Page images
PDF
EPUB

uses to bar dower; A appoints to a purchaser in fee; will A's covenants for titles run with the land? Give your reasons.

4. An estate is conveyed to such uses as A shall appoint, and in default of appointment to A for life, remainder to the right heirs of A. A's marriage takes place previous to 1854; is A's wife entitled to her dower? If so, can A nevertheless make a good title to a purchaser free from dower?

5. What is meant by a condition precedent, and what change has been effected by the Common Law Procedure Act in reference to the mode of averring its performance in pleading?

6. Why is it that contradictory customs cannot be coexistent in the same place? Can you mention any customs which have been held to be unreasonable?

7. What degree of care and vigilance is required from a gratuitous bailee, and from a bailee for hire? In what leading case is the law upon this subject specially considered?

8. State the leading rules applicable to the construction of Acts of Parliament.

9. What was the ancient rule of the common law as to contracts entered into by lunatic? In what cases will they be set aside in equity.

10. Å father dies indebted to a son for moneys received to his use, the father having by his will bequeathed a share of his residuary personal estate to the child, greater than the amount of his debt. Is the child entitled to claim both the debt and the share of the residue? Mention the leading rules relative to the

subject.

11. A testator devises lands to A, and charges them with the payment of debts and certain annuities bequeathed by the will; A sells the land; can the purchase money be safely paid to him alone by the vendee, without the concurrence of the annuitants? State the reasoning on which the rule applicable to the case is founded.

12. In what cases will a settlement made by a woman

previously to marriage, without the knowledge of her intended husband, be set aside at his instance after the marriage has taken place?

Besides in the branches of the public services already mentioned, it is stated by heads of various other

departments that " some acquaintance with the general

principles of law would be an undoubted recommendation to those who look to rising in their respective offices."

11. MATHEMATICS.

This subject is generally divided in two branches, in which the following or similar examination papers are given, viz. in

a. Pure Mathematics.

1. The top of a tank is a rectangle, whose sides are 9 feet and 15 feet: what must be its depth with the same horizontal section throughout, in order that it may contain 12,960 gallons, one gallon containing 277.274 cubic inches?

If the tank were cylindrical, what must be the radius of its circular section, so that its depth and content may be the same as above.

2. A person bought 180 shares at the rate of 2 shares for 77., and 180 more at the rate of 3 for 71., after which he sold them all at the rate of 5 for 14l. Did he gain or lose by his bargain; and what was his gain or loss?

3. Inscribe a circle in a given triangle. If the two exterior angles at the base of a triangle be bisected by two straight lines which are produced to meet, the line joining the point of intersection with the vertical angle will bisect the vertical angle.

4. Define similar rectilineal figures: show that if two triangles are equiangular they will be similar.

If perpendiculars be drawn to the three sides of a triangle show that the triangle formed by the intersection of these perpendiculars will

5. Solve the following equations:

3

1

(1) x2 + x (1 − a3) = x1 (6 + a1)—6 a1.
(2) y1 = x2 (5y-3x)
x2=5x-3y

6. Find the sum of the first (n) square numbers. In the arithmetical progression (1)+(3+5)+ (7+9+11)+(13+15+17+19)+ &c. prove that the sum of all the numbers in the nth bracket = n3.

7. Find by logarithms the number of digits in (512)", and find also by logarithms a fourth proportional to 00625, 005, 064, having given log102=301030.

8. If (a) (b) (c) are integers, show when the solution of the equation ax + by=c cannot be effected in whole numbers.

A number consists of three digits, and the sum of the digits is 18. If 774 be added to the number, and the result be divided by 3, the quotient will be the original number with its digits inverted. Find the number.

[merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

sin (a-a1)=0.

sin (a1 a2) sin (a2 - a) sin (a — a1)

PIP2

+

+

[blocks in formation]

10. Find the area of a quadrilateral figure inscribed in a circle in terms of its sides.

If a, b, c, d, be the four sides of any quadrilateral
figure, d1, d2 the diagonals, (e) the straight line
joining the middle points of the diagonals,
Prove a2+b+c2 + d2 = 4e2+d12+822.

[blocks in formation]

12. Find the equation to the ellipse referred to any two conjugate diameters as axes.

If TPt be a tangent at any point P of an ellipse intersecting the major and minor axis in T and t; prove PT. Pt = CD2 where CD is the semiconjugate diameter to CP.

13. If a right cone be cut through a given point so that its section is an hyperbola, find its axes.

If the angle of the cone be 90°, how must the cutting plane be drawn that the hyperbola may be equilateral?

14. If a, b, c, be the sides of a spherical triangle, and if the arc (8) be drawn from the angle (A) to bisect the side (a),

[blocks in formation]

b+c

b.

C

COS

[blocks in formation]

b. Mixed Mathematics.

1. A point placed at the centre of an equilateral triangle is urged towards the angles by forces equal to 1, 2, and 3 lbs. respectively: determine the direction and magnitude of the resultant.

2. Find the centre of gravity of the frustum of a pyramid cut off by a plane parallel to its base.

3. Show that the principle of virtual velocities holds good for the wedge.

4. In what time would a body falling in vacuo by the action of gravity acquire a velocity of 1000 feet in a second?

5. (a) Two inelastic balls moving in the same direction, but with different velocities, come into collision :

(b) Discuss the question on the supposition that

the balls are elastic.

6. A projectile being discharged in vacuo with a given velocity describes a certain parabola: prove that if the elevation be very slightly altered, the new parabola will intersect the former one at the remote extremity of the focal chord passing through the point of projection.

7. Prove that if the force varies inversely as the square of the distance, the attraction of a spherical shell on a particle within it will keep it in equilibrium.

8. The force varying inversely as the square of the distance, determine the direction in which a particle is attracted by a finite portion of a very thin straight rod.

9. A hemispherical vessel standing upon its base is filled with a fluid: prove that the pressures perpendicular to the plane and curved surfaces are equal.

10. Show that when a body is immersed in a heavy fluid, the resultant of the horizontal pressures at all points of the surface of the body is zero.

11. Explain the principle of Bramah's press.

12. Describe the construction of Galileo's telescope, and explain why it is not available for astronomical purposes.

12. NATURAL AND PHYSICAL SCIENCE.

This subject is almost entirely used in voluntary examinations, as a test for the liberal education of the candidate. The examination papers are ordinarily divided under the following headings:

a. Chemistry.

1. Define the term element. What elements are gaseous, what are liquids, under the ordinary conditions of the globe? What changes do these undergo by considerable alteration of such conditions?

2. State the law of multiple proportions; and illus

« PreviousContinue »