struck on the left breast by a cannon shot. The shock threw him from his horse with violence; he rose again in a sitting posture; his countenance unchanged, and his steadfast eye still fixed upon the regiments engaged in his front. No sigh betrayed a sensation of pain; but in a few moments, when he was satisfied that the troops were gaining ground, his countenance brightened, and he suffered himself to be taken to the rear. Then was seen the dreadful nature of his hurt. As the soldiers placed him in a blanket his sword got entangled, and the hilt entered the wound. Captain Hardinge, a staff officer who was near, attempted to take it off, but the dying man stopped him, saying: "It is as well as it is. I had rather it should go out of the field with me." And in that manner, so becoming a soldier, Moore was borne from the fight.-Napier.

MATHEMATICS.

REV. W. N. GRIFFIN, M.A.

1. What is the value in English money of 83628 francs, when a franc is worth 93 pence?

2. Find the rent of 3 acres 3 roods 29 perches at the rate of 17. 3s. 4d. the rood.

3. Express 136 lbs. as the decimal of 1 cwt. 1

qr.

4. An income first pays parish rates, and on its amount thus reduced an income-tax of sixpence in the pound is levied. These deductions are together 35 per cent. of the original income. How much in the pound are the parish rates? [To be solved without algebra.]

5. Prove the rule for pointing the figures of a number of which the square root is to be extracted. Compute to two places of decimals the value of

6. Having given log 1.28=k, find log 016; and by aid of the tables compute the value of

8. Find two numbers whereof the greater added to a quarter of the less exceeds the less by 6, and the less added to a third of the greater falls short of the greater by 2.

9. Assuming the Binomial Theorem obtain the series

a* = 1 + kx +

+

+

1.2

1.2.3

where k is the logarithm of a to the base e, and e is

10. The complements of the parallelograms which are about the diameter of any parallelogram are equal to one another.

Prove that these complements are the greatest when the parallelograms about the diameter are equal to one another.

11. Define a circle. If a point be taken within a circle from which there can be drawn more than two equal straight lines to the circumference, that point is the centre of the circle.

12. If two straight lines be parallel, the straight line drawn from any point in the one to any point in the other is in the same plane with the parallels. State the axiom required in the demonstration.

13. Three equal circles touch one another. Compare the area of one of them with the area of the circle which circumscribes them all.

2. A lump of metal worth 1907. is formed by a fusion of gold and silver, the values of which are 37. 17s. 6d. and 58. an ounce respectively, the weight of the gold is 75 of the whole weight, find the weight of each metal contained in the mixture.

3. A farmer purchased 749 sheep, and sold 700 of them for the price he paid for the whole; he afterwards sold the remaining sheep at the same price per head as the others; find his gain per cent.

4. What is meant by the modulus of a system of logarithms? Given the logarithm of a number to

any base, show how to find the logarithm of a number to any other base. If e be the base of Napier's system,

+ &c. to 10 terms.

+(001)

(x+y+z)3 − (x3+y3+ z3)=3(x+y) (x+z) (y+z) Eliminate y and x from the equations

(1) (x-3) (x-2)+(x−3) (x−1)+(x − 2) (x − 1) =2.

(2) (ax+by)2 + (ay—bx)2=2{ { + }

2

Take away the second term from the equation y3-9y2+15y+25=0, and solve it by the method of

Cardan.

7. Show how to find the number of homogeneous products of (r) dimensions that can be formed out of n letters a, b, c, and their powers.

Find the number of terms in the expansion of (a+b+c+d).

8. Show how to convert any given fraction into a continued fraction, and prove the law of formation of the successive convergent fractions. Find by this method the three first convergent fractions to 3.1416.

9. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.

Prove that the area of any right-angled triangle is equal to the rectangle contained by the semi-perimeter, and the excess of the semi-perimeter above the hypothenuse.

10. Inscribe a circle in a given equilateral and equiangular pentagon.

Show that the base of an isosceles triangle, whose vertex is at the centre of a circle, and the angles at the base each equal to three-fourths the angle at the vertex, is the side of a regular pentagon inscribed the circle, and that the base of the isosceles triangle whose angles at the base are each equal to double the angle at the vertex is the side of a regular decagon inscribed in the same circle.

11. Assuming that similar polygons may be divided into the same number of similar triangles, show that the polygons have to one another the duplicate ratio of their homologous sides.

ABCD is a trapezium, BD, AC the diagonals, E, F, G, H the points of bisection of the four sides AB, BC, CD, DA respectively, join these points of bisections by straight lines cutting the diagonals in K, L, M, N, prove the figure KLMN to be a trapezium similar to ABCD, and equal in area to onefourth the area of ABCD.