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are a few trades peculiar to Brighton, among which we observe professional rubbers, and those who carry out "Medicinal Gymnastics." That Brighton is a healthy place, admits of no manner of doubt, notwithstanding the attack made on it recently by an influential London daily, which has resulted in inflicting great injury on many people, by depriving them of the mode of earning a livelihood. The ordinary Londoner is easily alarmed, and a breath of suspicion on the sanitary arrangements in Brighton was amply sufficient to deter him from enjoying his usual holiday there. He preferred Hastings, Southend, Worthing, places which have basked in the full sunshine of popularity during the last few years. But the tide. is already on the turn, and Brighton will shortly be in as great popularity as in the days when Mrs. Fitzharris dwelt in its suburbs, and George the Fourth in the Pavillion. There are several comfortable Club Houses. The Brighton Club in Old Steine, the New Club in King's Road, the Brighton and Sussex Club, also in Old Steine, the Union in King's Road, the Prince's Club in Hove, and the Pelham Club in Bedford Street. The Army and Navy has already been mentioned.

Real Knowledge and Cram.

WE have often heard that the schoolmaster is abroad. At the present day we might aptly say that the examiner is abroad. The number of examinations of various kinds has increased enormously of late years. There are the multifarious examinations conducted by the authorities of the Universities. There are the examinations for admission to the learned professions. There are the numerous examinations for scholars and teachers in connection with the Board Schools. Then, finally, and most important of all to the general community, there are the competitive examinations for admission to the Civil Service. Examination, in fact, is an ordeal that nearly everybody has to go through in the course of an ordinary lifetime.

The necessity of passing examinations has given rise to the practice of special preparation for that purpose. This preparation has been appropriately called "cramming." "Cramming" has been the means of introducing a new word into the English language, and at the same time of giving rise to a new profession, that of "Crammer."

Cramming is a practice that has been much denounced. It is very generally felt to be an evil. The vast difference between cramming a boy and educating him is universally acknowledged. Yet it may well be asked, what constitutes cramming? wherein does "cram" differ from real knowledge? If cramming consists in

learning something for the purpose of passing an examination, is it not at the same time a process of education? These are questions to which we shall attempt to give an answer.

It was long ago remarked by Leibnitz that there are two distinct kinds of knowledge, the one" intuitive" the other "symbolical." Intuitive knowledge consists in knowing the thing itself, symbolical knowledge in knowing it by description or definition. Knowledge is intuitive when it comes to us directly through the senses. Thus our knowledge of domestic animals is intuitive, while our knowledge of animals we have never seen is symbolical, although they may be perfectly familiar to us by name. Much of our knowledge is of necessity symbolical. When we say that the distance of the sun from the earth is 92,000,000 miles, we are making use of symbols, the real significance of which we can neither perceive by the senses, nor realise in imagination.

It must be observed that there is no sharp line of demarcation between intuitive and symbolical knowledge. We can perceive immediately whether a figure has thereon four sides, and our knowledge of triangles and quadrilaterals is consequently intuitive. But our knowledge of a figure of one hundred sides is symbolical. We know such a figure by name only, we can neither recognise it by the senses nor figure it completely to the mind. But it is impossible to say at exactly what number of sides our knowledge of polygons ceases to be intuitive. Similarly, with respect to animals or plants we have never seen, our symbolical knowledge may be as vivid as if it were intuitive, or their names may be mere symbols of the unknown, with no more meaning than and

in algebra. The power of different persons of realizing in imagination a description or a drawing, varies greatly. To many minds the realisation of a simple geometrical solid, such as a tetrahedron, is an absolute impossibility. To such persons, a "tetrahedron" will always remain nothing more than a mere symbol, until a model of the thing itself has actually been seen. To convey an exact idea of anything by description. only, is extremely difficult. It requires not only exactness on the part of the describer, but a certain amount of previously acquired knowledge, as well as some mental exertion on the part of the person who would realise the description. Most persons who have had a plant pointed out to them would know it again, yet they would find it very difficult to describe it to another person so as to enable him to recognize it. Nevertheless, a botanist can describe a species so as to be readily recognised by anyone who understands the technical terms used in the description.

It ought to be the aim of the student, meaning thereby," one who desires to learn," to acquire

intuitive knowledge, a real knowledge of the thing itself. This, however, is frequently a matter of some difficulty. It is very often much easier to learn a definition by heart than to understand it. But this acquirement of clear conceptions contributes more than anything else to that training of all the faculties of the mind which ought to be the chief object of education. On the other hand, the acquisition of symbolical knowledge is merely a matter of memory. We may readily illustrate the difference between these two kinds of knowledge from any natural science, such as Botany. A student who can on inspection refer a plant to its natural order, must have some real botanical knowledge. But a man may learn that the "Brassicaceae have cruciferous flowers and tetradynamous stamens," without in the least knowing the meaning of the words employed. Yet he may correctly apply this purely verbal knowledge to a given case. If he learns that cabbage and mustard belong to the brassicaceae, he will be able to describe these species as having cruciferous flowers and tetradynamous stamens. The acquirement of knowledge of the above kind. is worse than useless. It is the systematic learning of such verbal formulæ that essentially constitutes cramming. A man who has laid in a good stock of such "cram," useless as it is for all practical purposes, may yet make a decent show at an examination. A "botanist" of the type above supposed, may work a very creditable paper on the characters of natural orders and genera, and yet not be able to tell a buttercup from a furze blossom. In the same manner the man who has crammed chemistry, might be able to tell an examiner that "oxygen is a dyad element, whose atomic weight is 16," without having the faintest conception of the meaning of the words he uses.

Although an examinee who has crammed himself or been crammed by others, may often acquit himself with credit, he is peculiarly liable to break down altogether. As he relies exclusively on his memory of words, which of all the faculties of the mind is the least to be trusted, he is extremely apt to make the most absurd mistakes; such as no one with the slightest real knowledge of the subject would ever fall into. A student who has a real knowledge, however imperfect, of a subject, will be able to show it; but an imperfectly crammed student will generally only succeed in writing nonsense. A good example of the results of imperfect cramming is the answer given by a schoolboy to the question "Who was Esau?" he replied, "Esau was a writer of fables who sold his copyright for a bottle of potash." The way in which words of similar sound are here confounded with each other shows that there could have been no real knowledge of their meaning,

That it should be possible for "cram" to take the place of real knowledge is undoubtedly a great evil. It is not merely that real knowledge alone serves any useful purpose in life, but the acquisition of real knowledge of a subject usually shows greater ability. It is not easy to see how this evil is to be altogether remedied. The modern practice of conducting examinations exclusively by written papers, greatly favours cramming. An oral examination is much more likely to show any shortcoming in the conception3 of elementary principles. A practical examination in any subject that admits of it is a certain test of real knowledge. The questions too may be framed in such a way as to put cram at a disadvantage, and examiners usually do so as far as possible. Some examiners set a few questions, to answer which correctly, requires a practical knowledge of the subject, and do not pass anyone who fails to answer them. One check on cramming which we believe would prove very effective, consists in giving negative marks to careless or absurd answers. As above remarked, stupid mistakes are usually the result of cramming. This device is, however, rarely used; the only examination where any such method of marking is adopted, being, as far as we know, these of the Incorporated Law Society.

The existence of these defects has led many to denounce the whole system of competitive examination for appointments under Government. It was recently declared by a leading review that

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a worse method of selecting candidates than competitive examination, could not be invented." The slightest consideration ought to show the absurdity of such sweeping condemnation. Most of the qualifications required by clerks in the Civil Service are such as are easily tested by examination. In such matters as Orthography, Writing, English Composition, and Arithmetic, there can be no question of cramming. is simply a matter of memory. Proficiency in Writing, Composition, and Arithmetic, or in any subject in which ability to do anything is required, can only be attained by practice; cramming is impossible. It is only in subjects where one has to know something, and particularly in scientific subjects, that cram is possible, and then it cannot altogether take the place of real knowledge. On the whole we think the complaints commonly made against competitive examinations, are utterly unfounded. The system of competitive examinations has doubtless some faults, but these might be by better methods, to a great extent eliminated.

G. J. B.

INTERMEDIATE EDUCATION EXAMINATIONS, 1883.

SENIOR GRADE.

ARITHMETIC AND ALGEBRA.

Time, 3 Hours.

(No credit will be awarded for an answer unless the work is given in full.)

1. A gallon of water weighs 10 lbs. ; a cubic foot of water weighs 1000 ounces; a cubic centimetre of water weighs 1 gramme; a centimetre is 3937 inch. Find the number of grammes in a pound, and the number of cubic centimetres in a gallon, each to two places of decimals.

2. Find the square root of 2165 accurate to the nearest unit; and also of 00012345679.

3. A person buys articles at 8 shillings a gross. He divides them into 5 equal lots, which he sells at 2s. a score, 1s. 6d. a dozen, 1s. 3d. a dozen, 2d. each, 15s. a hundred, respectively. Find the rate of profit gained.

4. A property whose net rental will be £100 a year for the next 5 years, and then £150 a year for ever, is to be sold. What is its value, taking the market rate of interest at 4 per cent.?

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7. Two men start to run round a circular course in opposite directions at the same time; they meet in 10 seconds. A third man starts after the second at an interval of 3 seconds, and overtakes the second 5 seconds after he passes the first. If the first run twice as fast as the second, compare the speed of the third with that of the others.

8. If

(x+3y) = p y (y + 3x) = I x2-y=r

find the relation that must exist between p, q, "'.

9. Write down the formula for the number of sets of r things that can be formed out of n things.

Find the total number of distinct sets that can be formed out of 10 objects.

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10. Write down the formulæ for the expansion of (1+a)" and (1 + 2)7 Explain in what sense, and under what conditions, they are truc.

11. Find the value of

1860
to 6 decimal places, and of (218) to 4 decimal places.
(1.002)10

12. Sum the series

1+ 2+ 3+ 4+... to n terms; and to infinity when possible,

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1.

2.

3.

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Then
and

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276-48 cubic inches

1 lb. 27.648 cubic inches

1 cubic centimetre (3937 inches)3=06102338 cubic inches=1 gramme.
27-64806102338-453-072 grammes in 1 lb.

276-4806102338=4530-72 cubic centimetres in 1 gallon.

Answer: 453-072 grammes=1 lb., and 4530·72 cubic centimetres in 1 gallon.

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Since the articles purchased at 8s. a gross are divided into 5 equal lots, which are sold at different rates, we shall calculate the profit upon 5 gross

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4.

Therefore

15s. Od. per 100 = 21s. 7d.

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The market value of this property is equal to the excess of the present worth of a perpetuity of £150 per annum over that of an annuity of £50 (i.e. £150-£100) for 5 years; reckoning interest at 4 per cent. per annum.

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Note. In the latter as the index of x is 2n it must be an even number, therefore, the terms of the divisor being connected by the sign plus, every alternate term of the quotient is minus; or all the even powers of x are minus.

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x+1

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2n-2 + x2n—3—x22-4+ &c., ad infinitum

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The result of each division is an infinite series, the first term of which is x2-1, and the common ratio, in the former

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and in the latter

6.

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Subtracting (a) from (6)—

Then

42-2x=10w

42+5x=17w

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also

4z=18w-3y=18w-6w=12w

z=3w.

Substitute these values in equation (ô), and

w+2w+3w+w=6

i.e., 7w=6

or,

w; whence x=4, y=14, and 2=24. Ans.

7. Since the speed of the First is twice that of the Second, and that running in opposite directions from the same point of the circular course they meet in 10 seconds, the First runs and the Second of the course in that time; the First will therefore complete the round in 5 seconds; that is, go the whole circuit in 15 seconds; and consequently the Second in 30 seconds.

Now, as the Third, 3 seconds later, starting from the same point after the Second overtakes him 15 seconds after the Second started, that is, when half round the course, the Third runs the half round in 12 seconds, and consequently the whole in 24 seconds.

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The speed of the Third is therefore of that of the First, and of that of the Second. Answer.

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