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14. Determine the time of quickest descent when a particle descends along a rough plane to a vertical circle from a point within it.
15. Determine the motion of a cylinder which rolls down an inclined plane.
16. Explain the methods by which the position of the equinoctial points and the obliquity of the ecliptic are ascertained.
17. Explain the method of obtaining the latitude from two altitudes of the Sun and the time between; and determine the correction arising from the ship's change of place.
18. Find when the part of the equation of time, which arises from the obliquity of the ecliptic, is a maximum.
1. If two metallic bars have the same length of temperature, t, and that at a higher temperature, t', their lengths are in the ratio of 1: m; what is the ratio of their coefficients of expansion ?
2. If a glass ball and attached capillary tube hold of mercury at 32° W grains, and that when heated by t degrees Fahrenheit w grains of mercury are expelled, what will be the coefficient of the apparent expansion of mercury for 1° Fahr. ?
3. Explain the method adopted by Dulong and Petit for determining directly the cubic expansion of iron.
4. Give also their method of investigating the absolute expansion of mercury without knowing the expansion of glass.
5. If the apparent expansion of air in glass for 180° = —, what will be the absolute expansion, that of glass for the same range being?
6. If a metallic rod measures 10 in. at 60°, and 10.024 in. at 300°, what is its coefficient of expansion for one degree expressed as a vulgar fraction?
7. What is the rule given by Dr. Lloyd as most accurate in Ireland for deducing the mean temperature of the day from a single observation made with a maximum and minimum thermometer?
8. Assuming with Fabre and Silberman that the specific heat of methylic alcohol is 0.671, and its specific gravity 0.818; and further assuming that, when into a quart of such alcohol at 50° nine ounces of metallic filings at 200° are thrown, the temperature of the mixture becomes 61°; calculate the specific heat of the metal.
9. A cubic foot of air at 40° is heated until its volume is doubled, and is then suddenly compressed to its original bulk; what temperature does it now exhibit?
10. Mention the process of Mayer for determining specific heats, and give the theory of it.
11. A volume v of moist air including vapour, whose elastic force is 0.058, has the temperature of 80°, and supports a pressure of 30.85 inches of quicksilver; if such air was deprived of its vapour, and brought to the mean temperature and pressure, what would its volume become?
12. Give the formula for determining the dew-point from observations made with a wet and dry thermometer, and explain the principle on which it has been investigated.
13. If the wet thermometer placed in perfectly dry air showed the temperature of 60°; what depression of temperature must it have undergone, neglecting the last factor in the dew-point formula, and assuming the maximum force of vapour at 60° to be 0.5178 of an inch of mercury?
14. Water was found to boil at the hotel in Bray at 211°.6, and on the top of the Sugar Loaf at 215; from these data calculate by the barometric formula the difference of heights, the force of vapour at 2119.6 being 29.702, and at 215°, 31.83 inches of quicksilver.
N. B.-The temperature of the lower station was 60°, and of the upper
15. A glass ball had at 52° the capacity of v cubic inches. Filled with air at to, its weight was w grains. Filled with the vapour of a liquid at to, its weight was w'. At the time of first weighing the pressure was p; at the time of the second weighing it was p', and the coefficient of the expansion of glass for 180° is 7. From these data calculate the specific gravity of the vapour.
1. The theoretic views of Franklin as originally propounded were defective; in what particular?
2. When a glass rod is rubbed with silk, each becomes electric, the former positively, the latter negatively. How is this explained on the hypothesis of Franklin, and on that of Dufay?
3. If two similar conductors, A and B, mounted on insulating supports, -the former being charged with electricity, the latter neutral,-be made to touch, the charge of A is divided between it and B; in what ratio?
4. When an insulated conductor, A, is under the influence of induction, Pouillet says, that an insulated conductor may be selected of such dimensions, that upon placing it in contact with A, it will not deprive it of either of its elementary fluids. How does he arrive at such conclusion?
5. If ƒ be the electric charge of an insulated conductor at a particular point, and f' the charge at same point at the end of a second, what do we 2(f-f) know of the fraction f+f'
6. In comparing the thickness of the electric tunic of a charged conductor at two points of its surface, how did Coulomb apply the correction rendered necessary by the fact that the experiments were not cotemporaneous ?
7. Write the expression for the accumulation produced by any variety of condensing apparatus, and give the proof of it.
8. How was it proved by Gay Lussac, and how by Becquerel, that the positive charge of electricity in the atmosphere augments as we ascend?
9. With a given medium, rotated with a given velocity, a charge of greater intensity can be communicated to a jar than to a battery; why is this the case?
10. What are the electric conditions of an insulated dry pile at its extremities, and at its middle point, and how are they accounted for?
11. If in a voltaic battery we double the number of couples, and double the surface of each, what will the effect of this be on the intensity of the current ?
12. Explain how, with the aid of a tangent galvanometer, the resistance R in a single cell may be computed.
13. In a pile consisting of n similar couples how do you express the amount of weakening experienced by the current as the consequence of the interposition of an interpolar?
14. If you have a given surface of zinc at your disposal, how do you cut it into plates for a battery of such size that the intensity of the current shall be a maximum ?
15. If in a battery the number of couples be doubled, and the surface of each doubled, what will the effect of this be upon the intensity of the current?
History and English Literature.
1. Mention the principal causes of the high prerogative of the Tudors. What, according to Hallam, was the principal grievance under that family? It has been said that the Tudors were as absolute as the Cæsars; Lord Macaulay objects to the comparison?
2. Discuss the political bearings of the divorce of Catherine of Arragon. 3. A remarkable case in the reign of James I. affords a signal instance of the danger of that indefinable, uncontrollable privilege of parliament which has sometimes been asserted?
4. How does Hallam account for the implacable resentment of the citizens of London against Charles I. ?
5. Give some account of the administration of Lord Wentworth in Ireland.
6. How does Hallam defend the Scots for delivering the king to the English parliament ?
7. He gives several striking instances of the arbitrary government of Cromwell?
8. The reign of Henry VI. affords several important precedents in the constitutional law with respect to regencies?
9. By whom was Henry murdered, according to Shakspeare? Discuss the probability of the charge.
10. Give some account of Robert Stillington, Bishop of Bath and Wells.
11. Mr. Froude considers that the labouring classes in England during the reign of Henry VIII. were much better off with respect to material comfort than they are now, or ever have been since. What are his grounds for this opinion?
12. What conclusion with respect to the state of religion in England in the sixteenth century is deduced by Lord Macaulay from a review of the Drama of the Elizabethan age?
I. "The existing European languages may be nearly all comprehended under five divisions."
a. Enumerate these divisions, and state how many of them belong to the Indo-European family.
b. What is the principal exception indicated by the word "nearly" in the sentence quoted above?
2. “Original English," "Broken English," "Mixed English.” Explain these terms, and show that the succession of the corresponding stages represents the entire History of our Language.
ENGLISH LANGUAGE AND LITERATURE.
3. Among the periods and persons presented to us in the plays of Shakspeare, Craik mentions the following: "The Athenians of the days of Alcibiades, the proud patricians and turbulent commonalty of republican Rome, Roman Britain and Britain before the Romans, Venice, Verona, Padua, Illyria, Navarre, and the Forest of Arden." Name the plays to which the several members of this enumeration refer.
4. Explain fully the following quotations from Shakspeare (Knight's Text), and comment on any remarkable words which occur in them :
a. "Qualities are so weigh'd that curiosity in neither can make choice of either's moiety."
"Time shall unfold what plaited cunning hides:
Who covers faults at last with shame derides."
"Our means secure us, and our mere defects
"For Banquo's issue have I fil'd my mind."
"Sleep, that knits up the ravell'd sleave of care."
"The dram of ill
"Wear thou thy wrongs:
The title is affeer'd."
"Man but a rush against Othello's breast,
"Old fools are babes again; and must be us'd
With windlaces, and with assays of bias,
5. Write notes on the following words :-Groundling, haggard, intrinse, jesses, leets, list (the noun), mobled, pelting, peak (the verb), unhousel'd, unbonneted.
6. What use does Bacon in his Essays make of the following topics?— a. The importance attributed by Demosthenes to "Action."
b. "The part of Epimetheus might well become Prometheus, in the case of Discontentments."
c. The fable of the birth of Pallas.
d. "Dry light is ever the best."
Translate the following passages into English
I. Beginning. τοῦτ' ἐστὶν ἤδη κἀποθαυμάσαι πρέπον, κ. τ. λ.
Ed. Col., 1586-1603.
2. Beginning, Εὐδαίμονες οἷσι κακῶν ἄγευστος αἰών, κ. τ. λ. Ending, πράσσει δ ̓ ὀλιγοστὸν χρόνον ἐκτὸς ἄτας.
3. Beginning, ὦ χεῖρες, οἷα πάσχετ ̓ ἐν χρείᾳ φίλης, κ. τ. λ. Ending, ἄφιλον ἔρημον ἄπολιν ἐν ζῶσιν νεκρόν.
4. Beginning, κεῖνος δ' ὑπ ̓ αὐτὴν ἐσχάτην στήλην ἔχων, κ. τ. λ. Ending, πῶλοι διεσπάρησαν ἐς μέσον δρόμον.