his power exceed the Consular power? When was this office finally abolished; and what is Cicero's allusion in this passage?

"Non modo regno quod pertuleramus, sed etiam regni timore sublato." -PHILIPP.

10. The prerogatives of different republican offices were combined to form the imperial government of Augustus? State severally their character and functions in this administration.

11. Give some account of the law of "Majestas" at Rome, from its origin to its final development under the Empire.

12. The prevailing forms of philosophy at Rome, under the later Republic, and the Empire, were different; how does Merivale connect this with external circumstances? and show that these forms of philosophy acted at once both as cause and effect.

LOGIC.

D. TOLEKEN.

1. Distinguish between the matter of a proposition and modality; and give Archbishop Whately's views respecting the latter.

2. How do Murray and Walker differ respecting the nature of conversion ? What is Archbishop Whately's opinion? Prove the laws of

conversion.

3. How are the contradictories of hypothetical and disjunctive propo

sitions formed?

4. How does Archbishop Whately analyze the following argument? Does his account appear correct?

Every true patriot is disinterested.

Few men are disinterested.

.. Few men are true patriots.

He mentions subsequently a different analysis of similar reasonings ? 5. Investigate how many valid combinations of premises are possible. 6. State the relative advantages of the second and third figures of syllogism. What is the enstatic figure, and why so called ? Give an example of its application.

7. How does Archbishop Whately reduce the modes Baroko and Bokardo?

8. In "Reductio ad impossibile" can conclusions of reducend and reduct agree in quantity and quality?

9. Enumerate the fallacies classed by Archbishop Whately under the head of "Ignoratio Elenchi."

10. Several philosophical errors have arisen from confounding two kinds of "Discovery"?

POLITICAL ECONOMY EXAMINATION.

PROFESSOR CAIRNES.

Morning.

1. Explain the relation of political economy to statistics, to history, and to political philosophy; and point out a danger to which economists are liable in reasoning from historical data.

2. Explain the advantage or disadvantage (as the case may be), which a country experiences from a high or low range of local money rates (wages and prices); and give examples in point.

3. It is maintained by a writer in the "Edinburgh Review" (July, 1843), that "cost of production is the real governor, not only of domestic, but of international, values." If you think this principle sound, reconcile it with the fact mentioned by Mr. Senior, that the produce of the labour of one Englishman exchanges for the produce of the labour of five Poles. If you do not think it sound, refute the doctrine.

4. Adam Smith says: "High profits tend to raise prices more than high wages." Explain the relation of profits to prices; also of wages to prices; and sustain, or refute, as you think fit, Adam Smith's doctrine. Explain also the relation of "rent" to prices.

5. Supposing the productiveness of industry to be increased-1st. in articles which enter into the consumption of the labouring classes; 2nd. in articles consumed only by the richer classes :—what are the circumstances which will determine the effect of this increased productiveness of industry, in each of the above cases, on wages, and on profits?

6. Mr. Buckle, in his "History of Civilization (p. 62), argues thus:"We see that, other things remaining equal, the food of a people determines the increase of their numbers, and the increase of their numbers determines the rate of their wages:"-from which he infers that, the more abundant the food of a people, the lower will be their real wages, and consequently their general physical condition. If you think this a sound inference, how do you justify the policy of repealing the Corn Laws? If you do not think it a sound inference, point out the fallacy.

7. Again, in the same work (p. 67), the same writer argues thus:"The wealth of a country can only be divided into wages, rent, profits, and interest, and, inasmuch as interest is on an average an exact measure of profits, it follows that, if among any people rent and interest are both high, wages must be low." Mr. Buckle then proves that rent and interest have always been high in India (rent, as he asserts, having been generally one-half of the produce, and the rate of interest having generally varied from 15 to 60 per cent); from which he concludes that the general population of India has always been very poor. Now, granting the facts to be as asserted; granting also that interest is an exact measure of profits; does Mr. Buckle's conclusion follow from his premises? If you think not, point out the defect in his argument.

8. Distinguish "capital,” on the one hand, from wealth in general, on the other hand, from currency; and, keeping these distinctions in view

a. Explain in what way, if at all, a good system of banking economizes "capital."

b. Explain in what way, if at all, the carrying on of a war, by means of borrowing, diminishes the "capital” of a country.

9. State the ultimate and proximate causes which regulate the rate of interest; and, keeping this statement in view

a. Explain the causes of the high rate of interest incident to periods of commercial embarrassment.

b. Explain the effect on the rate of interest of international movements of bullion.

Evening.

1. M. Chevalier, in his work on "The probable Fall of Gold," states his opinion that the depreciation of gold will be injurious to the working classes, because, although their money wages will ultimately rise in proportion to the depreciation of money, they will not rise as fast as the prices of the commodities which the working classes consume. If you think M. Chevalier's view sound, explain how it is that, in the event supposed, the prices of commodities will rise more rapidly than the wages of labour. If you think it unsound, point out wherein it is fallacious.

2. It has been argued that the cost of gold has not been reduced by the gold discoveries, because the price of labour in the gold countries has risen as much as the productiveness of labour in raising gold has increased; and that, consequently, no reduction in the value of gold can take place until the wages of labour are lowered. If you think this argument sound, explain how it is that the value of gold has fallen in the gold countries. If you do not think it sound, point out the fallacy.

3. Mr. Newmarch, in his "New Supplies of Gold," has the following passage:"Taking into account the cost of insurance, freight, commission, and charges, it is very doubtful whether, to yield a profit, go'd bullion can be consigned from Australia to London at a higher buying price than 678. or 688. the ounce." Does Mr. Newmarch here state correctly the conditions on which the profitableness of exporting gold depends? If you think he does, account for the fact that, while the price of gold has been the same in Melbourne during the last five years as in London (viz., £3 178. 10d. per ounce), gold continues to be exported. If you think he does not, state the true conditions.

4. Mr. Stirling, in his work on "The Gold Discoveries" (pp. 80, 92), explains the advance of prices which occurred in Australia, in the absence of a Colonial Mint and pending the arrival of sovereigns from England, on the principle that cost of production may, in the case of money as of other things, act through a potential, without any actual, increase of supply. Show, on general grounds, that the principle in question could not take effect in the case of money; and prove, from a phenomenon which then presented itself in the Australian money markets, that the principle did not take effect.

5. On the assumption that the Paper Duty does not violate any of the four maxims of taxation laid down by Adam Smith, and that the revenue derived from it is indispensable to the State,-how far is the charge well founded that this duty is a tax upon knowledge?

6. The Poor Rate may, according to the principles on which it is assessed, fall on the landlord, on the consumer of raw produce, or on the farmer. What are the circumstances which determine on whom it falls?

7. The proprietors of monster shops state their principle of business to be "low prices and quick returns." Suppose this principle to be generally adopted, would the result be a more rapid turning of the aggregate capital of the community? If not, state on what condition the rapidity, with which the aggregate capital is turned, depends.

8. It is urged by the supporters of the Bank Act of 1844, that "if the paper circulation is to be preserved constantly conformable in value to gold, it must conform in quantity also to gold." This is true in a certain but not in the sense which the argument for the Bank Act required?

sense,

BISHOP LAW'S MATHEMATICAL PREMIUMS.

SIR WILLIAM ROWAN HAMILTON.

A.

QUATERNIONS.

I. The normal at the end of the variable vector p, to the surface of revolution of the sixth dimension, which is represented by the equation

and the tangent to the meridian at that point, are respectively parallel to the two vectors,

and

v = 2(p − a) - tp,

T = 2 (1 − 2t) (p − a) + t2p;

so that they intersect the axis a, in points of which the vectors are, respectively,

2. If dp be in the same meridian plane as p, then

t (1 − t) (4 − t) dp = 37dt, and S!

-

3. Under the same condition,

pdt

=

4 - t
3

do

4. The vector of the centre of curvature of the meridian, at the end of the vector p, is, therefore,

5. The expressions in Question I give

v2 = a2 t2 (1 − t)2, r2 = a2 t3 (1 − t)2 (4 − t) ;

hence

the radius of curvature of the meridian is, therefore,

and the length of an element of arc of that curve is

thus the auxiliary scalar t is confined between the limits o and 4, and we may write t = 2 vers 0, where 0 is a real angle, which varies continuously from o to 27; the recent expression for the element of arc becomes, therefore,

ds = 3 Ta. tde, and gives by integration s = 6 Ta (0 - sin 0), if the arc s be measured from the point, say F, for which o = a, and which is common to all the meridians; and the total periphery of any one such curve is = 12π Tα.

7. The value of a gives

4 (02 — a2) = 3a2t (4−t), 16(Vao)2 = — a1t3 (4 − t)3; if, then, we set aside the axis of revolution a, which is crossed by all the normals to the surface (a), the surface of centres of curvature which is touched by all those normals is represented by the equation,

4(02 — a2)3 + 27a2 (Vao)2 = 0.

(b)

8. The point F is common to the two surfaces (a) and (b), and is a singular point on each of them, being a triple point on (a), and a double point on (b); there is also at it an infinitely sharp cusp on (b), which tends to coincide with the axis a, but a determined tangent plane to (a), which is perpendicular to that axis, and to that cusp; and the point, say F', of which the vector a, is another and an exactly similar cusp on (b), but does not belong to (a).

==

9. Besides the three universally coincident intersections of the surface (a), with any transversal, drawn through its triple point F, in any given direction ß, there are always three other real intersections, of which indeed one coincides with F if the transversal be perpendicular to the axis, and for which the following is a general formula :

p = Ta. [Ua + {2SU (aß)}3 Uß].