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1. How is an observatory clock set to the true sidereal time. If there were reason to believe that the right ascension of no star had yet been determined with sufficient accuracy, how should we proceed?
2. If we have the observatory clock set to the true sidereal time, how can we set another clock to ordinary mean solar time?
3. How is the time of the Moon's rising on a given day found? How does the problem differ from that of finding the time of rising of a star ?
4. Given the mean anomaly of a planet, find the eccentric anomaly.
5. Find the centre of gravity of a shell whose bounding surfaces are nonconcentric spheres whose radii are a, b, the distance of the centres being D.
6. Find the principal parameter of the parabola described by a body projected along a smooth plane of given inclination, with a given velocity, and at a given elevation.
7. The Sun was observed to pass the meridian at 11h59m 18.76 by chronometer, the equation of time being + 13m 22.58. Required the error of the chronometer both for apparent and for mean time.
8. Prove the following formulæ for the latitude (~) and longitude (1) of a star S:
sin (6 – w) sin 8 sind =
cos (0 - w) tan a
obliquity of ecliptic. 9. What are the principal quantities given in the Nautical Almanack?
10. A body falls from a given point towards a centre of force, the attraction at any distance r being To find the whole time of descent.
11. The centrifugal force of the Moon in her orbit is 0.00889 feet per second, while the centrifugal force of bodies at the Earth's equator is 0.11126 feet per second. Hence, and from the periodic time of the Moon, viz., 27 days, 7 hours, 45 minutes, calculate her mean distance from the Earth, in terms of the Earth's mean radius.
12. Determine the coefficient of friction between a rough body and an inclined plane, in terms of the angle of elevation, from observing that the least force that will suffice to move the body up the inclined plane
is n times the least force that will sustain it on the plane.
13. Explain the method of finding the latitude at sea from two altitudes of the Sun, and the time between. Determine the correction arising from the ship’s change of place.
14. Prove that the equation of time caused by the obliquity of the ecliptic is a maximum, when the sum of the Sun's longitude and right ascension is 90°.
15. Find how much the time of a star's rising is altered by refraction.
16. A beam rests on a horizontal plane, and is prevented from slipping by a peg; find the least force which should be applied at a given point in order to upset it.
17. A bent lever, whose sides are inclined at a given angle, makes oscillations in its own plane about the angular point; find the length of the isochronous simple pendulum.
18. Find the least coefficient of friction which will enable a sphere to roll down a rough inclined plane without sliding.
1. If the specific gravity of dry hydrogen at 60°, and under a pressure of 30, is 0.0691 ; what will it be at the same temperature and pressure when saturated with humidity ? [N. B.—The force of vapour at 60° is assumed to be 0.5178.]
2. In Baume's hydrometer for liquids heavier than water, if N represents the number of the division cut on the stem of the instrument by a given liquid, how do you show that the specific gravity of the liquid will be
N 3. To what specific gravity do 17° on Twoddle's hydrometer correspond ?
4. Give the law of cooling as laid down by Newton, and deduce from it an expression for the velocity of cooling. State, also, the electrical question in the investigation of which this expression is employed.
5. What are the experiments, and what the method of calculation, employed by Lavoisier and Laplace in determining by the method of cooling the specific heat of the flask employed in their experiments ?
6. Write the expression which gives the relation between c and c', the specific heats of a gas under a constant pressure and a constant volume, and mention its arithmetical value in the cases of air, oxygen, and bydrogen.
7. If 126 grains of the vapour of absolute alcohol, at its boiling point of 173°, be conducted into 1180 grains of water at 60°, what will be the temperature of the mixture, assuming that the specific heat of alcohol is 0.64, its latent heat 374°, and that no caloric is developed by chemical action ?
8. If a cubic inch of water, weighing 252.46 grains at 60°, be converted into vapour of maximum density at same temperature, what will be its volume, the force of the vapour being 0.5178 of an inch of mercury ?
9. A mass of air at 60° is heated so as to double its volume, and then reduced by sudden compression to its original bulk. What will its temperature become!
10. If 86 cubic inches of dry air at 60°, and under a pressure of 30, be heated to 120°, and, the pressure having fallen to 28, be then charged with vapour whose force is 2.9 inches of quicksilver, what will be its volume ?
11. Give the expression which includes the theory of the wet-bulb hygrometer, and mention the hypothesis on which it has been investigated.
12. If in perfectly dry air, whose pressure is 30.35, f = 0.35, what is the depression of temperature shown by the wet thermometer ?
13. A heated surface, kept at a constant temperature, applied to one extremity of a wooden tube, produces the same elevation of temperature at the other end, no matter what angle the surface makes with the axis of the tube. Deduce from this the law of the intensity of radiant heat emanating from the surface at different angles.
14. If two distant sources of heat whose temperatures are t and ť, when made to act separately on the ball of a thermometer, produce stationary temperatures exceeding that of the air by 0 and e', then 0 : 0 :: t:ť. Why is this the case ?
MR. GALBRAITH. 1. Explain the mutual reaction of Richmann's plates, and deduce the expressions for the accumulations of electricity on the two surfaces.
2. In order to try the accumulating force of a condenser, I touch the collecting-plate with a proof-plane, and, on bringing it to Coulomb's balance, find a deflection of 60°.5; the other plate, treated in the same way, produces 6oo. What number expresses the force ?
3. How is the electric intensity expressed in terms of the angle of repulsion between the balls, if we take into account the oblique action of the repulsion on the force of torsion?
4. By what methods did Coulomb investigate the laws of electrical attractions and repulsions? Give the details of one experiment.
5. A small pith ball, in the neutral condition, is attracted towards an electrified body acting at a distance; explain the reason of this action, and prove that the force is proportional to the diameter of the ball, and inversely proportional to the cube of its distance.
6. What is the normal electric condition of the atmosphere? To what cause is this probably due ? In what way did Biot ascertain this condition experimentally?
7. Demonstrate, on mathematical principles, the law of distribution of free electricity in ellipsoidal conductors.
8. If a single current is derived, determine the ratio of the intensity of the principal current to that of the primitive.
9. If a battery be formed of b rows of a cells in each row, prove that the intensity in the interpolar will be given by the equation
aR + br. 10. How should thirty-six cells be arranged in order to obtain the greatest possible intensity in the interpolar, supposing the interpolar resistance to be equal to the resistance of one cell?
History and English Piterature.
1. The following question was argued before all the judges in the Exchequer Chamber in the reign of Charles I. :-“Whether the king had a right, on his own allegation of public danger, to require an inland county to furnish ships, or a prescribed sum of money by way of commutation, for the defence of the kingdom?” State the arguments on both sides.
2. Trace the progress of “privilege of parliament under Henry VIII. and Elizabeth.
3. In the interval between the parliaments of 1614 and 1621, several events greatly aggravated the king's unpopularity. Give some account of them.
4. Mr. Hallam asserts that there are few circumstances in our history which have caused more perplexity to inquirers than the conduct of Cromwell and his friends towards the king in the year 1647-in what respect? Give some account of the adventures of Charles during the latter months of that year.
5. State the different theories of Selden and Madox as to the characteristics and attributes of baronial tenure.
6. What account does Mr. Knight give of the state of Scotland under James V. ?
7. Who were the heirs female in remainder to the Crown, named in the will of Henry VIII. and the devise of Edward VI.?-and what descendants of the Queen of Scotland were passed over by both Henry and Edward ?
Ś. What is the historical evidence for the common statement that 72,000 criminals were executed for theft and robbery in the reign of Henry VIII.
9. Write a short account of the Lincolnshire insurrection in the same reign.
10. Relate the history of the Yorkists from the meeting of the parliament at Coventry till the proclamation of Edward IV.
11. Consider the effect of the death of Isabella of Castile on the political influence of Henry VII. on the Continent.
12. Give some account of the life and adventures of Henry, Earl of Richmond, before his accession to the English Crown.
1. Give an account of the dramatic writers commonly grouped together as the immediate predecessors of Shakspeare.
2. State all the facts you know, which can be used for the purpose of determining the chronological order of Shakspeare's plays. 3. Explain fully the following sentences from Shakspeare :
“ Woul't drink up Esil” [or, eisel] ? b. “ This quarry cries on havoc."
“ When devils will the blackest sins put on,
They do suggest at first with heavenly shows." d. “ Even then this forked plague is fatal to us,
When we do quicken."
And he grows angry.”
Let me not name it to you, ye chaste stars !
It is the cause,- yet I'll not shed her blood.”
« This is some fellow
Quite from his nature. i.
Nothing almost sees miracles
“ For this business,
Not bolds the king.” 4. Explain the following expressions :-“The sledded Polacks ;" < this eternal blazon ;" “ plighted cunning;” “wounds untented;" mous state;" “this unbolted villain ;'“ ye taking airs;" “the toged consuls ;' sightless couriers ; " " thrice-driv'n bed of down.”
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