from Him, which, day after day, control all things to the furtherance of His name and glory; that a kingdom has been set up which has steadily progressed in one uniform direction for the last two thousand years, which, in spite of change, and convulsion, and war, and flood, and fire, has advanced in its grandeur and in its strength, prevailing over all opposition, stretching away from land to land, and from shore to shore, overleaping mighty oceans, penetrating into the sands of the desert and the ice of the Pole? Is there evidence, clear and sufficient, that a religion begun in shame and ignominy-promulgated by means most unlikely to obtain success—waging eternal war with the lusts and passions of mankind-supported by no earthly power,— has found its way into the cabinets of princes, and into the huts of peasants, directs the counsels of monarchs, and the daily life of slaves, and is the general principle of action which more or less stringently animates the intelligent and civilized portion of the human race? Is there proof that such a religion exists at all? Then there is proof that the kingdom of Christ is set up, that “the Lord God Omnipotent reigneth ;" and the past is the pledge of the future, that He shall "reign for ever and ever."



Morning. 1. The diffusion and improvement of Political Economy has been greatly impeded by those who have confounded it with the sciences and arts to which it is subservient. Show clearly and fully how that has come to pass.

2. What are the principal differences between the definition of Wealth adopted by Mr. Senior, and those by other writers ? Mention the objections to each of the latter.

3. Show how, and how far, value is regulated by the cost of production, where there is equal competition. Enumerate the four kinds of monopolies which interfere with the operation of equal competition; and point out to what extent, when at all, the cost of production governs value in each.

4. State and explain the Ricardo theory of rent. In enunciating it, the author commits three inaccuracies? He and the French economists fall into opposite errors, from each attending to but one of the causes on which the amount of rent depends ?

5. Is it convenient to classify the improvements which form the greater part of the value of the soil of every well-cultivated district as capital? Or, to classify as wages the extraordinary remuneration of the labourer who happens to be assisted by extraordinary talents ?

6. Prove that as a community advances in wealth, as compared with population, the inequalities in the rates of wages in different employ. ments are relatively diminished.

7. Explain how an effect on values will be produced by either of the following circumstances :

a. A rise or fall of general profits. 6. A rise or fall of wages, whether estimated in cost or commodities.

8. What are the advantages of a mixed metallic currency? How have they been attained hitherto, and to what extent are they secured for the future in this country?

9. How would you estimate the direct pecuniary gain to a country resulting from the coinage being subject to a seigneurage instead of being free? What are the limits to such a gain? Does a seigneurage affect the steadiness in value of the currency?

10. During most of the present year bills of the best security have been discounted in the London money market, at from 6 to 7 per cent., while the dividends on consols have never exceeded 34 per cent. on the sums employed in purchasing such stock at the different prices it has attained within the same period :

a. How can you account for parties investing in the funds, and not the other securities, under such circumstances ?

b. Does it necessarily follow that a smaller return for the money is gained in the former than in the latter investment?

11. What caused the great exportation of silver from Europe and America to the East until a comparatively recent period? What checked the drain for a while, and what caused it to recommence a few years ago ? At the rate it is at present proceeding, it cannot go on long?

12. In a lately published Essay by Colonel Sykes, on “The External Commerce of British India,” the author points out that the annual value of the goods exported from that country exceeds on an average by several millions that of the goods and bullion imported. Thence he concludes that this balance should have been paid by further remittances of bullion, had it not been cancelled by bills drawn from London in favour of the East India Company; or, to use his own words, "had not the annual pecuniary wants of the East India Company, miscalled the tribute of India, come to the relief of commerce and the money market,” and "assisted merchants in the discharge of their annual debt to India." Point out the fallacy in the preceding.

Evening. 1. Mr. J. S. Mill states (Book 11. ch. sv. $ 5) that the advances of the capitalist, for purposes of production, consist of wages of labour; and he lays down in substance (Book 1. ch. v. $ 8) that when wealth, which would otherwise have been employed in productive industry, is borrowed for unproductive expenditure, the result is an abstraction pro tanto from the funds for the payment of productive labourers:

a. Explain the first of the preceding propositions.
b. In the sense in which it is true, does it bear out the second ?

2. Were ground-rent not required from the occupiers, manufacturers and shopkeepers might lower their prices, yet continue to make average profits upon all their capital; but farmers generally could not do so ?

3. Bank notes are a more powerful instrument for raising prices than bills, and bills than book credits ?

4. It is often alleged that inconvertible paper currency cannot be issued in excess so long as the issuers have property to the value of what they are allowed to put into circulation. Show the fallacy of this, pointing out at the same time what is the kind of depreciation of paper which is averted by the solvency of the issuer, and what is that which cannot?

5. What is the advantage of a paper currency, convertible into the gold or silver which it represents, over one representing some other article, such as corn, cotton, land, &c., and convertible into same?

6. In order to estimate the immediate burthen of excise or custom duties, some financial writers proceed thus :_They calculate the proportion of the price charged by the retailer for the taxed article, to that of the aggregate amount of the duty, and of the wholesale price without the duty; and then increase the latter alone (that is, the wholesale price without the duty) in the same proportion. This, they contend, would be the retail price were there no excise or customs charged; and the difference between it and the actual retail price they assign, accordingly, as the burthen of taxation. What is the fallacy in this mode of calculating what the retail price would be in the absence of the duty?

7. It is sometimes thought that a speculator may make profit by first buying such quantities of any given commodity as to lead to an artificial scarcity and rise of price, and then selling off at the increased price. Show the fallacy of this, and prove that the result of such an operation on the market ought to be a loss on the speculator.

8. Adam Smith includes the seed corn of a farmer in his fixed capital, and the food consumed by his cattle in his circulating capital. Is this classification convenient?

9. In England, when a person insures his establishment against loss by fire, he is fully protected to the amount of his policy of insurance. But in France, under the average clause, he would be entitled to receive no more from the insurance office than the fractional part of the amount of his policy determined by the proportion between the value of the property lost, and that of the entire property, such as it was before the fire. Hence, prove that, measured by the amount of protection afforded by an insurance for any sum less than the entire value of the property, the same per-centage charge on the sum insured is a heavier burthen in France than in England; and show also that in the former case the bur. then is variable, and cannot be estimated beforehand.

10. In 1850 the official value of the exports of the United Kingdom amounted to £197,000,000, and the declared to £71,000,000; and in every year that such accounts have been published, a discrepancy of a similar character has been observed. The official value of the imports the same year was £100,000,000 :

a. What is the meaning of the official value of the exports, and when first introduced ?

b. What is the meaning of the declared value of the exports, and when first introduced ?

c. If we had returns of the declared as well as of the official value of the imports, why is it likely these would exhibit no such discrepancy ss that observed in the case of the exports ?





1. Prove the following theorem by means of the separation of symbols : A"(uzvx) = UzA"Vx+ AuxA"-102+1 +

n (n - 1)

A? 4x An-2 Vx+2 + &c. ... 2. Find the ultimate value of

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when r becomes a very large number.

3. Form a linear equation in finite differences having given solutions. 4. Prove the following theorems :

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5. Find the equation of the of curves possessing the property that all the chords passing through a certain fixed point are of the same length.

6. If the rectangle under the parts of the chord passing through the fixed point is invariable, what is the equation of the class of curves?

7. A geodetic line traced on a cone intersects itself in a series of points: what relations exist between the mutual distances of these points, and between the successive angles of intersection?

8. Prove M. Liouville's formula for the radius of geodetic curvature, viz. :


sin i


P2 pi 9. If a curved surface be the envelope of a sphere whose centre traverses a curve of double curvature, and whose radius is variable

a. The locus of the intersection of the successive characteristics is an. arête de rebroussement. How is its equation determined

b. In what case do its two branches coalesce ?

10. What is the general method of determining the equation of the line of striction on a proposed gauche surface ?

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cos i


ALGEBRA, AND THE DIFFERENTIAL AND INTEGRAL CALCULUS. 1. The result of the elimination of the arbitrary functions o, y from the equation

F{2, y, z, q(u), 4(x)} = 0, (where u = f (x, y, z)) will always be an equation of the second order.

2. If the quantities under the functional signs o, y were different, this would not be generally true. 3. If the solution of the equation

Rr +298 + Tt + Pp+29+ V = 0 be of the form

2 = ap(u) + B4 (u) + y; a, b, y being functions of u and y, show that

P R 8

Q T' 4. The equation

rys 282y + tal = px + 4y - 3 may be reduced to the form

+ 2 = 0

dv2 by putting

I= # COSU,

y = 4 sin o. 5. Hence give the complete solution of the equation with two arbitrary functions. 6. Show that the integral




RTR taken through the entire surface of an ellipsoid, depends upon elliptic functions of the first and second kinds, P being the perpendicular from the centre on the tangent plane, ds the element of the surface, and R, R' the principal radii of curvature.

7. If p be the radius of curvature of a curve, described on a given surface, which renders Suds a maximum or minimum, prove

du du du
+ cos ß

+ cos y
p'? u2 dx dy

dz p' being the radius of curvature of the normal section passing through the tangent to the curve, and a, ß, y the angles between the plane of this section and the co-ordinate planes.

8. The equation which the calculus of variations furnishes for the determination of the function 2, which renders

Vdxdy a maximum or minimum (where

V=f(x, y, 2, p, q, r, s, 1)) is in general of the fourth order. Prove this, and determine the exception which exists to this rule.

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cos a

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