13. A. Principal sentence co-ordinate with B.

14.

Rab I

saw

completion of predicate.
subject.
predicate.

almost every week adverbial extension of predicate.

on the Wednesday 2nd adverbial extension

and

of predicate. copula.

(a.) This phrase is clearly illogical. The words introduced by "of" ought to signify the class out of which some one newspaper has the largest circulation. "Any Liberal newspaper," however, is obviously not the name of a class, for "any" is a distributive, and "newspaper" is in the singular number.

(b.) "Neither" ought only to be used when two things are referred to. In this instance, there being three causes, "none" is the correct word to use.

(c.) The conjunction "or" does not here connect similar parts of speech. The sentence should read "that has been, is, or shall be published."

(d.) At the time of the "meaning," the "writing" was not done, and was essentially a future action. "I meant to write to you" is the correct expression.

(e.) The verb in the subordinate sentence should be in a similar tense to that in the principal sentence, viz.: both present, or both past. "If I am old enough to be married, I am old enough to manage my husband's house."

(f.) The verb should here be in the plural number. For the nature of the predicate ("to go together") shows that there must be two subjects, viz.: "a rise in rents," and "[a rise in wages."

66

(9.) The construction of this sentence implies that the verb understood in the second clause is "belongs," whereas it should be in the plural number, belong, and consequently ought to be expressed.

(h.) "Running" is a verbal noun, and should be preceded by the pronoun in the possessive case, "I heard of his running away."

(i.) Is being a substantive verb should have the same case after it as before it-"It is I." The syntax of the last two sentences is defended by some authorities.*

15. Prosody is that branch of grammar which treats of the rules of versification.

English verse is chiefly regulated by accent. Every verse usually consists of a certain number of syllables, out of which a given number are accented, the accented and unaccented syllables being arranged in a determinate order, which, as well as the number of syllables, depends on the nature of the metre in which the verse is written. Generally speaking, two lines which rhyme have the same number of syllables, with the accents in corresponding places. To this rule, however, there are many exceptions, particularly as regards the unaccented syllables.

Two words are said to form a perfect rhyme when they fulfil the following condi tions:

(1.) The vowels (of the accented syllables if they are of more than one syllable) must be alike in the two words. (2.) The consonants following the vowel must be alike. (3.) The consonants preceding the vowel must differ. Rhyme is entirely regulated be the sound and not by the spelling of the words. If any of the above mentioned See Alford's "The Queen's English"

*

conditions are not fulfilled the rhyme is imperfect.

A line of blank verse consists normally of ten syllables, of which five are accented, the accents falling on the even syllables. An additional syllable is occasionally added at the end of a line.

PRELIMINARY EXAMINATIONS ROYAL COLLEGES OF PHYSICIANS & SURGEONS, EDINBURGH, APRIL, 1883. GEOMETRY.

Euclid, Books I. and II.

1. Define a Circle, a Rhomboid, a Trapezium, and Parallel Straight Lines.

2. The angles at the base of an isosceles triangle are equal to each other.

3. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

4. To divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.

5. To describe a square that shall be equal to a given rectilineal figure.

Euclid, Book III.

1. Equal straight lines in a circle are equally distant from the centre, and conversely.

2. The angles in the same segment of a circle are equal to one another.

3. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.

ANSWERS.

N.B.-All the above are propositions of Euclid.

Roger Z. sends us the following query :- "The price

of land about London is every year rising 4 per cent. on previous prices, while the purchasing power of gold as regards general commodities is fallingper cent. per annum. A proprietor sells half his land this year for £8,000, and invests the proceeds at 5 per cent. He proposes to sell the remainder three years hence, and to invest the money in the same way. What income would now represent the purchasing power of the income he will have obtained when the sales are completed ?"

SOLICITORS' PRELIMINARY, FEBRUARY, 1883.

ARITHMETIC.

1. Explain the terms, "unit," "notation," "numeration," "abstract numbers," "concrete numbers." Which of the four fundamental rules apply to the latter, and under what conditions?

2. Show how an extension of the ordinary system of notation, may be made to include fractional and integral arithmetic in one and the same system.

3. What is the number which you increase by 34 when you add to it its 3rds and its ths?

4. Prove that if the numerator and denominator of a fraction be multiplied or divided by the same number its value is not altered.

5. Simplify the following: (a) 5 of 1's (6}).

(1)

ད“ས

(c) of 13 of 21% of

(a)

1 ⚫01

⚫0069

4+00005·002 × 0125

6. If to the and of my age you add 15 years, the result will be my age 9 years hence. How soon shall I be 50 years old.

7. The two hands of a watch are in a straight line. After what lapse of time will they resume that position?

8. Two trains are started at the same moment to meet each other. The first does three miles more an hour than the second, and at the end of twelve hours the trains meet of the way. What is the distance of the two starting points?

9. Four partners gain £21,175. The first is to have £4,250 more than the second; the second £1,700 more than the third; and the third £1,175 What does each partner

more than the fourth. get respectively?

10. A person has £12 4s. Od. in half crowns, florins, and shillings; and the number of coins of each kind are respectively as the numbers 7, 5, and 3. Find the number of coins of each kind.

ANSWERS BY AN LL.B.

1. Unit. "By unit is meant a single object or thing considered as one and undivided." B. Smith. Notation is the art of expressing any number which is already given in words, by figures, and Numeration the art of expressing any number in words which is already given in figures.

Abstract Numbers are those which have no reference to any particular kind of unit, and Concrete Numbers are those which have reference to some particular object.

Concrete numbers referring to same kind of things may be added or subtracted whether of the same or different denominations; in the first case the process is called "simple," in the second "compound." In multiplication the multiplier must always be abstract, but the multiplicand may be concrete and consist of one or various denominations; in the former case the operation is "simple," in the latter "compound."

In division if the divisor be an abstract number the dividend may be either of one or of various denominations; if of one, the operation is "simple," unless there is a remainder: otherwise it is 66 compound." If both divisor and dividend are concrete, they may be reduced to the same denomination and the operation is "simple division," and the quotient is abstract. In a word, concrete numbers cannot be multiplied together.

2. Figures in the units' place retain their intrinsic value, while those to the left of the units' place increase tenfold at each step from the units' place; therefore, according to the same notation, as we proceed from the units' place to the right, every successive figure decreases tenfold. can thus represent whole numbers or integers and fractions under a uniform notation, by means of figures in the units' place and on each side of

it.

3. Therefore

27

=

We

of the number = 1 and this = 34. 2, and the number 24. Answer. 4. If the numerator and denominator of the fraction be multiplied by 3, the resulting fraction 929 is, which is the same value as, because in the fraction the unit is divided into 9 equal parts, and two of those parts are taken; in the fraction the unit is divided into 27 equal parts, and 6 of such parts are taken. Now there are three times as many parts taken in the second fraction as there are in the first fraction; but 3 parts in the second fraction are only equal to one part in the first; therefore, the 6 parts in the second fraction are equal to the 2 parts taken in the first; consequently, By a con= 27. verse process might be proved equal to3.

=

110

= 10,43 = 25% + 18118 15223

220

220

29

8 × 1 × 8 = 1 Answer.

1143 110 3429 220

228

=

3. Answer.

15 49

•0069

(d) 100

⚫0069 •4000751 •0069 × 9000000 3600676

=100-3600676

360005500 3538576 884644 3600676 900169 6.+=3% of your age, and since according to the question if 15 years be added, the result will be your age 2 years hence; if 6 years be added it will give your present age; and therefore ths of your age equals 6 years, or your age is 35 years; consequently you will be 50 years old in 15 years. Answer.

7. The minute hand to get back to the same position must gain 60 minute spaces on the hour hand, but in 60 minutes it gains 55 such spaces, therefore, 55: 60: 60: 65151.

The hands will consequently be again in a straight line after a lapse of 1 hour 5,5 minutes. Answer.

8. The slower train has travelled 36 miles less than the other in 12 hours, but it has travelled the whole distance less, consequently the distance of the two starting places is 3 x 36 = 108 miles. Answer.

=

9. The first partner gets £4,250 + £1,700+ £1,175 £7,125 more than the fourth; the second £2,875 more than the fourth; the third £1,175 more than the fourth.

Deducting the total of these sums from £21,175, there remains £10,000 to be equally distributed among the four partners; to this sum of £2,500 the excess that each of the first three partners receives must be added. fourth, £2,500. Answer. receives £9,625; second, £5,375;

S. d.
10. 7 Half-crowns = 17 6
5 Florins
= 10
0
3 Shillings = 3 0

1. State what are the axioms assumed in the theory of Statics.

2. Shew that if three forces acting on a point keep it in equilibrium each force is proportional to the sine of the angle between the directions of the other two.

3. A weight Q hanging freely over a pulley supports P, which rests on an inclined plane. Determine the position of equilibrium and the pressure on the inclined plane.

4. Two forces act on a rigid body in the same plane but not at the same point. Determine the magnitude, the point of application, and the direction of the resultant.

5. Explain what is meant by the arm, the moment, and the axis of a couple; and prove that the effect of a couple upon the equilibrium of a body is not altered if its arm be turned through any angle about one extremity in the plane of the couple.

=

6. Draw two diagrams representing the system of pulleys in which W 2" P, and that in which W-(2-1) P,and state what are their respective advantages.

7. Weights in the proportion of 1, 2, 3, are placed at the three angles of a triangle; find by a geometrical construction the centre of gravity.

8. What laws have been established by experiment as regards the friction of plane surfaces? How is the friction estimated? Shew that the coefficient of friction between two given substances is equal to the tangent of the inclination of the plane of one of them when the body formed of the other is about to slide down.

9. The lengths of the arms of a false balance are (a) and (b), and the weight W appears to balance P at the shorter arm (b), and Q at the longer arm (a). Shew that if the balance be of uniform density and thickness,

=

P-W b W-Q

10. A uniform beam A B of given length and weight has its extremity A resting in a horizontal groove A C, and its extremity B in a vertical groove BC, and is kept in equilibrium by a string DC fixed at a given point D on the beam. Find the tension of the string, and the limits, as to the length and the point of attachment of the string, under which equilibrium is possible.

Let A B be the arm of a couple, and A C, BE the forces. Let the arm revolve about A into the new position AD. At A introduce two equal and opposite forces, A. Hand A K, each equal to A Cor B E. Similarly at D introduce two opposite forces, D L and D M, also equal to A C. Produce BE and D M till they intersect at P. Join AP. Then A P bisects the angle DP B, and P A produced bisects the angle HAC. Hence the resultant of DM and BE acts along A P. The resultant of A H and A C acts along PA, and is equal in magnitude but opposite in direction. The forces A H, A C, DM, BE, are therefore in equilibrium, and may be removed. If these are removed there remain the equal forces AK, DL, acting at the extremities of the arm A D. Hence this latter couple has the same statical effect as the original couple consisting of the forces AC and BE, at the extremities of the arm A B.

Produce

4. Let A B and CD be the forces. A B and C D till they meet in E. Set off EH equal to B A and E K equal to DC, and complete the parallelogram E H L K. Then L E represents the magnitude and direction of the resultant. The point of application may be anywhere in the straight line E L, or EL produced.

5. The arm of a couple is the perpendicular distance between the parallel forces which constitute it.

The moment is the length of the arm multiplied by the magnitude of one of the forces.

The axis is any line perpendicular to the plane of the couple in length representing the

moment.

6. In the system No. 1, we have a greater power for the same number of movable pulleys, but it requires an additional fixed pulley which is not required in No. 2.

7. Let the weights 1, 2, and 3 be placed at the angles A,B,C, respectively of the triangle ABC. In BA take BD one-third of AB. Join CD. Bisect CD in G. Then G is the required centre of gravity.

8.

=

For since AD: DB:: 2 : 1, D is the centre of gravity of A and B; and the centre of gravity of C and D must be half-way between. C and D, since 3 = 2 + 1.

I. Friction is proportional to the pressure between any two given surfaces.

II. Friction for the same pressure is independent of the extent of the surfaces in contact.

III. When two bodies have been some time

in contact the amount of friction is increased.