Is the following proposition universally true? "If two plane triangles have three elements of the one respectively equal to three elements of the other, the triangles are equal in every respect." Enumerate the cases proved in Book 1 and state what case is omitted. SECTION II. 1. Divide a given 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. 2. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. In what sense is the area of a triangle said to be equal to half the product of the base and altitude? What propositions of Euclid may be adduced to prove it? 3. The difference of the squares of two unequal lines, is equal to the rectangle contained by their sum and difference. SECTION III. The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. Is this proposition true, if the base be greater than a semicircle? If so, why has Euclid omitted it? 2. A segment of a circle being given, describe the circle of which it is the segment. 3. In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is less than a right angle; and the right angle in a segment less than a semicircle is greater than a right angle. State the converse propositions in the first three books of Euclid, which are not de:onstrated ex absurdo. SECTION IV. 1. Find the value of 8632 articles at £1 14s. 3d. each, and of 23571 at 6s. 7. 2. (1) The planting of a rood of ground costs £27 18s. 6d.; what must be paid for the planting of 23 acres 3 roods 25 poles? (2) A bankrupt's liabilities are estimated at £37583; what are his aasets if he can pay 13s, 74d. in the £? 3. (1) A manufacturer employs 50 men and 35 boys who work respectively 12 and 8 hours of the day during 5 days of the week, and half-time the other day; each man receives sixpence and each man 2d. an hour. What is the whole amount of wages for a year? (2) If the sum earned on the half day be laid by from week to week by each of the above persons, what would be the sum saved in years; and what would be the share of every man and every boy if their 5 years' savings were invested for 10 years at 5 per cent. compound interest? SECTION V. 1. (1) If a carding machine throws off 54lbs. of wool in 2 hours 46 minutes 30 seconds, in what time will it throw off 24lbs. ? (2) How much land, at 27s. per acre, should be given in exchange for 480 acres, at 35s per acre? 2. If a plot of building land, 272ft. 6in. long by 35ft. 8in. broad, be sold for £76,545, how much will a plot 283 yds. 2ft. long by 74ft. 2in. wide cost? Explain as to an elder class of children every step in the working of this sum. 3. If 24 men, in 2-5 days of 12.5 hours long, can dig a trench 139.75 yards long, 45 yards wide, and 2.5 yards deep, what length of trench will 90 men dig in 4.2 days of 96 hours long, the trench being 4,875 yards wide and 3.2 yards deep? Explain the way in which you state this sum as you would to a Pupil Teacher. No. 92. PAPERS FOR THE SCHOOLMASTER. OCTOBER 1, 1858. The Relation between the Master and his Apprentice. The schoolmaster and schoolmistress are called upon every year to sign an official certificate to the personal character and diligence of their pupil-teachers. The indentures pledge them to overwatch their moral development year by year. By example, by precept, by careful inquiry, and a circumspect jealousy in regard to their apprentices' every-day life, they are bound to help the great interest of the people's education. It is the great body of religiousminded men that are the real promoters of public education; and though they may be anxious for the mental improvement of the working classes, they are infinitely more interested in the spread and growth of Christian influences. We need, paramountly, masters who are fitted for the work, not because they have been accidentally drawn to it, not because of its respectability, not because mental employment more accords with their taste than mechanical, but because their own hearts burn with the desire of using the great Christian lever, fitted to lift up the multitude to a sense of their responsibilities. The Christian schoolmaster awakened to this view of his mission will understand his accountability to his pupil-teachers. They will not be to him so much mechanical appliance, or so much teaching power for the daily service of his school; but they will be to him the pliable and tender saplings under whose future branches the children of the nation are to find their shelter, and from whose fruits their tender natures shall be fed. Who can estimate the consequences of unfaithfulness, not only as regards the interests of the children committed to his immediate care, but of those children now unborn who shall fall under the fostering hand of the apprentices who have never read in his words or actions the real estimate of a schoolmaster's character? Let it be seen that he is but a hireling, and careth not for the lambs, but for the price of keeping the fold then every word he speaks in the religious lesson with unholy familiarity, every action destitute of sympathy either with the children or apprentices, educates for evil, as it tells upon the latter, betrays the sacred cause to which he is called, and brands upon him the charge of a faithless shepherd. On the other hand, a religious-minded and conscientious master, who shews himself alive to the highest interests of his pupil-teachers, will never neglect the daily duties of a more positive character which he owes to them. He will in his every-day instruction, which he is bound to give them, gather them as a friend to open out the Scriptures as the fountain of life, and to make their ordinary, or, as it is generally, though somewhat strangely, called, secular instruction useful and real. He will never stint them of the time to which they have a lawful claim for their instruction. He will discover not only their general failings, but their individual ones, and labor to correct them. We are anxious to take the occasion of pointing out to masters and mistresses where the candidates for Queen's Scholarships whom they send up are defective. They are not deficient in exact knowledge of grammar, or arithmetic, or geography, but when called upon to paraphrase or to draw up notes of lessons, they grievously fall short from a want of grasping the subject, and for want of power to express themselves. The former defeet they betray by missing the leading idea altogether, or by giving undue and enormous prominence to that which is subordinate and incidental. The latter defect arises from the slender vocabulary of their homes and the want of communion with more educated persons in their earlier and present life. To remedy the defect, they should have access to a good school library, and be required to analyse chapters of selected works. The habit of paraphrasing, in the hands of a good master, who is himself capable of weighing words and sentences, and of comparing them with the original, is the best means for giving to pupil-teachers the power of language. To prevent that extempore mode of writing, and that looseness of style, which leads to looseness of thought, we entreat masters to aim at more successful efforts, by cultivating in their apprentices a laconic and terse instead of a loose style of composition. We give the following article as a specimen of what we mean. It will be seen that we have avoided one long and disconnected rigmarole, and made the answer as exact and precise and yet as full as possible. WHAT PARTICULARS ARE TO BE BORNE IN MIND IN MAKING A TIME-TABLE? In constructing a "time-table" the following particulars should be borne in mind: : A. (1). The social condition of the children, and what arises out of it, viz., (2). The average age at which they are withdrawn from school, and also (3.) The subjects taught in the school, both as regards— (a) their elementary or more mixed character, (b) the probable future employment of the children. (4.) The appliances with which the school is supplied. (5.) The teaching-power of the school, in regard to pupilteachers or assistant-teachers, as well as the extraneous help of the clergyman or of ladies in girls' schools. B. The above particulars would enable the master to determine and to present in the time-table (1.) The number of classes. (2.) The number of school-hours. (3.) The subjects taught. (4.) The time allotted to each subject according to its practical importance. (5.) The succession of the lessons, so as to secure quiet ones by the side of noisier ones. (6.) The individual contact of the master with all his children. (7.) The proper distribution of the teaching power Educational Intelligence. ASSOCIATED BODY OF CHURCH SCHOOLMASTERS. BRISTOL DISTRICT. The usual quarterly meeting of the members was held on Saturday afternoon' the 11th of September, Mr. Serjent, District President, in the chair. An able and interesting paper, giving a resumé of the principal educational intelligence during the preceding quarter, was read by Mr. Baden, of Christ Church School, Clifton, and many subjects of interest and importance were thus brought under the notice and discussion of the meeting. It was unanimously resolved to nominate the following as fit and proper persons to serve the general offices of the body during the ensuing year (1859):-Mr. Serjent, Bristol President; Mr. Hughes, Oxford Treasurer; Mr. Williams, York Secretary. Arrangements for holding the next Annual Conference of the body in Bristol on the 29th and 30th of December, were next discussed and all the suggestions of the Committee were unanimously adopted. The meeting, which was well-attended, and characterised throughout by great cordiality and harmony of feeling, was then closed in the usual way. NOTTINGHAM AND NOTTINGHAMSHIRE SCHOOLMASTERS' ASSOCIATION. The quarterly meeting of the members of the " Nottingham and Nottinghamshire Schoolmasters' Association" was held in Trinity Girls' Schoolroom, Nottingham, on Saturday last, the 11th instant, when the Rev. G. H. Smyttan, Rector of Hawksworth, near Bingham, delivered an eloquent and instructive lecture upon "The Suggestiveness of Christian Architecture," for which he received the unanimous thanks of the meeting. The afternoon's proceedings were opened by a lesson to a class of boys, on "The Common Pump," by Mr. Whitlow, of Old Radford National School, which was judiciously criticised by the members present. Mr. Cockrem, of Lenton National School, then introduced the subject of "Locomotion." After affording information upon the state of roads in this country in early times, he proceeded to consider the means then used for the transition of goods and for travelling. His subject was illustrated by some diagrams. Before the meeting was closed Mr. Cockrem made some remarks respecting the appropriation of the surplus funds of the society, and further expressed his opinion that the Association should not be confined in its influence as it at present is to the town and its immediate neighbourhood, but that it should be extended throughout the county. It is to be regretted that so few country masters avail themselves of the opportunities afforded by this society of improving themselves professionally. The present opportunity is taken of cordially inviting them to its meetings. A motion will be brought forward at the next meeting, which will be held on the second Saturday in December next, to the effect that all members residing at a greater distance than six miles from the place of meeting shall have part of their travelling expenses paid. E. W. HEMMING, Secretary. EAST KENT CHURCH OF ENGLAND SCHOOLMASTERS' AND SCHOOLMISTRESSES' ASSOCIATION. The usual monthly meeting of the Association was held at the Parochial Schools, Deal, on Saturday, September 11th, Mr. J. R. Hadfield, of Christ Church School, Ramsgate, occupied the chair. The meeting having opened with prayer, and the minutes of the last meeting read, the chairman, in a few remarks, opened the subject of discussion, and called upon the secretary, who read a synopsis of Mr. Casse's Paper, which the members proceeded to discuss, especially the new school scheme for mixed schools in agricultural parishes, by which it is intended to distribute the benefits of the day school to evening scholars. The attendance of the day school be: Two days per week. Mornings-9 a.m. to 12 a.m Three days per week. |