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SECTION IV. 1. State fully to what causes the difference between mean solar and sidereal time is to be attributed.

2. Explain a method of determining the longitude.

3. Show how the apparent time may be determined (by construction upon the black globe) from an observed altitude of the sun.

4. Why do similar eclipses return after an interval of 19 years ?

Geometry and Trigonometry. 1. If two angles of a triangle be equal to one another, the sides also which subtend or are opposite to the equal angles shall be equal.

2. If at a point in a given straight line two other straight lines on the opposite sides of it make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

3. Equal triangles on the same base and on the same side of it are between the same parallels.

SECTION II. 1. In a given straight line find a point equally distant from two given points, one in and the other above or below the given straight line.

2. A walk is to be made along two adjacent sides of a rectangular garden 100 feet long and 80 feet broad; the area of the walk is to be half that of the garden : what must be its width ?

3. Given one angle of a triangle, a side opposite to it and the other two sides, to construct the triangle.

4. In a right-angled triangle the sum of the sides is 70, and the sum of the hypothenuse and perpendicular falling upon it from the opposite right angle 74, determine the triangle.

SECTION III. 1. Show that

Sin (a + b) = Sin a Cos b + Sin 6 Cos a. 2.

Cos a = 1 2 Sin? a.
Tan a = Cot a 2 Cot 2 a.

3.

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SECTION IV. 1. Show that in a plain triangle

Sin A. b Sin B.

b Tan ? (A - B.) 2.

a + b Tan (A + B.)

S (S 3.

a) (S 6) (S – c) bc

2 Sin A =

a

SECTION V. 1. At a horizontal distance of 197.3 feet from the base of a spire I observe the elevation of its summit to be 50° 56': what is the height of the spire ?

2. I observe the elevation of the summit of a spire standing on a horizontal plane to be 18° 21', I then approach it in a straight line 562 feet, and find the elevation to be 51° 56': what is the height of the lower ?

3. In order to find the distance from one another of two objects, A and B, situated on opposite sides of a piece of water, I measure their distances respectively from a third object C, and find C A to be 562 feet and C B 320 feet, and the angle A C B 128° 4'. what is the distance from A to B ?

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Algebra and Differential Calculus.

SECTION I. 1. Write under its simplest form

-70-16*c X 3 a 6-50 2. What is the square root of a*

468 Зc

9 * 3. Show that

+ J2

1 + $ N 2 4. Reduce to its lowest terms

a + 2 ax + 43
as
2 ax
4 a x

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SECTION II. 1. Solve the equations

5

25

3 22 21 2.

20
6
2

Зх 3.

72c 6 n*+1 + x2 33" + 6*** +
1
X + 1

1
4. 2 (y + x) = a, y (x + z) = b, z ( x + y) = c.

SECTION III. 1. There are 17 silver coins, consisting of crowns and shillings, and their joint value is 21. 13s. Od.: how many are there of each?

2. A person has a certain number of sovereigns which he tries to arrange in a square; at the first trial he has 130 over; he then enlarges the side of the square by 3 sovereigns, and has 31 over : how many sovereigns had he ?

3. In what different ways may I lay out 17701., in sums of 31l. and 21l. each?

4. If a sum of £a be borrowed at r per cent., and £b be repaid at the expiration of each successive year, in how many years will the debt be liquidated, allowing compound interest?

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Agricultural Chemistry.

SECTION I. 1. Show how atmospheric air may be analyzed. 2. Show how water may be analyzed.

3. What are the characteristic properties of ammonia; what is its chemical constitution; and how is it manufactured ?

SECTION II. 1. Distinguish between the organic and inorganic parts of plants and show how they may be separated.

2. What is the chemical constitution of the organic parts in plants ? In what proportions do their chemical elements severally enter into those vegetable substances which serve for the food of man and beast ? 3. What are the chief constituents of the inorganic parts in plants?

SECTION III. 1. State some facts as to the proportions in which inorganic matter enters into the constitution of different vegetable substances, and different parts of the same vegetable substance.

2. What are the principal constituents in the inorganic portions of soils, and what is their classification ?

3. State some facts as to the natural alternation of plants on the same soil, and account for it on chemical principles, and for the advantages derived from the artificial alternation of crops.

APPENDIX (E.)
Report of W. Sterndale Bennett, Esq., Professor in the Royal

Academy of Music.
DEAR SIR,

15, Russell Place, Fitzroy Square, May 6, 1847. I HAVE great pleasure in forwarding you a highly favourable report of the progress of the students at Battersea College, in their musical studies. My examination took place in November last, and I could not fail to observe the very decided improvement which had taken place since I last visited the college in November, 1845.

The singing was highly satisfactory, and the answers of the students to some theoretical questions, which I put to them, were generally correct. The deficiencies to which I alluded in my former Report had been "partially supplied, and Mr. Hullah had adapted his system (as I think) very successfully, according to the musical wants of the students. They have now an excellent practice room, an organ, a resident musical assistant (Mr. Martin), an opportunity of applying their musical attainments in the morning and evening service, which latter I had the pleasure to attend, and to hear some very pure and devotional singing, and these advantages have tended to raise the state of musical feeling amongst the students, and which will, I think, be permanent. Altogether, I am of opinion, that although the stay of the students in the college is very limited, the study of music may be successfully pursuedi by them with a view to ultimate usefulness, and by means of the system now adopted, they may be enabled to impart a clear view of the rudiments of music and singing to those placed under their care.

I remain, Dear Sir, yours very truly, Professor Moseley.

William STERNDALE BENNETT.

| Report on St. Mark's College, Chelsea, by the Rev. H. Moseley,

M.A., F.R.S. MY LORDS,

The present number of students in St. Mark's College is 51, whose average age is 17, and of whom 16 are above the age of 18, and 19 under 17 years of age, I have appended to this Report a Table (Appendix A.) in which-annexed to a number designating each student—is a statement of his age and standing in the institution, his previous means of instruction, his attainments on admission, and the circumstances under which his premium is paid.

It will be seen that 21 of them are from private schools, 19 from National schools, 6 from Diocesan schools, 2 from St. Mark's practising school, one from a British and Foreign school, and one from a workhouse school. Eleven knew the rudiments of Latin on their admission, 5 a little of algebra, and I had made considerable progress in his mathematical studies.

The course of instruction remains nearly the same as at the date of my last inspection, no other alteration having been made in the time table* than such as was of a temporary nature.

The number of hours devoted weekly to each occupation of the students will be found recorded in the following table :

Number of Hours devoted Weekly to each OCCUPATION of the STUDENTS.

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Chapel

6 0 Evening Worship

3 30 Scriptural Knowledge and Chris

2 5 tian Doctrine (i.ē. Articles) Church History and Bible Lite

Lite.} 2 20 rature Latin

6 15 English Grammar, English Lite

7 10 rature, and History Geography

2 30 Writing

0 30 Arithmetic

0 20 Geometry .

2 50 Algebra and Trigonometry 2 20 Mechanics and Natural Philo

20 sophy Music :

7 10 Drawing

4 0 Normal Lessons

30 Private Reading

1 30 Preparing Lessons Meals.

8 45 Leisure

6 0

2 0 6 0 5 20 1 20 1 20 1 10 2 25 2 40

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6 0 2 45 2 30 1 20 0 35 1 20 5 40 0 35 7 10 4 0

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* See Minutes for 1841-5, p. 588.

Inadequacy of the present Buildings. No alteration has been made in the buildings since the date of my last Report. They afford inadequate accommodation to the present number of students; and, not having been erected for the use to which they are now applied, they are ill adapted to it. I may, perhaps, be permitted to add that in their architectural character they do not accord with the dignity and importance of the object to which they are devoted, and that in this respect they present a remarkable contrast to the training-schools which have been erected by local educational Boards.

As there is no adequate accommodation for the present number of students, of whom 25 are lodged without the walls, and as your Lordships' recent minutes will greatly increase the number of applications for admission, a necessity appears to have arisen for enlarging the fabric; and a plan for this object has been prepared by the Principal, which embraces-Ist. Dormitory chambers for as many students as will complete the number of 150,* with full provision for household and industrial occupations. 2ndly. A hall capable of accommodating 200 persons at dinner, with corresponding domestic offices in particular, a laundry, bakehouse, and brewery; with due provision for a separation of these offices from that portion of the building occupied by the students. 3rdly. A sick-ward, distinct from, but contiguous to, the domestic part of the establishment. 4thly. A large lecture-room and theatre, with a laboratory and class-rooms adjoining, and dwelling-rooms for all the masters above.

These buildings Mr. Coleridge proposes to arrange in two courts contiguous to the present building, and entered by a gateway. The college library, the secretary's and steward's offices, the matron's apartments, and the servants' sleepmg-rooms, are provided for in the Principal's present residence.

It would be presumption in me to express any opinion upon the architectural merits of Mr. Coleridge's plan; but I may, perhaps, be permitted to convey to your Lordships the sense I entertain of the importance of placing this and the Battersea training institutions—destined as they are to exercise a powerful influence on the education of the country-on a scale, in respect to the fabric of each, and the accommodation they afford for the lodging and instruction of the students, in some degree commensurate with the educational movement now in

progress.

Subjects tendered for Examination. The following is a list of the subjects tendered to me for examination :

*

Forty is the maximum number which the college will at present fully accommodate.

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