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7. A railway carriage weighing 7 tons, and moving at 30 miles an hour, describes a portion of a circle whose radius is 1380 ft. Calculate its centrifugal force in tons.
8. A goods train weighing 200 tons, and travelling at 20 miles an hour, runs into a passenger train of 50 tons standing on the same line. Find the rate at which the remains of the passenger train will be propelled along the line, supposing coefficient of elasticity = }.
9. On the middle point of the upper surface of a homogeneous cube whose side =l, rests a sphere also homogeneous, the specific gravity of which is to that of the cube as 3:45. Find the comparative magnitudes of the sphere and cube, so that the centre of gravity of the system
1 may be distant from that of the sphere by a length
10. A weight P, after falling freely through h feet, begins to pull up a heavier body Q, by means of a cord which connects them, and plays without friction over a pulley. Find the height through which Q will ascend.
11. Two heavy rods are connected by a smooth hinge. Their other ends are also respectively connected with smooth hinges to a vertical staff. Find the magnitude and directions of the pressures on the hinges, and of the mutual action of the rods at the joint.
12. From the centre of gravity of a cube placed on a rough inclined plane, draw the right line which represents in magnitude and direction the force which will just suffice to move the body up the plane, while increasing the body's pressure on the plane in the ratio of 1: m.
13. Find the position of equilibrium of a beam in a hemispherical bowl, when part of the beam projects beyond the rim.
14. The interval between the threads of a screw is gth of an inch, the diameter is 3 inches, and the radius of the circle described by the power 2 feet; find what power will be required to overcome a resistance of 1000 lbs. :-(1.) Neglecting friction; (2.) Allowing for the friction along the thread of the screw. The coefficient of friction being 0.15.
15. A ball of 56 lbs. weight, after traversing 4 ft. of the bore of a cannon, leaves it with a velocity of 1000 ft. per second ; what mean pressure (over and above friction and the resistance of the air) must have been exerted on it to produce this velocity?
16. Two perfectly elastic spheres meet directly with equal velocities; find the relation between their masses, in order that one of them may be reduced to rest by the collision.
17. A body describes an orbit round a centre of force attracting directly as the distance; find the time of revolution, and the equation of the orbit.
18. A uniform rod rests within a rough vertical circle; investigate its limiting positions of equilibrium.
1. A barometer tube contains 6 inches of air over the mercurial column, if the tube is plunged 10 inches deeper into the trough the air will occupy only 4 inches; find the height of the column before and after depression, supposing the atmospheric pressure to be 30 inches, and the temperature constant.
2. Suppose the temperature to change from 74° F. to 32° F., what will these heights be ?
3. If a mass of dry air be taken which weighs 10.95 grains, prove that its volume in cubic inches, multiplied by its pressure in pounds per square inch, is the exact measure of its absolute temperature.
4. Prove the following expression for the weight in grains of a given volume of gas in cubic inches, the pressure and temperature being expressed in inches of mercury, and degrees Fahrenheit,
5:37 5Vps W=
460+t 5. Prove the following expression for the weight in grammes, the volume being in litres, the pressure in millimetres, and the temperature in centigrade degrees
273+ 6. If 30 oz. of mercury held in a glass flask, the weight of which is 5 02., is able to melt 2 oz. of ice in Lavoisier's calorimeter in descending from a temperature of 174°F. Calculate the specific heat of mercury.
7. Let 500 grs. of steam, having a temperature of 214° F., be condensed in a pound of water, having a temperature of 60°F.; if the temperature of the water be raised to 129° F., calculate the latent heat of steam. The pound of water is contained in a glass flask, the weight of which is 2500 grains.
8. Deduce the expression for the volume of steam as compared with that of the water which has yielded it in terms of its pressure in pounds per square inch, and its temperature.
9. What empirical formula will give this volume in terms of the pressure alone ?
10. Prove the following formula for the height of a mountain as determined by the barometer.
h H (in fathoms) = 10000 log
1. A handle, with an arm 2 ft. long, turns an endless screw, which works a wheel with 60 teeth; and a chain, supporting a weight of 5 tons, is coiled up on the shaft of this wheel, the shaft being 6 inches in diameter. What force must be applied to the handle to balance this weight?
2. Find the centre of gravity of a trapezoid, whose parallel faces are a and b, and their mutual distance is h.
3. The velocities acquired in running down all inclined planes of the same height are equal; how is this property modified by friction ?
4. Find the quickest line of descent between two circles in the same plane.
5. Find the motion of two spheres of equal size and perfect elasticity, after oblique impact
History and English Literature.
1. What causes are assigned by Hallam for the great difference which existed between the French and English systems of feudal policy?
2. Write out as many of the clauses of Magna Charta as you can remember, and comment shortly on any expressions which appear to require elucidation.
3. Richard, Duke of Gloucester, has been charged with the murders of Edward, Prince of Wales, and of his father, King Henry VI. Consider the justice of each of these imputations.
4. What is Sir Francis Palgrave's theory as to the origin of Borough Representation ? For what reason is it rejected by Hallam ?
5. Relate the history of trial by jury in England during the AngloSaxon period.
6. Write a short historical essay on the reign of Edgar the Peaceable.
7. “With respect to those who were indebted for their seats among the lords to the king's writ, there are two material questions: whether they acquired an hereditary nobility by virtue of the writ; and, if this be determined against them, whether they had a decisive or merely a deliberative voice in the house.”
Discuss both of these questions.
The Witan of Calne,
1. Examine the question-Whether, and how far, there is a Scandinavian element in the English language?
2. What is Mr. Guest's explanation of the way in which the transformation of Anglo-Saxon into English was brought about? How is this view criticised by Mr. Craik ?
3. Give a complete account of the several ways in which the e final, characteristic of Chaucer's English, seems to have originated.
4. Render the following passages of Chaucer into modern English, and comment fully on any remarkable words or forms which occur in them :
“ With him ther was his sone, a yonge squier,
A lover, and a lusty bacheler,
his ladies grace.
He slep no more than doth the nightingale." b. “But of his craft, fro Berwike unto Ware,
Ne was ther swiche another pardonere.
He made the person, and the peple, his apes.” 5. Explain the following words, which occur in Chaucer's Prologue : alderbest, covine, goliardeis, halwes, lodemanage, mistere, sausefleme, wastel, wonning
6. Write grammatical notes on the following phrases :
“If the salt have lost his savour b. “He asked an alms."
“In one hour so great riches is come to Dought." d.
Doth not behave itself unseemly.”
“Whom say ye that I am ?” 7. Trace the following words to their origin in the Latin language : ally, charm, engine, lieutenant, pay, sir, spend, trespass.
8. Coleridge says: In order to get the full sense of a word, we should first present to our minds the visual image that forms its primary meaning." Treat in this manner the following words: attention, caprice, desultory, hypocrite, integrity, reprehend, succour.
κ. τ. λ.
Translate the following passages into English : I. Beginning, χοροί χοροί και θαλίαι μέλουσι θήβας ιερόν κατ' άστυ, Ending, νόμον παρέμενος, ανομία χάριν διδούς:
Hercules Furens, 763–779. 2. Beginning, oυ πρoκαλυπτομένα βοτρυώδεος, κ. τ.λ. Ending, άχεσι συνοδός;
Phænissæ, 1485-1517. 3. Beginning, επεί πρός ακτάς ήλθομεν θαλασσίας, κ. τ.λ. Ending, ελευθέρους πρύμνηθεν εστώτας νεώς.
Iphigenia in Tauris, 1327-1349. 4. Beginning, ευρείας φάρυγγος, ώ Κύκλωψ, κ.τ.λ. Ending, ανθρώπων θέρμ’ απ’ άνθράκων κρέα.
Cyclops, 356-374. 5. Beginning, νέος μεν ούν ων αμφί βωμίους τροφάς, κ. τ.λ. Ending, κρυπτοι γένωνται παίς τ' έχη τα πρόσφορα.
1. Write a note on the mythology of the Iphigenia in Tauris.
partiality for the philosophy of Anaxagoras.