2. Show the divisions of the page of a register, by which the date of the transfer of each boy in a school from class to class may be recorded and easily referred to. What would be the advantages of such a register? What other means could you devise for recording the progress which each child is making? 3. What are the most important statistics to be recorded in a school; 1st., to aid the schoolmaster in his work; 2nd., for the information of the school managers; 3rd., for the information of the Legislature? SECTION III.-1. Give examples of the questions in mental arithmetic which you would propose to a class of children of about eight years of age, and of those which you would give to your first class. 2. What different methods have been proposed for teaching children to read, and on what grounds? 3. On what principle is the method of Pestalozzi in teaching Arithmetic founded? Describe the tables used in teaching by that method, and the way in which they are applied. SECTION IV.-1. Describe some of the characteristic defects of teaching in elementary schools. 2. What are the advantages of oral instruction, and what its disadvantages? What are the advantages of making this instruction collective, what are its disadvantages, and how can they best be guarded against? 3. What are the advantages of questioning as a method of teaching? Is it expedient to limit all oral teaching to that? If not, in what manner, and to what extent, may exposition best be united with it? 4. What relation ought oral teaching to have to the teaching of books? SECTION V.-1. Write the heads of a lesson on the parable of the Rich Man and Lazarus, with a special reference to the practical instruction which it is intended to convey. 2. What are the faculties of children which it is the object of education to exercise and cultivate, and what expedients of instruction have a special application to each ? 3. What are the characteristic dangers of the schoolmaster's profession; 1st., with reference to himself; 2nd., with reference to his scholars; 3rd., to the parents of his scholars; 4th., to the managing of his school? SECTION VI.-1. Show that the happiness of children ought to be respected in a school. 2. In what respects may the selfishness of a teacher be prejudicial to the interests of his scholars and to his own? What facilities are afforded him for the indulgence of it? THE ENGLISH LANGUAGE. SECTION I.-1. How do nouns ending in y form their plurals? Give examples of words which do not admit a plural, and of others in which the singular and plural are alike. Give definitions of an adjective and a preposition, and illustrate them by examples. 3. Give reasons for the corrections you make in the following sentences. "Her Majesties' Service." "I bought this book at Smiths' the booksellers." And supply the ellipses in the following. "I love Thomas better than he." "I love Thomas better than him." SECTION II.-1. Give examples of a noun formed from the past participle of a verb, and of a diminutive noun. 2. What part of speech is that which, not being the name of an object, is, nevertheless, capable of forming either the subject or the predicate of a proposition? 3. Put the proper stops to the following passage, explain it, and give the derivations of the words printed in italics : The gardens of the world produce only deciduous flowers perennial ones must be sought in the delightful regions above roses without thorns are the growth of paradise alone SECTION III-1. Correct the following passage, and parse it The sun upon the calmest sea, Appears not half so bright as thee. 2. Write a paraphrase of the following passage, and parse the words printed in italics. To what three poets does it refer? Three poets in three distant ages born, (Dryden. SECTION IV.-Paraphrase one of the following passages Heaven may not grant thee all thy mind; (Cotton.) Why sleeps the future, as a snake enrolled, Long lines of mighty Kings-look forth, my soul ! The living Waters, less and less by guilt (Wordsworth.) SECTION V.-1. Give the derivations of the words printed in italics in the following sentence, and paraphrase it:-" Of composition there are different methods. Some employ at once memory and invention, and with little intermediate use of pen, form and polish large masses by continued meditation, and write their publications only when in their own opinion they have completed them." 2. Of what other languages is the English language, as now spoken, made up, and how were they severally incorporated with it? Give examples of words derived from each. 3. Give some account of the great writers whose works mark epochs in the history of the English language. PHYSICS. SECTION I.-1. What happens to a ray of light coming from water into air? What experiment illustrates this? Will the ray pass through the surface of the water at whatever angle it is incident upon it? 2. On what principle is it, and by what experiment, that the different coloured rays which compose white light can be separated? 3. Describe and explain the construction of the astronomical telescope. Why must the focus of the eye-glass coincide with that of the object-glass? Why do we see distant objects more clearly with the telescope than with the naked eye? SECTION II.-1. How may a bar of hard steel be converted into a magnet? 2. What is meant by induced magnetism? Is such induced magnetism ever produced in the iron of a ship, and by what cause? Has any expedient been adopted to neutralize its effect on the compass? and what? 3. What is an electro magnet? How is it made? How may it be made to lose its magnetic properties instantaneously? How has it been applied in the electric telegraph? SECTION III.-1. How may oxygen gas be obtained, and what are its properties? 2. Write down all you know about carbon. tion and the combustion of fuel? What has it do with respira 3. What are the component elements of water? How may hydrogen gas be obtained from it? What becomes of the oxygen of the water in this experiment, and what of the acid? SECTION IV.-1. Why is the atmosphere less dense as we ascend higher in it? Do you see any connexion between the temperature at which water boils and the height of the barometer? 2. Describe some simple experiment showing that metals expand when heated. In what way does this property affect the rates of clocks and watches, and how are its effects compensated? INDUSTRIAL MECHANICS. SECTION I-1. A man capable of lifting 200 lb. wishes to raise a ton weight by means of a crow-bar five feet long. Where must the weight bear upon it, the fulcrum being at one end and the man lifting at the other? 2. Describe any one of the different systems of pulleys, and show what is the relation between the power and weight? 3. How low must a single hoop be placed round the staves of a tub nine feet high and full of water, that it may just prevent them from opening at the bottom? Prove the rule you use in answering this question. SECTION II.-How many cubic feet of water must descend a river every minute to drive a wheel of four effective horse-power, by means of a fall of 16 feet, the wheel yielding '68 of the work of the fall. 2. What is the cost of excavating 40,000 cubic feet of earth, and transporting it to a mean horizontal distance of 700 feet; allowing three pickmen to every two shovellers, and to each workman 2s. 6d. per day. 3. Two men undertake to dig a drain 500 feet long, and to carry the material in barrows to a heap at the end of it. Into what two parts must they divide the work, so that one-half of the labour may fall to the share of each? EUCLID. SECTION I-1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 2. Equal triangles upon equal bases, in the same straight line, and towards the same parts, are between the same parallels. 3. If the square described upon one side of a triangle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 4. In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. N.B.-The first case only of this proposition is to be proved. SECTION II.-1. If a straight line drawn through the centre of a circle cuts another at right angles which does not pass through the centre, it bisects it. 2. To draw a straight line from a given point, without the circumference, which shall touch a given circle. 3. To inscribe a circle in a given triangle. 4. To inscribe an equilateral and equiangular quindecagon in a given circle. SECTION III.-1. The sides about the equal angles of equiangular triangles are proportionals. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral figure inscribed in a circle is equal to the sum of the rectangles contained by its opposite sides. SECTION IV.-1. Given the base, the vertical angle, and the perpendicular in a plane triangle, to construct it. 2. If one diagonal of a quadrilateral bisects the other, it divides the quadrilateral into four equal triangles. 3. From a given point without a given straight line, to draw a straight line making an angle with the given line equal to a given rectilineal angle. 4. If two circles intersect, the common chord produced bisects the common tangent. 27, HIGHER MATHEMATICS. SECTION I. Find the 30th term of the series 20, 13, &c. 2. The sum of a series is 15350, its last term 302, and its common difference 3; what is its first term? 3. The sum of an infinite geometric series is 3 and the sum of its two first terms 2; find the series. SECTION II.-1. In how many ways can the 3 highest places in a class of 8 be filled differently? Prove the formula you use in working this example. 2. Find all the positive integral values of x and y which satisfy the equation 3x+5y=26. SECTION III.-1. Investigate a formula for the value in n years of a sum of money £a at r per cent. compound interest, the interest being payable q times a year. 2. Find the present value of an annuity of £a to commence at the expiration of p years and to continue q years, allowing r per cent. interest. 3. Prove the binomial theorem in the case in which the index is a positive integer; and apply it to determine the first four terms of the expansion of (1+x) - *. SECTION IV.-1. Define the Logarithm of a number, and investigate a formula for determining its value in a converging series. 2. Show that Sin (A + B) = Sin A Cos B + Sin B Cos A. 3. Show that if a, b, c be the sides of a plane triangle and S half their sum, the area of the triangle S (S-a) (S—b) (S−c). SECTION V.-1. Show how to differentiate the product of two functions, and perform the following integrations :— 2. Prove Maclaurin's theorem, and apply it to determine an arc in terms of its tangent. 3. Investigate expressions for the area of the segment of a circle and for the solid content of a segment of a sphere. Correspondence. A HINT TO SCHOOLMASTERS AND SCHOOLMISTRESSES, AS WELL AS TO THOSE WHO HAVE TO SELECT THEM. SIR,-While I was thinking over the qualifications requisite in a teacher, and putting down the heads of information necessary to be obtained previous to a personal interview, I unconsciously put down one of the following alliterated triplets, and, having for amusement's sake attempted to form others, and succeeded to an extent which might easily be increased, I send you the result. It may chance that you will think the insertion of my fancy, in some shape or other, may interest some of your readers. It might be used as a help to selfknowledge by a Teacher, and as somewhat of a guide to one who was selecting a Teacher. Age, Authority. Height, Health, Home (native). Faith (creed), Form (robust, &c.), Dress (neat, &c.), Tact (managing different dis positions), Temper, Teachableness (secret of im- Mind (originality), Method. Head (ingenuity), Diligence, Decision. Hand (needle, &c.). Painstaking, Piety (reverence), Practice (consistent). Perhaps some of your correspondents may desire to add to this list, SCHOOL SERIES, edited by REV. G. R. GLEIG, M.A., INSPECTOR-GENERAL OF MILITARY SCHOOLS. HISTORY OF ENGLAND, IN TWO PARTS. (Longmans.) This little work is put forth by its author as a specimen of a series. His object, as stated by himself, is substantially this. He tells us, in the preface, that he is anxious to remedy what he considers to be a manifest defect in the school literature of this country, viz., that school-books have been hitherto compiled merely for the purpose of teaching the mechanical art of reading; and so are made up of a jumble of extracts from which the scholar can receive no distinct impression on any one subject; he proposes, therefore, to put forth a series of class-reading |