

Two forces of 3 lbs. and 4 lbs. respectively, acting at a point 0, are represented by straight lines OA, OB whose lengths are 3 inches and 4 inches. If the length of the line joining A and B be 6 inches, find the magnitude of the resultant of

the forces.

4. What is meant by the resolved part of a force in any given direction?

A force of 10 lbs. acts along the side AB of an equilateral triangle ABC, what is the resolved part of this force along the side AC?

5. Find the resultant of any number of parallel forces whose points of application are known.

Six parallel forces, of 6 lbs., 5 lbs., 4 lbs., 3 lbs., 2 lbs., and 1 lb. respectively, are applied at points which all lie in the same straight line and which are distant respectively 1 inch, 2 inches, 3 inches, 4 inches, 5 inches, 6 inches from one end of the line. Find the magnitude and point of application of their Resultant.

6. Define the moment of a force about a given point.

If three forces be represented by the three sides of a triangle taken in order, prove that the algebraic sum of the moments of these forces is the same for every point in the plane of the triangle.

7. Find the centre of gravity of three equal weights placed at the three angular points of a triangle.

A square board ABCD is made into a table by inserting three equal legs into it, one at the corner C and the others at the middle points of the sides AB, AD. A weight is placed on the table at its corner A as it stands upon a horizontal floor. Find how great this weight may be without overturning the table; the weight of the top of the table being 18 lbs., and that of the legs not being taken into consideration.

8. How can the centre of gravity of a body be practically determined by balancing the body upon a sharp edge?

9. Define a Machine. What is meant by the Modulus of a machine?

Find the ratio of the power to the weight in the case of a lever of inconsiderable weight acted on by two forces which are not parallel.

10. Find the condition of equilibrium for a system of pulleys, round each of which a separate string passes: the strings all being parallel and all being attached to the weight.

If in such a system there be one fixed and three moveable pulleys, and if the weights of the moveable pulleys be 1 lb., 2 lbs. and 3 lbs. respectively; find the greatest weight and the least weight which can be kept in equilibrium on this combination by a power of 7 lbs., it being understood that the moveable pulleys may be arranged in any order that is preferred.

TUESDAY, November 27, 1883. 9-12.

HYDROSTATICS.

1. SHEW that the surface of a heavy inelastic fluid at rest is horizontal.

(A)

Two rectangular cisterns standing on a horizontal plane are joined at their bases by a leathern pipe resting on the plane. If one of them be 5 ft. long and 3 ft. broad, and the other 4 ft. 6 in. long and 3 ft. 4 in. broad, and water be poured into either, then, when the water is at rest, the pressures on the bases will be equal.

2. Define Specific Gravity. If 5 cubic inches of silver weigh as much as 21 cubic inches of plate glass, and the specific gravity of silver be 10-5, find that of plate glass.

A uniform rod 10 inches long floats vertically with 9 of its surface immersed in a cylindrical vessel containing water. If alcohol S. G. 8 be now poured on the water to the depth of 5 inches, shew that the upper surfaces of the rod and alcohol will coincide.

3. Find the conditions of equilibrium of a body floating in a fluid and wholly immersed in it.

A cubical block of wood, S.G. 6, whose edge is one foot, floats, with two faces horizontal, down a fresh-water river and out to sea where a fall of snow takes place causing the block to sink to the same depth as in the river. If the specific gravity of sea water be 1025 and the weight of a cubic foot of fresh water 1000 oz., shew that the weight of the snow on the block is 15 oz.

4. Describe Nicholson's hydrometer, and shew how the instrument may be employed for comparing the specific gravities of a solid and a fluid.

Shew that the apparent weight of a body when suspended in a fluid composed of equal volumes of two fluids which mix, without change of volume, is equal to the arithmetic mean between its apparent weights when suspended successively in the two fluids.

5. Shew that the pressure of the atmosphere is accurately represented by the weight of the column of mercury in the barometer.

If a body be suspended by an elastic string, explain how the length of the string will be affected by a fall in the barometer.

6.

Describe the syphon, and explain its action.

If the longer branch be inserted into a closed vessel from which the air has been partially exhausted, describe the effects on the action of the instrument.

7. Describe the mercurial thermometer. Why is it important that, when the fixed points are marked, the instrument should be in the same position relative to the horizontal plane as that in which it is to be used?

A Reaumur thermometer marks 12° indoors when a Fahrenheit thermometer marks 41° in the garden; if their positions be interchanged, find how much they will fall and rise respectively.

8. State the law which connects the pressure and temperature of a gas at a constant volume.

When the roof of a cylindrical diving bell is 27 feet below the surface of the water the temperature of the air within it is 2o C., and the level of the water in the bell is 5 ft. below the roof. If now the temperature of the air in the bell be raised by 5o C., and the bell be raised until the level of the water in it be 1 ft. lower than at first, shew that the height through which the bell has been raised is 11 ft., the height of the water barometer being 34 ft.

9. Define Latent Heat. What is meant by saying that the Latent Heat of steam at 100° C. is 537 thermal units?

How many thermal units will be required to convert 50 lbs. of water at 50° C. into steam at 100° C. ?

10. Describe the method of measuring the amount of heat which passes out of a body by means of the calorimeter of Lavoisier and Laplace.

Two chains A and B are contained in a jar which is maintained at a temperature 114° C. A consists of 9 links of iron and 11 links of copper, and B consists of 9 links of copper and 11 links of iron, and each link weighs one ounce. The chain A is taken out of the jar and placed in a vessel containing 198 oz. of water at 13° C., and causes the temperature to rise by 1°C. Had both chains been placed in the vessel, the temperature would have risen by 2° C. Shew that the specific heat of copper is 09.

11. Explain what is meant by the term conduction of heat, and describe some method of comparing the relative conductivities for heat of different substances.

The lid of a metal urn is th of an inch thick, and its area contains 100 square inches. If the inner surface of the lid be 1°C. hotter than the outer surface, find the number of therms passing through the lid in one hour, taking the specific thermal conductivity of the metal to be 0092 at the temperature in question, the units of length and time being one inch and one second respectively.

12. Explain the formation of dew, and describe the kind of night favourable for its formation.

Why do winds as they ascend the slopes of mountains become moister?