1. Let a base line AB be taken = 1000 yards; if the angles CAD and CBD (each of which is the difference of two observed angles) are, respectively, 26° 38′ 50′′, and 39° 6' 30", and if BAD = 49° 40′ 44′′, and ABC =55° 18′14′′, it is required to find the distance CD.

2. If b=7, and A = 41° 45′ 6′′, and C= 87° 16′ 16′′, find the values of a and c.

3. Find the values of the following integrals:

4. Integrate the following differentials: x sin x dx, x cos x dx.

5. Integrate ex xdx, ex x2dx.

6. Integrate sin 2x dx, sin 3x dx, sin 1x dx.

7. Apply the methods of descriptive geometry to draw through a given point a plane parallel to a given plane.

8. Draw through a point a right line perpendicular to a given right line.

9. Through a point draw a plane parallel to a given line.

10. The sides a, b, c of a triangle are given by the equations

α = 38.5

b = 92.4

C = 100, I

it is required to calculate the sum of all the elements of c, multiplied each by the square of its distance from the angle opposite to c.

being given, develop B and log A in a series progressing according to the series and cosines of the multiples of x.

3. Develop cos u and sin u in a series progressing according to the sines and cosines of the multiples of m, when

5. {I

n

a cos x} 2 is to be developed in a series progressing according to the cosines of the multiples of x; show how the ratios of two co

efficients

=

Pi can successively be obtained, and the coefficients,

is known, be found by the formula :

when ao

6. If

cos n sin dy

2

2(cos y cos)

{1-2a cos y + a2}

dt in a series according to the powers of and

I

Ο

find a limit for the remainder of the series if broken off at a certain point. 8. Find the value of the same integral between the limits - ∞ and +∞,

1. Show that there is but one solution in the system of equations,

2. If a developable surface be circumscribed to a given surface, prove that, at any point of the curve of contact, the tangent to this curve and the rectilinear generatrix of the developable surface are conjugate diameters of the indicatrix.

3. Show that the same is true of the tangent to a curve at each of whose points the normal makes a given angle with the axis of z, and the tangent to the curve of greatest inclination.

4. If a developable surface be circumscribed so as to touch along a line of curvature, and then unfolded into a plane, the arête de rebroussement of the developable surface will become the evolute of the line of contact.

5. Assuming for the variation of a definite integral the expression, SS V dx := a + Sẞdy

6. If it be required to make ↓ V d x a maximum or minimum, where

x, y, z, being connected by an equation which is of an order higher than V in both y and z; show that the solution may contain arbitrary con

a minimum, μ being a given function of the co-ordinates, and ds the element of the surface.

(a) If u be a homogeneous function, give the geometrical interpretation of the result.

POLITICAL ECONOMY PRIZE EXAMINATION.

PROFESSOR SLATTERY.

Morning.

1. Professor Rogers objects to the common definition of Political Economy, as the science of the laws which govern the production, distribution, and consumption of wealth, that most of the terms employed are ambiguous. Give your opinion as to the validity of this objection, and define the terms in which ambiguity may be supposed to lurk.

2. To the science of Political Economy, at least as hitherto treated, Auguste Comte objects, that, "the phenomena of society being more complicated than any other, it is irrational to study the industrial apart from the intellectual and moral." Discuss this objection, and state what you consider to be the relation of Political Economy to Social Philosophy.

3. In the following passages Adam Smith lays down doctrines directly at variance with two fundamental principles established in different parts of the "Inquiry into the Nature and Causes of the Wealth of Nations":

"The sovereign, for example, with all the officers both of justice and war, who serve under him, are unproductive labourers. . In the same class must be ranked some of the gravest and most important, and some of the most frivolous professions: churchmen, lawyers, physicians, men of letters of all kinds; players, buffoons, musicians, opera singers, opera dancers, &c."

"When the produce of any particular branch of industry exceeds what the demand of the country requires, the surplus must be sent abroad, and exchanged for something for which there is a demand at home. Without such exportation a part of the productive labour of the country must cease, and the value of its annual produce diminish."

State the principles referred to, and point out the opposition between them and the doctrines set forth in these passages.

4. Compare the theories of Rent propounded respectively by the "Economistes," Adam Smith and Ricardo; and state how far you consider the theory of the latter writer applicable to the case of countries where the land is cultivated by peasant proprietors, metayers, or cottiers.

5. Ricardo says:- "The same cause which raises rent, namely, the increasing difficulty of providing an additional quantity of food with the same proportional quantity of labour, will also raise wages." Can you reconcile this doctrine with the law of wages as stated by Senior and Mill, respectively?

6. Compare the explanation of the tendency of profits to fall as society advances given by Adam Smith, Wakefield, and Mill.

7. What are the general principles which govern Value in Exchange; and how far are they modified by the case of labourers cultivating for subsistence, and by the case of slave labour?

Evening.

1. Against our present banking system three principal objections are brought by a recent writer in the " Fortnight!y Review."

(a). The banking currency (notes) is fixed in amount, instead of being allowed to expand with the growing requirements of the community. (b). It is subject to a monopoly, without any safeguard against the abuse of that monopoly.

(c). A portion of the present bank issues is inadequately secured. Discuss these objections.

2. A writer in "Blackwood's Magazine" (May, 1865), says: "The conversion of floating into fixed capital means simply, an increase of busiThe construction of a railway is, as regards the community at

ness.

large, no more a conversion of capital into a 'fixed' form, than any increase of buying and selling is. The whole capital remains in the country, and immediately finds its way back to the banks; so that the case simply involves a temporary increase in the requirement for currency, such as is produced by an increase in any kind of business."

Define "capital," and apply your definition to the foregoing passage; stating how far you agree with the doctrine set forth in it.

3. "Though the greater or less quantity of money makes in itself no difference in the rate of interest, a change from a less quantity to a greater, or from a greater to a less, may and does make a difference in it." (Mill).

Prove both statements.

4. Some American economists were of opinion that the inflation of their currency during and after the late civil war caused an increase of imports, and a diminution of exports; do you accept this opinion?

What is the usual order of the consequences resulting from a depreciation of the currency?

5. "The same rule which regulates the relative value of commodities in one country does not regulate the relative value of the commodities exchanged between two or more countries." (Ricardo.)

If you accept this doctrine, state the principles which govern value, respectively, in the one case and in the other.

6. "A tax on the rent of houses may either fall on the occupier, on the ground landlord, or on the building landlord." (Ricardo.)

What are those cases, respectively?

7. Mr. Mill points out some cases in which an exception may be made to the general rule of equality of taxation?

8. Discuss the various modes by which it has been proposed to pay off the national debt; and the probable consequences of rapidly accomplishing such an object.

9. What are the grounds and what the limits of the Laisser-faire or non-interference principle?

EXAMINATION FOR PROFESSORSHIP OF ORATORY.

I.

Give a detailed syllabus of a course of five lectures on Rhetoric.

11.

Write a letter of advice to a young clergyman on the composition and delivery of his sermons.

III.

Write passages, to be introduced into your lectures, on the following subjects:

a. "Le style, c'est l'homme."

b. Loose and periodic style.

c. The characteristic features of the styles of any three great prose writers belonging to Greek, Latin, and English literature respectively.