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Section 2. 1. Show that any two angles of a triangle are together less than two right angles.
2. Draw a straight line through a given point parallel to a given straight line.
3. Show that in any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Section 3. 1. 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.
2. Show that if a straight line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole and that part together with the square of the other part. 3. Describe a square that shall be equal to a given rectilineal figure.
Section 4. 1. Show that a straight line drawn from the centre of a circle to the middle point of any chord in the circle, is perpendicular to that chord.
2. Show that the angle at the centre of a circle is double of the angle at the circumference upon the same base.
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.
Section 5. 1. Prove that every equiangular triangle is also equilateral. 2. Trisect a right angle.
3. Describe a circle which shall pass through a given point, and which shall touch a given straight line in a given point.
GEOGRAPHY AND POPULAR ASTRONOMY.
Section 1. 1. What is a strait? Name the straits known to you, and give the names of the countries they separate, and the seas they unite.
2. What are the boundaries of the Pacific Ocean? What groups of islands does it contain ? 3. What countries of the eastern hemisphere lie between the tropics?
Section 2. 1. What are the boundaries of Palestine ? What are its length, breadth, and area ? What was its population in the time of David ?
2. Wbat are the chief mountains of Palestine ? What facts are recorded in connexion with them in Scripture ?
3. Draw a map of Palestine and the surrounding countries, showing where those inhabited by the following nations were situated—the Hivites, the Ammonites, the Moabites, the Midianites, the Edomites, the Amalekites, the Philistines.
Section 3. 1. Name the three largest islands in the Mediterranean Sea, and give some account of one of them.
2. Trace one of the great rivers of Europe from its source to the sea, giving the names of the most important places upon its banks. Why are the longest rivers the widest?
3. What are the boundaries of the United States of America? What principal range of mountains traverses them, and in what direction ? What
are their chief rivers and seaport towns ? Give the names of six of the United States.
Section 4. 1. What are the boundaries of EnglandWhat are its chief rivers ? Name its six principal seaport towns.
2. What counties border on Leicestershire ?
3. Describe the Pennine range. Name the highest mountains which compose it, and the rivers which have their sources near the bases of these mountains. Of what kind of rock is this range chiefly composed ? What coal-fields lie near it ?
Section 5. 1. What is the cause of day and night?
2. Why are the days and nights of different lengths in different latitudes ? Explain this by a diagram.
3. Why is solar time different from sidereal time? and why is the time by the sun different from the time by a clock ?
Section 6. 1. If you looked at the heavens on a starlight night, how would the fixed stars seem to you to move? What causes this apparent motion of the fixed stars?
2. By what are the tides caused? Why does high water occur twice every twenty-four hours, and why later every day than the day before ?
3. Explain, generally, methods for finding the latitude and the longitude of a place.
MENSURATION AND INDUSTRIAL MECHANICS.
Section 1. 1. Prove the rule for finding the area of a trapezoid. 2. Describe and explain the Vernier. 3. Prove the rule for finding the area of a triangle.
Section 2. 1. A window has 16 panes, each measuring 14 inches by 9; required, the charge for glazing it at ls. 4d. per square foot.
2. How many acres are there in a triangular plot of ground, whose sides are 30, 40, and 50 chains respectively? and bow many in a trapezoid, whose parallel sides are 40 and 27 chains, and the distance between them 15 chains ?
3. What must be the external diameter of a cast-iron roller, 3 feet long and 2 inches thick, that it may contain 2 cubic feet of iron, without the arms and handle?
Section 3. 1. It is required to raise 100 cubic feet of water per minute, from a depth of 100 fathoms; what must be the horse-power of ihe engine employed ?
2. How many bushels of coals must be burned in a day of 24 hours, to raise 150 cubic feet of water per minute, from a depth of 100 fathoms, with an engine whose duty is 60 millions ?
3. A beam of given weight and dimensions is supported in an inclined position, with one end resting on the ground, by means of a cord fastened to the other end, and fixed to another point in the ground; show how the tension on this cord may be found.
Section 4. 1. Show that two weights will balance on a straight lever, where they are to one another inversely as their distances from the fulcrum.
2. Investigate an expression for the space described in a given time by a body falling freely by the force of gravity..
3. State and prove the principle of the parallelogram of pressures.
REPORTS ON ELEMENTARY SCHOOLS.
General Report, for the Years 1848 and 1849, on the Schools
inspected in the Southern District of England, by Her Majesty's Inspector of Schools, the Rev. HENRY MOSELEY, M.A., F.Å.S., Corresponding Member of the Institute of France. My LORDS,
The Southern District-comprising Hants, Wilts, and Berks-contains 170 schools aided by public grants, and 102 others which have invited inspection. There are 62 of these in which pupil-teachers have been appointed, viz., 35 in Hants, 22 in Wilts, and 5 in Berks. My labours in the district have, during the last two years, been limited to the inspection of these 62 schools
, and the periodical examination of their teachers, pupil-teachers, and candidates ; and other duties have now so
; increased upon my hands that, of this comparatively small number of elementary schools, I am compelled, with regret, to resign those in Hampshire to my colleague the Rev. W. H. Brookfield.
As a general result of my inspection, I may perhaps be permitted to bear testimony to the great progress which the cause of elementary education appears to be making in the public mind. It is obvious that more interest is taken in the schools than heretofore, and that, whether the educational movement is in alliance with your measures or hostile to them, it is still a movement in advance.
When, on the other hand, I look at the result of this public sympathy, and consider what is actually going on within the walls of our school-rooms, and the chance there is of any given child receiving a religious education (in any sense worthy so to be called), or of its being instructed in such elements of human knowledge as, when the child shall become a man, to make him a reasoning, an understanding man, as to the state of life to which it has pleased God to caļl him—and therefore, probably, a provident and industrious man—the view I take of the present state of the educational question is far less sanguine. I confess that I see nothing in what is now done for the child which may reasonably be expected to produce these fruits in the man. This impression would not moreover be shaken in my mind if schools as good as we now have (I mean the majority) were so multiplied that every child might attend them, and if the children actually did all'attend them as long as they now do attend them.
I see no relation between the means and the end-the cause and the effect it is supposed to be capable of producing. Education must be something more than this, to effect the good we expect from it; and I am contented to appeal, in evidence of this, to what has been done by it for the populations of many places where schools, amply sufficient in respect to numbers, equal in efficiency to the great majority of the present schools, and conducted on the same principles, have been in operation for the last 20 or 30 years—to the moral condition of those places, and to the number of persons educated in those schools, who are now regular communicants, or even attendants, at church.
We are too much accustomed to confound our notion of a religious education with that of religious instruction, and not to consider that a place should be sought for religion in the hearts and affections of children, as well as in their memories and their understandings. And, as to secular things, our idea of education almost always identifies itself with that which we ourselves have happened to receive. We can conceive differences in the degree, but not in the subjects of instruction, or in the manner of it. To all below us, we would give a greater or less fragment of the knowledge we ourselves possess, according to their standing; thus, reproducing ourselves, under different but inferior forms, in all the subordinate grades of society. It is thus that a very little learning, that dangerous thing, comes to be associated with our notion of the instruction which people in the lowest grades of society should receive. It would be one of the advantages of an education devised with a special reference to the pursuits of labouring people, that it would enable us to get rid of this thinness—this character of a little learning-in popular education.
In respect to the objects which it contemplates, it might be a thorough and a complete education, and yet the higher classes of society might continue to be separated from the lower, as they now are, by higher forms of knowledge, education being still graduated according to men’s social condition, but having an adaptation to each condition, and being good and complete with reference to that adaptation.
Friendless Places. There are many places which, in respect to education, are altogether friendless; to which it is practically denied by those locally interested in those places, who refuse to the Church or the State a voice in the matter, or who, at
* This distinction is thus ably stated in the Rev. W. H. P. Hamilton's recent pamphlet, entitled “The Privy Council and the National Society," "That education is the training of the whole man, and that without religiou there can be no such thing as education, in the just sense of the word, are truisms. It is obvious that in education thus defined the religious and secular elements are inseparably blended. But it is no less obvious that, although jointly necessary to constitute education, they are distinguishable from each other as branches of instruction. This no one will deny who considers the difference between a lesson in the Bible and a lesson in arithmetic. We may therefore contrast ó religious' with other'instruction; but it would be an abuse of terms to contrast religious ' with other' education,” p. 39.
best, only tolerate the education of their poor neighbours as an evil not to be avoided, and insist on its being conducted on the general principle (as Mr. Dawes says) not of being good but bad, and of withholding as much as one can of it. These friendless places the operation of your Minutes does not reach. Your Inspectors only visit, and your grants only aid places fortunate in having friends zealous for the welfare of the poor, and disposed to appreciate the resources of education in promoting it. But if a school have a zealous friend, the probabilities are that it will be, in some respect or another, a good school, * and of these good schools the best are those in which pupilteachers are appointed. The visits of your Inspectors being limited to these, they see elementary education under its most favourable aspect.
From 18 of the schools which I have inspected, I have col- Ages at lected the statistics recorded in the following table.
which the children leave the schools,
Pupil-teachers having been appointed in all these schools, it may, I think, be concluded that the promoters are zealous for their welfare, and that, in respect to efficiency, they are a good deal above the ordinary standard; and this impression is confirmed on my mind by the fact that the schools are increasing in numbers, 31 per cent. leaving them annually, whilst 45 per cent. are admitted. Yet, 5 per cent. only of the children who attend these schools are above 12, 54 per cent. are between 6 and 8, and 39 per cent. are between 6 and 7 years of age. There leave them annually 31 per cent. of the children, and as only 20 per cent. are above 10 years of age, it follows that 11 per cent. at least (and probably a much larger proportion) must leave them under 10 years of age.
Considering what is the amount of education which a child under the age of 12 years could receive, under the most favour
• The converse of this proposition is also true. Every school to be good must have a friend-somebody to love it,