Section 2.

In what districts do the following geological formations prevail, and what are their agricultural characteristics?

1. The tertiary strata.

2. The lower oolite.

3. The new red sandstone.

4. What general conclusions have been deduced from the analysis of soils?

5. What are the properties of the nitrogen in manures, and by what manures is it supplied in the greatest abundance?

6. Give some account of the different kinds of artificial manure, and of their properties.

DIFFERENTIAL AND INTEGRAL CALCULUS.

Section 1.

1. Define a differential co-efficient, and a second differential co-efficient. Find the first and second differential co-efficients of

a2 - x2

2. Write down Taylor's theorem; deduce Maclaurin's from it; and apply the latter to the expansion of a* in a series proceeding by powers of x.

2

3. Apply Taylor's theorem to the expansion of a2 - (x+h) in a series proceeding by powers of h. Explain the result when x is made equal to a; and show that the theorem is not untrue in that case. Section 2.

1. Show that the values of x, which make f(x) a maximum or a minimum, render df(x) =0. Find the least value of

dx

2

a2 + 4x2

2. State the conditions for determining the maximum and minimum values of functions of one variable; and determine the greatest rectangular beam that can be cut from a given cylindrical piece of timber.

3. Write down the equation to the tangent at any point of the curve whose equation is y = ax mx; and show what it becomes when that point is the origin of co-ordinates; and also when it is at a point of the curve corresponding to x = Find the greatest value of y; and trace the curve.

a 2 m

Section 3.

2. Write down the expression for finding the volume of a solid of revolu tion; explain its meaning in the theory of infinitesimals; and apply it to show that the volume of a right cone is found by multiplying the area of the base by one-third of the height. Show that the volume of any pyramid is found by the same rule.

3. Prove the expression for the differential co-efficient of a surface of revolution; and show that if a cylinder circumscribe a sphere, then two planes, each of which is perpendicular to the axis of the cylinder, include between them equal surfaces of the sphere and cylinder respectively.

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Report on St. Mark's College, by Her Majesty's Inspector of Schools, the Rev. H. MOSELEY, M.A., F.R.S.

MY LORDS,

January 29, 1848.

THE number of students resident in St. Mark's College at Christmas, 1847, was 60; of whom 25 had been there from one to three years, and the remaining 35 less than a year. Their ages varied from 15 to 20 years, the average being 17 years 7 months.

Nineteen of them, being 32 per cent., had been educated in National schools, two in Diocesan middle schools, two in other public schools, and the remaining 37, being 62 per cent., in private schools. Nineteen of them (being 32 per cent.) had some knowledge of Latin when they entered the Institution; and generally, their previous attainments were higher than those of the students in other Training schools which I have inspected. There was, moreover, this important difference in the circumstances under which the students of this Institution had entered it, as compared with others: no period of their lives had been given to manual labour. The process of their instruction had, in very few instances I believe, if any, been interrupted. No chasm had been interposed between the college and the school; the course of the one having taken them up where that of the other had left them. They had no experience of that dreamy profitless condition of the mind which is the concomitant of bodily toil. That aptitude to learn, which is the result of a habit of learning, had never in them been lost; nor had that dimness been suffered to come over the understanding which grows of disuse.

Thirty-three, being 55 per cent., were maintained in the Institution at the expense of their parents or other relations; some of these, however, being aided by exhibitions. Eleven were maintained altogether, and three, partly, by private patrons, being 23 per cent. of the whole.

The fees of the remainder were paid by Diocesan Boards, or by free exhibitions from the National Society.

Besides the students resident in the Institution, 31 schoolmasters, who had been educated in it, presented themselves for examination as candidates for certificates. They had been in charge of schools for various periods, ranging from three months to three years.

The time of the previous residence in the college of 26 of these schoolmasters had been three years, and of the remaining five two and a half years. Their ages varied from 17 to 24, the average being 18 years.

Since the date of my last Report, arrangements have been made for adding to the college a school for the reception of youths, from eight years of age to 13, as boarders. I have appended to my Report the prospectus of this school. (Appendix E.)