16. The sum of two numbers is 7, and the sum of their cubes is 91, find them. 17. The difference of two numbers is 56, and the difference of their cube roots 2, find them.

GEOMETRY.-2ND CLASS. BURSARY of £15.

1. Define a right angle, a square, and a circle.

2. The greater angle of every triangle has the greater side opposite to it. Prove this,-state the kind of proof,-the relation of this proposition to the one immediately

before.

3. If a parallelogram and a triangle be upon the same base, and between the same parallels, the triangle is half of the parallelogram. Prove this, and two of the preceding propositions required in the proof.

4. Bisect a given straight line. Show the series of dependencies of this problem upon the preceding propositions in Euclid.

5. The vertical angle and the base of a triangle are both bisected by the same straight line. What kind of triangle is it? Prove it.

6. The sum of two sides of every triangle is greater than twice the line drawn from the vertex to bisect the base.

7. If the four sides of any four-sided figure be bisected, and the adjoining points joined the figure thus found is what? And what part of the whole figure? Prove both answers.

VOL. II.

3 I

GEOMETRY.-3RD CLASS. BURSARY of £20.

1. Define a parallelogram,—and what is meant by a line cut in extreme and ma ratio.

2. If a straight line fall upon two parallel straight lines, it makes the alter angles equal.-Define parallel lines, and alternate angles.

3. If a line be cut into any two parts, the square of the whole line is equal to t squares of the parts, and twice the rectangle contained by the parts. Algebraically.

Show the s

4. Prove that angles in the same segment of a circle are equal. Prove also the p position upon which this immediately depends,—and the propositions in the First Bo of Euclid upon which this last depends.

5. The line which bisects the vertical angle of a triangle cuts the base into segment having the same ratio as the sides of the triangle.-How much of this can be pros by the First Book of Euclid?

6. Every line parallel to the base of a triangle is bisected by the straight line dra from the vertex bisecting the base of the triangle.

7. The angle in a segment greater than a semicircle is less than a right angle-Pr it; and find the area of a segment of a circle containing 60°, whose radius is 10 fe 8. The two sides of a triangle are 10 and 17 feet, and its base 21 feet.-What ? and its ? and its ? &c. &c. As many answer

its

as you can give.

No. VI.

Report on Bursaries, February 1845.

The Committee have had great satisfaction in the results of the first step which they have taken towards raising the qualifications of their teachers, and extending encouragement to them in proportion to their merits. Twenty-six young men appeared as competitors for bursaries. To them sets of carefully prepared questions were submitted; and after two days' competition, it was found by the professional examinations, and by the Committee, after consider ing the attainments of the candidates and their aptitude for practical teaching, that eleven of them had established a right to receive bursaries: which were awarded to them accordingly.

It is, however, well that all interested in this subject should know, that while the whole competitors, and especially, of course, those who were preferred to the bursaries, acquitted themselves most creditably, and in such a way as to afford ample promise of future advancement and excellence, the average attainments of the young men were still below the standard held up to them on the questions on which they were tried, and very much below the still higher standard which the Committee are desirous of holding up in future compe titions. They would, therefore, earnestly press upon all who may now be turning their thoughts towards teaching in connexion with the Free Church, upon ministers, school Committees, and all interested in the subject of Education, the importance, and, indeed, the necessity of stimulating industry and exciting ambition, with the view of not only maintaining, but of elevating the standard of literary and scientific acquirements, as well as of enlarging the religious knowledge, and deepening, as far as human means may, the piety of those to whom the education of a rising generation, in days like these, is to be committed. To this end the Committee will steadily direct their attention in future competitions. The next will probably take place in the beginning of September; but before that time more precise regulations, in regard to the bursaries, will be announced, than could be communicated prior to the first experiment.

Report on a proposed Scheme for creating a Teachers' Superannuation Fund; by the REV. H. MOSELEY, M.A., F.R.S., Her Majesty's Inspector of Schools.

MY LORD,

4 May 1849.

THE elementary teachers of the West Riding of Yorkshire, having presented to your Lordship, by the ands of the Rev. Frederick Watkins, Her Majesty's Inspector of Schools for that district, a memorial to the effect that:

--

"The establishment of a Mutual Assurance Society or Teachers, upon a secure and durable basis, in which eachers could confidently make periodical deposits, would relieve the anxiety which has long been experienced by them in providing the means of support in sickness and old age, and in contributing towards the maintenance of their families in case of death; and that such a society, if conducted under the auspices of my Lords the Committee of Her Majesty's Privy Council on Education, would, as they confidently believed, be received with gratitude by the great body of teachers throughout the kingdom.'

I was instructed by your Lordship to submit to you a statement of the reasons for which it was judged expedient that such an association should be formed, and of the plan on which it should be conducted.

I beg now to lay this statement before your Lordship, regretting that by the pressure of other official duties this has so long been delayed.

unprovided for in

liable.

It is not often that the stipend of the schoolmaster The schoolmaster is affords him the means of providing against sickness or time of sickness, to old age, or for the maintenance of his family in case of which he is peculiarly his death. The very spirit he is of, and which makes him a good schoolmaster, has a tendency to make him an unworldly man. It is but rarely that the funds of his school admit of an adequate maintenance being provided for him in times of sickness, and, at the same time, a competent substitute to relieve him of his duties in the school.

Thus he is induced to toil on when the state of his health requires rest, and sometimes (it is to be feared) when his recovery is rendered thereby hopeless.