represent the third force which keeps O in equilibrium, show that the triangle formed by the intersection of the lines drawn perpendicular to OP, OP1, OQ through P, P1, Q, is isosceles and rightangled.

2. Find the conditions of equilibrium of any system of forces acting in one plane.

Account for one of these conditions only being necessary, in the case of a lever attached to a fulcrum.

A uniform beam AB whose weight is (W) rests in equilibrium between a vertical wall BC and the horizontal plane AC, both smooth; CE is a string without weight attached to a point E in the beam. If BAC-a and ACE=8 show that the tension of W cos a

the string

3. Explain the construction of the screw considered as a mechanical power.

Find the equilibrium relation between the power (P) and the weight (W), when the screw is rough and the friction opposed to P.

4. If a beam AB is supported in a horizontal position at (A) and (B) and the weight be uniformly distributed along AB, find the moments of the strain at any point C of the beam.

About what point will this moment be greatest, determine its magnitude in this case.

5. What is meant by the modulus of a machine?

The mean section of a stream acting on the floats of a water wheel is 5 by 1 feet, its mean velocity is 40 feet per minute, it has a fall of 17 feet, the modulus of the wheel is 7; it is required to raise water by means of the wheel to a height of 300 feet, how many cubic feet will it raise per minute?

6. When is the impact of two bodies said to be direct? An imperfectly elastic ball (A) impinges directly with a given velocity upon another ball (B) of the same material at rest, investigate the velocity of each after impact.

If B afterwards impinge upon another ball C at rest, find the velocity of C, and show that it is the greatest when B is a mean proportional in its mass between A and C.

7. A projectile has a velocity of 1600 feet in a second, and is projected at an angle of 30°, find its horizontal and vertical distances from the point of projection after 12 seconds, gravity being taken at 32 feet.

Three equal balls are projected at the same instant from the same point with the same velocity, 1600 feet in a second, and at angles of 30°, 45°, and 60° respectively, find the height of the common centre of gravity of the balls above the horizontal plane after 12 seconds.

8. If Ō be the centre of oscillation, K the centre of gyration, G the centre of gravity of a body suspended from a horizontal axis passing through C, prove CG × CO=CK2.

Find an expression for the time of a small oscillation of an equilateral triangle, oscillating in its own plane about a horizontal axis through an angle perpendicular to the plane of the triangle.

9. Show how to find the pressure on any plane area immersed in a liquid.

If an isosceles triangle be immersed vertically in a liquid with its base horizontal and its vertex coincident with the surface of the liquid, and if the perpendicular from the vertex upon the base be bisected by a line parallel to the base, show that the pressure on the upper portion of the triangle is to the pressure on the lower portion as 1 to 7.

ENGLISH LANGUAGE AND COMPOSITION.

25

10. How is it shown that the elastic force of the air at a given temperature varies inversely as the space it occupies.

A cylindrical tube 2 feet in length and closed at its upper end, is immersed vertically in seawater, and it is found that the water has risen in the tube through 1 feet; find the depth to which the tube has been sunk, supposing 32 feet of seawater measures the atmospheric pressure.

ENGLISH.

G. W. DASENT, D.C.L.

1. Write a short life of any great man.
2. Describe London in a letter.

3. The English is said to be a composite language. Mention the principal elements of which modern English is composed, and write a few sentences illustrating your answer.

4. Write a grammatical sentence and then analyse it, showing the parts out of which it is made.

5. Explain accurately the meaning and use of Conjugation and Inflexion in Grammar.

6. Explain accurately the use of adjectives, pronouns, and adverbs in Grammar.

7. Distinguish between auxiliary, irregular, and defective verbs in Grammar. Write a few sentences containing examples of each of those classes of verbs.

8. Compare the English language as a means of expressing thought with any other language with which you may be acquainted.

9. Punctuate the following passage, and explain any peculiarities of accentuation or construction which may occur to you in it :

Time hath my lord a wallet at his back Wherein he puts alms for oblivion

A great-sized monster of ingratitudes

Those scraps are good deeds past which are devour'd

As fast as they are made forgot as soon

As done Perseverance dear my lord

Keeps honour bright To have done is to hang
Quite out of fashion like a rusty mail

In monumental mockery Take the instant way
For honour travels in a strait so narrow
Where one but goes abreast keep then the path
For emulation hath a thousand sons

That one by one pursue If you give way
Or hedge aside from the direct forthright
Like to an enter'd tide they all rush by
And leave you hindmost

10. Give a few rules for writing a good English style.

ENGLISH LANGUAGE AND COMPOSITION.

W. STEBBING, Esq., M.A.

Write Essays on the two following subjects :1. "Outward accidents conduce much to fortune. But chiefly the mould of a man's fortune is in his own hands."

HISTORY OF THE BRITISH EMPIRE.

27

2. How do museums promote the progress of science and learning?

3. In what respects is the English alphabet defective or redundant?

4. What circumstances most commonly lead to the introduction of new words into a language? Instance words so imported into English.

5. Explain the terms oblique, transitive, root, part of speech, as used in English grammar.

6. Distinguish between clause, sentence, phrase, paragraph, proposition.

7. What is meant in grammar by Concord? Give examples of the several kinds of grammatical concord.

8. Explain the form of the possessive case, singular, e.g., Father's. Will the same explanation suffice for the plural possessive, Fathers'?

9. Why is the past tense, killed, said to be regular, and struck, irregular, in formation? What is meant by the terms, regular, and irregular, as applied in English grammar?

10. The following sentences are incorrect or obscure. Rewrite them. "If this gentleman would make himself practically acquainted with the subject, he would not find it so simple as he is inclined to believe it, and is desirous to lead the public into the same error." "The king advises that between those officials, by whom business can be carried on by word of mouth, the writing of letters should not be allowed, as having a tendency to hinder controversies on unimportant matters." Many a Frenchman, German, and American are to be found in London."

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