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4. How has it been directly proved that a liquid in the spheroidal state is not in contact with the surface on which it appears to rest?
5. Assuming the coefficient of the apparent expansion of mercury to be 11864 for one degree Fahrenheit, and that the ball and tube of the thermometer, when filled with mercury at 32°, hold 1020 grains of the metal, but that when raised x degrees Fahrenheit the weight of the included metal is only 1014 grains; what is the value of x?
6. A thermometer, ball and tube (the latter being unsealed), holds at 32° 4000 grains of mercury; when occupied only by air, the temperature of the instrument is raised x degrees, then suddenly dipped vertically by the open end in quicksilver, and again cooled to 32°; the weight of the mercury which has entered the tube is found to be 20 grains, the height to which it has ascended 5 inches, and the barometric altitude 30 inches. From these data calculate the value of x, assuming the coefficient of expansion of air for 180° to be 0.367, and the coefficient of the expansion of glass for same range to be
7. Describe Deville and Trosst's mercury pyrometer, and give the formula of calculation which is applicable to it.
8. Describe the apparatus and method of experimenting employed by Regnault in determining the specific heats of solids by the method of mixtures, and give the formula which he has employed in calculating his results.
9. Fabre and Silberman used a peculiar process for determining specific heats; give an account of it, and explain how from two successive experiments made with it on water and some other substance the specific heat of the latter may be computed.
10. 2 lbs. of crushed ice at 24° are dropped into 9 lbs. of water at 80°, and the temperature of the mixture (which is entirely liquid) is 44° 72; what, to two decimals, is the latent heat of the ice, its specific heat being assumed to be 0.5?
1. Explain how with a positively excited body you would communicate to a conductor without touching it a negative electric charge.
2. How with a gold-leaf electrometer would you test the species of electricity possessed by an excited body so as to get an unequivocal result?
3. Explain how the law of electric attraction is determined by the method of vibrations, and give the theory of it.
4. What are the equations which express the rate at which a charged conductor loses its electricity by contact with the atmosphere?
5. How did Coulomb prove by experiment that the amount of electricity removed from a conductor by a proof plane is exactly proportional to its charge?
6. In a cascade battery, if the number of the jars, n, be infinite, and that the ratio of the charge on the inner and outer coating is, in the case
of every jar,; what will be the sum of the charges on all the internal coatings, that within first jar being represented by E?
7. Explain Wheatstone's method of estimating the velocity of electricity through a copper wire, and mention the numerical result at which he arrived.
8. Enumerate the conditions of electrolysis.
9. Pouillet proved experimentally in two ways that, though the interpolar be composed of a succession of different metals, the intensity of the current at every point is the same. What are the methods which he employed?
10. When the interpolar is an electrolyte, the expression for the intennE nE-e sity, 4, of the current, viz., A =· should be ; what does e nR + r' represent, and how was its value determined by Wheatstone?
BUTLER AND CICERO.
1. Give a complete analysis of Bishop Butler's chapter on a Future Life.
2. State the arguments adduced by Cicero in support of the position, "Animos remanere post mortem," and show the points of contact and divergence between his views and those of Butler.
3. Give an accurate statement of Butler's Theory of Habits, and show its relation to the Theory of Moral Discipline.
4. Give a summary of the various arguments adduced by Butler in proof of the existence of a Moral Government of the world.
5. The answers given to the objections against Religion cannot equally be made use of to invalidate the proof of it?
I. What was the summum bonum of the Epicureans, and what peculiarity thence results in their ethical system? Butler gives some instances of surprising confusion and perplexity in their writings. How might all this be avoided?
2. "There is no ground to assert, that those principles in the nature of man, which most directly lead to promote the good of our fellow-creatures, are more generally, or in a greater degree violated, than those which most directly lead us to promote our own private good and happiness"?
3. How does Butler "establish" the natural supremacy of reflection or conscience?
4. Write down the "Formula Stoicorum," and give Butler's explanation of it.
5. Give his proof that no degree of injury can supersede the duty of love and good will. How is capital punishment to be justified?
6. Admitting the assertion that all other commandments are included in the precept, "Thou shalt love thy neighbour as thyself," there are certain cautions and restrictions which require to be considered in stating particularly what is virtue and right behaviour in mankind. Explain this, and give some instances.
7. How does Butler prove that an undue degree of self-love contradicts its own end?
8. Show that covetousness forms no exception to the general proposition, that "benevolence and the pursuit of public good have at least as great respect to self-love and the pursuit of private good, as any other particular passions, and their respective pursuits."
9. Butler shows that it is probable that the Christian dispensation may have been, all along, carried on by general laws, no less than the course of nature?
10. The same principle which disposed the Author of Nature to make creatures of different moral capacities may perhaps account for several of his known dispensations?
1. Show that Moral Virtue and the Virtuous are concerned Tερì ndoνὰς καὶ λύπας.
2. Deduce Aristotle's definition of Moral Virtue.
3. State the means and the opposite extremes corresponding to εurpaπελία, εἰρωνεία, ἀκολασία, ἀπειροκαλία; and explain to what virtues and vices the terms are applied by Aristotle.
4. On what grounds does Smith reject Casuistry as a useless part of Moral Philosophy?
5. What are his arguments against deriving the principle of Approbation from a peculiar sentiment?
6. In some persons, animal resentment does not immediately subside; when this is habitually the case, to what source does Stewart trace the disposition?
7. In what manner may Materialism be successfully combated, according to Stewart ?
8. Amongst the arguments for a future life, Stewart mentions three from the analogy of the material world and the animal creation; state and develop these.
History, Political Science, and English Literature.
1. There are three suppositions conceivable to explain the assassination of John Sanspeur. Which does Hallam consider to be the most probable?
2. On the death of Charles le Temeraire, what question arose as to the succession to the duchy of Burgundy?
3. Give an account of the origin of each of the three houses of Orleans. 4. What princess is known in French history as "La Grande Mademoiselle"? Give some account of her life.
5. Write a short sketch of the military history of France during the Seven Years' War.
6. What were the principal measures of reform suggested by Turgot, and what was the cause of his fall?
7. Give some account of the Cornish insurrection in the reign of Henry VII. How does Bacon account for the leniency of the king after its suppression?
8. For what reasons does Hallam assert that "Oliver Cromwell was de facto sovereign of England during the interval from June, 1657, to his death in September, 1658"?
9. What view does he take of the political character of Edward Hyde, Earl of Clarendon ?
10. Give an account of the partition treaties. What lords were impeached in consequence of them? and what was in reality the objectionable part in the negociations?
11. William III. is blamed by Hallam for refusing his assent, in 1692, to a Bill for establishing the independence of the judges. How has he been defended for this exercise of the veto?
12. It appears from a remarkable passage quoted by Hallam, that even in the reign of Edward III. the succession to the English crown was supposed to be confined to the male line?
1. Find how much the time of the rising of the Sun is advanced by refraction.
2. In what manner may the deviation from the meridian of the common vertical circle passing through Alioth and the pole star be determined?
3. Prove the formulæ for the effects of aberration of light on the right ascension and declination of a star.
4. A body falls down a rough sloping roof of given height and inclination, and afterwards falls to the ground; find the whole time of motion.
5. A body is thrown vertically upwards with a given velocity, and afterwards falls to the ground; find the whole time of ascent and descent.
6. Find the time of oscillation of a cycloidal pendulum.
7. Given the errors in the observed altitudes of two heavenly bodies, required the resulting error in their observed angular distance.
8. In determining the direction of the meridian by bisecting the angle between the directions of the Sun at rising and setting, required the error arising from his change of declination in the interval.
9. Explain the most accurate method with which you are acquainted of determining for a planet, superior or inferior, the longitude of its node and the inclination of its orbit.
10. A weight W rests on a rough horizontal plane; if u be the coefficient of friction, required the direction and magnitude of the least force that will move it.
11. A weight W falling under the action of gravity draws another weight W', by a connecting cord, along a rough horizontal plane; if μ be the coefficient of friction, required the tension on the cord.
12. In the direct collision of two perfectly elastic balls m and m', given their velocities u and u' before impact, determine their velocities v and v' after.
13. A beam is hung from a fixed point by two unequal strings attached to its extremities; compare the tension of each string with the weight of the beam.