right acquired to be inchoate or complete? If you think it merely inchoate, what is necessary to perfect it? Iflustrate your answer by historical examples. What test is usually applied to ascertain the degree of civilization which entitles a non-Christian race to share in the privileges of international law, and to be considered sovereign over the territory which it occupies? Define eminent domain. What description of right to the national territory are sovereigns inter se assumed to possess, and why is the assumption necessary?

Define postliminy. What subjects of postliminy are recognised by modern international law?

What conditions must be satisfied in order that the goods of an enemy, taken at sea, may become the absolute property of the captor? State which of these conditions are required by the strict theory of capture in war, and which have been arbitrarily added by the custom of nations. What rules of the general national law were modified or disturbed by the permission given by the Orders in Council of 1854, "to all subjects of Her Majesty, and the subjects and citizens of any neutral or friendly state, to trade freely" during the then existing war "with all ports and places not being in a state of blockade," provided that no British vessel should enter or communicate with an enemy's port?

Do you consider that treaties are annulled by the breaking out of hostilities between the powers which were parties to them? Give authority for your answer; and, if it is in the affirmative, state what assumptions it involves as to the natural relation of states inter se.

Has a belligerent power the right to confiscate debts owing by its own subjects to subjects of the other belligerent?

What were the new rules which were attempted to be engrafted on the general international law by the armed neutrality of the northern powers in 1780? How far were these rules identical with those subscribed to by Great Britain at the Congress of Paris in 1856?

From what period is a treaty of peace binding-(1) on the contracting sovereigns (2) on their subjects?

POLITICAL ECONOMY.

Explain and illustrate the proposition that all capital is perpetually consumed and reproduced. What is meant by fixed, and what by circulating capital? On what conditions do the rise and fall of wages depend? What would be the effect of fixing a legal minimum of wages?

State concisely Ricardo's theory of rent. What is the value of the objection to it that there cannot be land in cultivation which pays no rent ? Define value and price. Can there be a general rise of values?

In what sense is it true that, in all employments, the rate of profit on capital tends to an equality?

To what extent does credit assist production?

What is the nature of the operation which is effected by means of the foreign exchanges? What is meant by saying that the exchange is "unfavourable" to a particular country?

Why does a tax on some one commodity generally raise the value and price of that commodity by more than the amount of the tax imposed? What foundation is there for the opinion that there can be a general oversupply of commodities?

What, according to the old mercantile theory, was an "unfavourable balance Analyze the doctrine that such a balance is an evil.

of trade?

MATHEMATICS AND PHYSICAL SCIENCE.

Set to Candidates for the TREASURY, and to Candidates for the ADMIRALTY, who selected Euclid as a subject for Examination. (vide pp. 6 and 20).

Воок І.

Distinguish between a "postulate" and an "axiom." Write down Euclid's three postulates.

PROP. XXI. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

PROP. XXXII.-If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.

Enunciate and prove the corollaries of the last proposition.

PROP. XLIV. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

The quadrilateral figures whose diameters bisect each other is a parallelogram.

Book II.

PROP. VI.-If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.

PROP. XII.-In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle.

In any isosceles triangle ABC, if AD be drawn from the vertex to any point in the base, show that the difference of the squares on AB and AD is equal to the rectangle of BD and CD.

BOOK III.

PROP. IX.-If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle.

PROP. XX.-The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

PROP. XXI.-In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. ABC is a triangle of which the angle A is acute; show that the square of BC is less than the squares of AB, AC, by twice the square of the line drawn from A to touch the circle BC as diameter.

If a quadrilateral is described about a circle, show that the angles subtended at the centre of the circle by two opposite sides of it are together equal to two right angles.

Воок І.

PROP. XXIV.—If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other; the base of that which has the greater angle, shall be greater than the base of the other.

PROP. XXIX.-If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite angle upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.

PROP. XLVIII.—If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.

Any line drawn through the bisection of the diagonal of a parallelogram to meet the sides is bisected in that point, and also bisects the parallelogram.

BOOK II.

PROP. IV-If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.

PROP. IX.—If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

AOB is the quadrant of a circle, whosc centre is O; from any point C in its arc draw CD perpendicular to OA or OB, meeting in E the radius which bisects the angle AOB: Show that the squares upon CD, DE, are together equal to the square upon OA.

BOOK III.

PROP, IV.—If in a circle two straight lines cut one another, which do not both pass through the centre, they do not bisect each other.

PROP. XX.-The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

PROP. XXXVI.—If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

If any line is drawn touching a circle, the part of it intercepted between the tangents at the extremities of any diameter subtends a right angle at

the centre.

Describe a circle which shall pass through a given point, have a given radius and touch a given line.

For Voluntary Examinations.

BOOK IV.

PROP. IV. To inscribe a circle in a given triangle.

PROP. XII. To describe an equilateral and equiangular pentagon about a

given circle.

Inscribe (1) a square, (2) a circle in a given quadrant of a circle.

BOOK VI.

Give Euclid's definition of proportion. PROP. I.-Triangles of the same altitude are one to the other as their bases. PROP. VI.-If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

PROP. XVIII.-Upon a given straight line to describe a rectilineal figure similar, and similarly situated, to a given rectilineal figure.

PROP. XXII.—If four straight lines be proportionals, the similar rectilineal figures similarly described upon them shall also be proportionals.

If two circles touch each other externally, the part of their common tangent between its points of contact is a mean proportional between the diameters.

BOOK XI.

PROP. IV.—If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through them, that is to the plane in which they are.

PROP. VIII.—If two straight lines be parallel, and one of them is at right angles to a plane, the other also shall be at right angles to the same plane.

PROP. XX.-If a solid angle be contained by three plane angles, any two of them are greater than the third.

Two planes being perpendicular to each other, draw a third perpendicular to both.

(3) xy + xyz - (xyz) — yz by x + (yz)

Show that the product of two quantities equals that of their greatest common measure and least common multiple.

Find the greatest common measure of—

35 x3 +47 x2 + 13x + 1 and 42 x + 41 x3

9x2

-9x-1

and explain how the

method of extracting the square root of numbers is deduced from the Algebraical rule.

Investigate a method for obtaining the cube root of an Algebraical expression, and find the cube root of

A watch gains as much as a clock loses; and 1798 hours by the clock are equivalent to 1802 hours by the watch: Find the rates of the clock and the watch.

A certain number of sovereigns, shillings, and sixpences together amount to 81. 6s. 6d., and the amount of the shillings is a guinea less than that of the sovereigns, and a guinea and a half more than that of the sixpences: Find the numbers of each coin.

Two minutes after a railway train has left a station A, where it had stopped 7 minutes, it meets an express train which set out from a station B when the former was 28 miles on the other side of A; the express travels at double the rate of the other, and performs the journey from B to A in 12 hours: Find the rate of each train, and the distance from A to B.