8. Write a short account of the "Pilgrimage of Grace."

9. Explain the origin of the Court of Star-chamber. Mention some of the most violent and unconstitutional proceedings of this tribunal. When was it finally abolished?

10. Write short biographical notices of

a. John Hampden.

B. Prince Rupert.

7. Henry Rich, Earl of Holland.

11. Enumerate the different Articles contained in the Petition of Right.

12. Relate, as minutely as you can, the history of King Charles I. from Nov. 12, 1647, to Jan. 20, 1648–9.

13. In what respects was the Habeas Corpus Act of 1679 defective as a measure protecting the liberty of the subject? By what subsequent Statutes have these defects been removed?

14. Origin of the War of the Spanish Succession? What was the "Grand Alliance"? How and when was the war terminated, and what were the principal provisions of the treaty ?

15. Relate anything you know of the political life of Sir Robert Walpole.

16. Give some account of the prosecution of John Wilkes in 1763, and also of the later proceedings against him in the House of Commons. Both of these were unconstitutional-in what respects?

17. Write short accounts of the battles of Fontenoy, Minden, and Camperdown.

18. What events remarkable in English history occurred in the following years:-1533, 1536, 1553, 1601, 1618, 1628, 1642, 1645, 1668, 1678, 1683, 1692, 1697, 1716, 1718, 1740, 1752, 1759, 1806, 1819?

GEOGRAPHY.

MR. BARLOW.

1. State, as approximately as you can, the latitude and longitude of each of the following_places:-Calcutta, Capetown, Dublin, Gibraltar, London, Quebec, St. Helena.

2. Sketch the outline of the southern coast of England, and mark the positions of Cowes, Dengeness, the Eddystone Lighthouse, Hurst Castle, the Lizard Point, Pevensey Bay, Poole, Portland Bill, Spithead, and the Start Point.

3. Draw a map of Wales, divided into counties.

4. Name as many towns as you can recollect which are situated on the Irish rivers, Barrow, Blackwater, or Shannon.

5. Describe the course of the Caledonian Canal.

6. Enumerate the British possessions in Asia and the Asiatic Archipelago, and give the date and manner of the acquisition of each.

7. Give some account of the physical geography of the Cape Colony. 8. Describe, as accurately as you can, the position of each of the following localities. If you know of any remarkable historical or political events connected with any of them, you may mention them:-Adam's Peak, Belize, Berbice, Carnsore Point, Clonakilty, Dornoch Firth, Bay of Fundy, Magherafelt, Market Bosworth, Morecambe Bay, NewtownButler, Nootka Sound, Ottawa, Peshawur, Peter Botte's Mountain, Rathlin Island, Spurn Head, Mount St. Elias, Tewkesbury, Tobago.

PROFESSOR INGRAM.

9. Where are the following places, remarkable as having been the scenes of important events:-Blenheim, Corunna, Crecy, Fontenoy, Lepanto, Navarino, Poitiers, Trafalgar, Trent, Utrecht ?

10. Draw a map of North Italy; trace on it the courses of the principal rivers ; and mark the positions of Ancona, Bologna, Ferrara, Modena, Mantua, Novara, Parma, Perugia, Piacenza, Ravenna, Rimini, Sienna, Verona.

II. Describe, as accurately as you can, the situation of each of the following places:- Archangel, Cagliari, Ceuta, Elsinore, Flushing, Odessa, Scutari, Trieste, Valetta.

12. On what rivers are the following places situated :-Antwerp, Berlin, Bordeaux, Florence, Hamburg, Lisbon, Lyons, Orleans, Pesth, Petersburg, Rouen, Seville, Warsaw?

13. Describe the mountain-systems of the American Continent.

14. Where are the following places, and to what European powers do they severally belong :-Cayenne, Cuba, Goa, Guadaloupe, Java, Labuan, Madeira, Manilla, Mozambique, Pondicherry, Trinidad?

15. Of what parts of the world are the camel, the giraffe, the kangaroo, the llama, and the reindeer, natives? In what countries are cotton, indigo, coffee, tea, cinnamon, and mahogany produced?

16. State and explain the phenomena of the trade-winds.

LLOYD EXHIBITION EXAMINATION.

DR. GRAVES.

1. Let a curve be defined by an equation between 0 and 7; 0 being the angle between the tangent and a fixed right line, and the portion of that right line intercepted between the tangent and a fixed point upon it. Find in terms of 0 and r—

a. The length of the tangent.

b. An expression for the radius of the osculating circle.

c. The equation of the evolute of the given curve.

d. The general equation of the circle.

2. Two cycloids, the radii of whose generating circles differ by a very small quantity, have the same base and axis; how does the breadth vary of the narrow strip bounded by the two curves?

3. Prove, geometrically, that the difference between the tangent and the chord of a very small circular arc is ultimately double the difference between the chord and the sine.

5. Determine the maxima and minima values of the function

a2x

(a - x)2

6. Discuss the form of the curve whose equation in rectangular coordinates is

1

y + 1 = ex

7. Ascertain whether the curve

y3 = ax2 + x3

has an asymptote or not. If it has, find the equation of the asymptote. 8. Form the equation whose roots are the squares of the differences of the roots of the equation

1. Show that the determination of the motion of a material point (acted on only by gravity) on a surface of revolution round a vertical axis may be reduced to the integration of functions of one variable.

2. If a heavy bead, strung on a fixed, rough, circular wire, receive a given impulse in the direction of the tangent to the circle; determine the arc described before it is reduced to rest.

3. Determine the amount of vis viva lost in the collision of two imperfectly elastic bodies.

4. A heavy particle is constrained to move on a vertical circle, starting without velocity from the extremity of the horizontal diameter; at what point of its course is the weight of the apparatus equal to that which it would be if the particle were at rest?

5. A beam resting on two smooth planes is kept in equilibrium by a cord attached to its centre of gravity and to a fixed point; where should the point be situated in order that this may be effected with the weakest possible cord?

6. How is this modified if the planes be rough?

7. A beam which is capable of turning round a smooth fixed hinge at one extremity rests with its other extremity against a smooth vertical wall; determine the pressures on the hinge and wall.

8. One extremity of a beam rests on a smooth inclined plane, the other extremity being attached by a string to a fixed point; determine the position of equilibrium.

ASTRONOMY AND OPTICS.

MR. M. ROBERTS.

1. Find the errors caused by parallax in the hour-angle and declination of a heavenly body.

2. If the longitudes of a planet in three different points of its orbit be denoted by a, b, c, and the corresponding latitudes by a, ß, y; prove that

tan a sin (b-c) + tan ẞ sin (c-a) + tan y sin (a - b) = o.

3. Determine the proportion of the rate of increase of the Sun's right ascension to the rate of increase of its longitude, in terms of the obliquity of ecliptic and declination.

4. Prove Brinkley's formula for atmospheric refraction,

5. Determine the refractive index of a prism in terms of the refracting angle and minimum deviation.

6. A ray whose direction is parallel to the axis of x is incident on a parabola whose equation is x2 = 2ay, at the point x=y=2a, and refracted into a medium whose index of refraction is V2; find the corresponding point on the caustic formed by parallel incident rays.

7. Find the caustic by reflexion of rays incident perpendicularly to the axis of a parabola.

8. Deduce the equation of the curves of accurate refraction, and show that the circle is included among them.

M'CULLAGH PRIZE EXAMINATION.

PROFESSOR JELLETT.

r. Assuming the general equations of rotation of a body, acted on by a distant body L, to be

deduce the value of the luni-solar precession in terms of the masses and mean distances of the Sun and Moon, the principal moments of the Earth, the length of the day, and the obliquity of the ecliptic.

2. Show that the secular variation in the obliquity of the apparent ecliptic is diminished by the action of the Sun and Moon, which produces the precessional motion.

3. If the Earth were a homogeneous hollow shell, bounded by spheroids of revolution having their centres and axes coincident; and if the thickness of the shell at any point were a given function of the ellipticity of the inner surface; show that this thickness might be determined by observation of the precession.

4. Assuming, as the law of the Earth's density,

show how to determine the value of q by observation of the precession. N. B.-The Earth is supposed to be a solid spheroid.

5. A solid body, acted on by gravity only, is revolving on a fixed, indefinitely thin, horizontal axis, attached by two staples to an indefinitely rough vertical wall; at the moment when the centre of gravity attains its greatest height, which is greater than that of the axis, the staples are drawn. Determine the subsequent motion.

6. A solid of revolution turns round a fixed point in its axis, different from the centre of gravity. If the original deviation from the axis be small, and the velocity of rotation very great, show that the axis will always remain nearly vertical.

THEORY OF ROTATION.

MR. TOWNSEND.

1. Prove the following geometrical properties of the rotation of a rigid body

:

a. Any number of rotations round axes passing through a common point compound a single rotation.