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3. If from any point without a circle two straight lines be drawn, one of which cuts the circle and the other touches it; the rectangle contained by the whole line which cuts the circle and the part of it without the circle shall be equal to the square of the line which touches it.
SECT. IV.-1. About a circle to describe a triangle equiangular to a given triangle.
2. To describe an isosceles triangle, having each of the angles at the base double of the third angle.
3. To inscribe an equilateral and equiangular pentagon in a given circle.
SECT. I.-1. Define the unit of work, and prove that if a pressure of 5 lbs. be exerted through 7 feet, the number of units of work done is represented by 7 x 5.
2. State the principle of the parallelogram of pressures, and describe fully an experiment by which it may be proved.
3. Prove that in a straight lever the power and weight are inversely as their distances from the fulcrum.
SECT. II.1. What is the strength of a wire, inch in diameter, of iron which will bear 25 tons per square inch?
2. A train weighing 50 tons travels on a railway at the rate of 20 miles an hour, the resistances of friction and the air being estimated at 8 lbs. per ton; at what horse-power does the engine work?
3. The piston of a steam-engine is 36 inches in diameter, the length of the stroke is 6 feet, and it makes 6 strokes per minute; under what effective pressure per square inch must it work in order to yield 75 horse-power at the piston?
SECT. III.1. A bar of iron 15 feet long, and supported at its extremities, has 3 cwt. suspended from a point distant 6 inches from one point of support; what is the pressure on the other point of support, first, when the weight of the bar is neglected, and secondly, when 15 lb. is allowed per foot for the weight of the bar?
2. Exhibit, by means of diagram, any useful combination of three pulleys, and determine the relation between the power and weight in that combination.
3. A weight is suspended from a given point in a cord whose extremities are fixed to any two given points; show how the tensions on the two parts of the cord may be determined by means of a scale and compasses.
SECT. IV. Describe fully one of the following machines, illustrating your description by a diagram: 1. A thrashing machine. 2. A gas-meter.
SECT. V.-Describe one of the following machines, illustrating your description by a diagram: 1. A flour-mill. 2. An organ.
Write the first line of your first answer as a specimen of copy-setting in large hand, and the first line in your second answer as a specimen of copy-setting in small-hand.
SECT. I.-1. What are the advantages, and what the disadvantages, of the individual and the simultaneous methods respectively of teaching to read; and how may the disadvantages best be obviated? If you are acquainted with any union of the two methods which has been adopted with advantage, describe it.
2. After the mechanical difficulties of reading have been overcome, what are the difficulties which the elementary teacher has chiefly to contend with in the manner of reading; and how may they best be overcome?
3. What are the characteristics of a good manner in reading? What works may be used to teach accentuation and intonation?
SECT. II.1. What are the characteristics of good writing as adapted to the purposes of elementary instruction? In what respects does what is called "calligraphy" fall short of this object? Describe the steps to be taken successively to form the handwriting of a child.
2. Describe Mulhauser's method of teaching to write, and illustrate it by a series of models adapted to the teaching of it.
SECT. III.-1. What is the best means of correcting dictation-lessons?
2. When the mechanical difficulties of "writing from dictation" have been overcome, what other things may the same process be employed to teach, and how best?
3. What faculties of the mind are exercised in "composition-lessons?" Write down the subjects of a graduated series of composition-lessons.
SECT. IV. Describe fully the expedients best to be adopted in teaching one of the following rules of arithmetic, so that the reason of every step in the working may be understood, and illustrate them by examples: 1. Subtraction. 2. Long Division. 3. Compound Multiplication by more than one figure in the decimal coinage.
1. The Supplementary Questions are not to be attempted by any candidate of the first year who has not answered one question in each of the preceding Sections. No such candidate may answer more than two of the Supplementary Questions.
2. Candidates of the second year, and teachers in charge of Schools, may not answer more than six questions, but may choose them from any part of the Paper.
SECT. 1.-If music were more generally cultivated in our public schools, what effect would it have on the general progress of our pupils?
SECT. II.-1. What do we employ in order to represent to the eye the different pitch of the musical
2. What is an interval, and what is the distinguishing interval between the major and minor modes? 3. Which major key has 4 sharps, and which minor key 4 flats? What is the relative major key to D minor.
SECT. III.-1. Write the common chords of C, G, and F, major and minor, with their inversions. 2. Why and how are consecutive fifths and octaves to be avoided?
3. What is meant by modulation? What rule or rules would you lay down as a guide in modu
lation? (1) Starting from a major key, and in a short piece-"a song or a tune"-what is the usua! course observed in composition? Give an example. (2) Starting from a minor key, and in a piece of small dimensions, what is the usual course? Give an example.
1. Classify the various voices, male and female.
2. Draw a diagram showing the lines taken from the full stave of 11 lines to form the particular staves for separate voices.
3. Write any two of the following exercises:
1. Write the middle note C in the four clefs.
2. Write the lower treble D
for the three other parts.
3. Write the lower treble E for the three other parts.
5. Show on the following stave the alternations between the dominant 7th in its four positions and the tonic.
6. Give the chords of No. 1, compressed harmony, in extended harmony in No. 2; and show the practical advantage resulting from a simple extension of the chords.
SECT. I.-1. State generally the relations (of one word to another) which are expressed by the cases of nouns in Latin.
2. Does the Latin language contain any article (part of speech)? What Latin word has been classed under this title, and for what purpose?
3. Decline through all cases, of both numbers: passus (gen. passus), mensis (gen. mensis), lalus (gen. lateris).
4. Decline (case, gender, number,) the following adjectives: curvus, sacer, fortis, ferox. SECT. II.-1. Decline the personal pronoun tu and the relative pronoun qui.
2. Give the possessive forms of ego, tu, ille, nos, vos.
Point out the difference of concord in the following Latin and English versions: He cut off his own feet-Ipse suos pedes sibi abscidit. She cut off her own feet-Ipsa suos pedes sibi abscidit. off their own feet.
Turn this last line into Latin in further illustration of your answer.
3. What is the difference between declension and congujation as applied to Latin verbs? each part of your answer by examples.
4. What are the concords between noun and verb? pronoun and verb? noun and adjective? Give an example of each.
SECT. III.-1. Give the following tenses at length, from the verb possum: The present indicative, the perfect indicative, the future indicative, the pluperfect subjunctive.
2. Compare the Latin with the English language as regards the employment of auxiliary verbs. Give examples throughout your answer.
3. Render into Latin the following expressions: I shall love; I shall have heard; I may have been advised; By ruling; To have advised; Ye may have been; (Worthy, or in order,) to be loved; They would be ruled.
SECT. IV.-1. Name the undeclinable parts of speech in Latin. Which of these words, though undeclined themselves, may affect the declension of other words? Give instances in each case.
2. Examine the correctness, or otherwise, of the following expressions: Ante domino, apud urbem, sine matrem, juxta patrem, cum fratre, post sororem, pro patriam, trans monte. Is the government of one case rather than another by prepositions entirely conventional, or is it capable of being accounted for by any general difference of meaning?
3. To what extent will the meaning of Latin words guide you to the gender of them? Why is not this rule sufficient? What other rules have you got to supply its failure?
4. Give the gender and genitive case singular of the following nouns: Mars, October, Britannia, argentum, sedes, birtus, sanguis, opus, rus.
SECT. V.-1. Give the 2d person, present indicative; 1st person, perfect indicative; infinitive mood, gerunds, participles active, participles passive, of each of the following verbs: Specto, scribo, traho, peto, capio, trado, deleo, frango, intelligo.
2. Translate the following sentence into English literally:
"Vera autem et sapiens animi magnitudo principem se esse mavult quàm videri. Etenim, qui ex errore imperitæ multitudinis pendet, hic in magnis viris non est habendus."
Parse every word as far as the first full stop. Prove from this passage the rule for concord between relative and antecedent.
The papers on this subject are the same as those set to Female Students, some account of which is given at p. 11 in our last Number.
[The Committee of the National Society are thankful for any communication likely to assist SchoolManagers and Teachers, or otherwise promote the work of Church Education; but they do not necessarily hold themselves responsible for the opinions of the Editor's correspondents.]
To the Editor of the National Society's Monthly Paper.
NOTES ON OUR LORD'S MIRACLES.
V. The piece of money in the fish's mouth. (St. Matt. xvii. 21-27.)
t. The order of the remaining miracles is uncertain, with the exception of the last 1. This miracle took place on the same lake with the preceding.
of in Matribute-money' (v. 24) must be distinguished from the tribute-money spoken poses,—sucării. 19, which was a tax imposed by the Roman government for civil purcompulsory, anche maintenance of magistrates, soldiers, &c.,—the payment of which was a voluntary offeringected by the obnoxious publicans. This was a tax of another kind, the support of the Templeve, it is not demanded, v. 24), for a religious purpose, viz. victims for the daily sacrificership, large contributions being needed for the purchase of fore, paid not to Cæsar but to repairs of the fabric, &c. This was a tribute, thererequired from every Israelite for th In the Law (Exod. xxx. 11-16), a half-shekel was of the collection of this tax are to be purposes at each numbering of the people. Traces x. 32. In our Lord's day, it appears fr Jewish writers to have grown into an annual und in 2 Kings xii. 4; 2 Chron. xxiv. 5-9; Neh. payment. Our Lord is now resident at "the house" (v. 25), in which a miracle ha pernaum, probably in Simon Peter's house, collectors of the tribute address themselves there re to him. Does his master consider een already wrought (Mark i. 29). The Himself bound to contribute to the support of the Temple? Peter, knowing His zeal for the honour of His Father's house (John ii. 17), answers without hesitation, Yes.
Musing on his answer he enters the house, perhaps to inquire whether he has answered aright. His question is anticipated by our Lord, who is aware of what has happened; and he is reminded that his master, being the Son of God, is Himself the receiver, not the payer, of religious offerings. To avoid misrepresentation, our Lord pays the tax, but pays it by a miracle. Peter is sent to cast a hook into the lake, and in the mouth of the first fish which seizes it is found the exact sum needed for the payment of two persons.
24. "The tribute-money:" literally the didrachma, a Greek coin worth fifteen pence, equal to the half-shekel of the Hebrews.
25. "Prevented," anticipated: see the collect at the end of the Communion Service. 26. " Of strangers." This was the case. The emperor of Rome levied taxes upon conquered provinces, such as Judæa, rather than upon his own city of Rome.
"Then are the children free," exempt from payment. By the children' our Lord means Himself. This tribute was money paid to God; and from this payment, even by the laws of men, He, the Son of God, was free. Our Lord asserts His divine nature: that He is Son of the King of Israel, Lord of the Temple (Matt. iii. 1).
28. "Lest we should offend them :" that none might say, as they afterwards did say (Matt. xxvi. 61), that He cared not for God's Temple.
"A piece of money:" a stater (see the margin), which was a coin equal to two didrachmas, and therefore the exact sum required for two persons, "for me and thee.”
This small sum might have been obtained from a disciple. Why does our Lord procure it by a miracle? Certainly not because He was poor. All His miracles were for others, not one to relieve His own wants. In order that men may know the truth, may see the majesty which belongs to Him, even while He foregoes His rights. Power and humility are here united.
Did our Lord refuse to pay a civil tax? (Matt. xxii. 19). Son of man He was one of Cæsar's subjects (Rom. xiii. 7). a religious tax? Because He was the Son of God. Mention He speaks of His divine nature. (John viii. 58; and v. 18. 19.)
Why not? Because as a Why did He refuse to pay other passages in which Matt. xxi. 37; and xxviii. H. W. T.
SIR,-Having read with much interest Mr. Flint's " Subjects for Discussion," I am induced to offer a few remarks on one of the points.
During the last five or six years I have combined a certain amount of industry with the education of the girls' school in my parish. It has worked remarkably well, and improved not only the habits of the children themselves, but through them has extended improvement into their cottage homes, in the tidiness of which I can see a visible change for the better of late.
Our girls' school is under a mistress, and numbers between 50 and 60 scholars. We endeavour to teach household work within the school, by making the cleaning, both of the school and the mistress's dwelling, part of their education. Each week one girl is fixed on to take charge of the daily sweeping and dusting the school-room, and in winter, cleaning the fire-place properly with black-lead, being provided with suitable brushes; the hearth is also scoured with stone, the fire-irons polished, and the fire laid according to rule (which is no small duty learned): to accomplish all this, this one girl must be in the school at least half an hour before the bell rings. At first we had some difficulty in getting this done regularly, but now they take a pride and pleasure in it.
Friday afternoon the school breaks up half an hour earlier, and the room is wane most thoroughly and under strict rules. Four girls are fixed on each week to scrubfloor. Each girl wears a large canvas apron, and each is provided with a bu, and thus bing-brush, sand (for no soap is used for the floor), a flannel, and a
a arge one), and armed, each girl begins in one of the four corners of the room (a v duty to oversee scrubs her way to the centre. My schoolmistress makes it a engaged, two others this work, and see that it is well done. Whilst these are employed in scrubbing every table, box, and even ing the cloak-room, and washing all the windows within reach, being provided with a Thus ten girls every week are employed for that important branch of female education, school-room is remarkable for the extreme
two more are cleaning the of steps expressly for so doing. hours in learning and practising and the result is, our and wholesomeness of its atmosphere. them to wash clothes; and as the
simplest machinery generally works the asiest, we have purposely kept this branch of industry on a small scale. Every for night the schoolmistress, for the use of her house, employs the services of a respectabe woman to wash, and with this is combined a washing lesson. Four of the elder girls, under her teaching, wash the clothes, household
linen of the mistress's residence, their own white tippets, school-pinafores, dusters, &c. A small washhouse, with boiler, and posts and lines in the garden, is all that is required. Two days in the fortnight are sufficient, one for washing, the next for ironing. The same girls are employed for about three months at a time, and then another set is taken; thus all the elder girls have their turn. We give a limited allowance of soap and starch, and provide the tubs and smoothing irons, which, with care, last for years. The expense in money is small; but it requires something more important than money; it demands, even on this miniature scale, constant vigilance that good rules are followed out, a watchful eye that time is not wasted, neatness and order in doing the work, and as strict discipline as if the girls were in school. To obtain this, the hearty co-operation of the mistress is requisite, that she occasionally looks in and sees that all is right; and the village matron must be a well-disposed person. We have been fortunate for seven years in having a most conscientious, painstaking mistress.
I consider our National schools, and the residences of our schoolmistresses, contain ample field for household-work training. I doubt the expediency suggested in the enquiry, of taking school-girls for a day in the week into a lady's house. Servants rarely have patience and tact to teach the young; and children of that age are soon scattered in a new scene, and more likely to be amused than instructed. Far better, I should say, to bring industry into the school-room, and let the mistress's residence be a model of neatness, cleanliness, and order.
I will not trespass longer, but I could give you the system we adopt in needlework, and the important branches of "darning and patching," which Mr. Flint so wisely commends.-I am, &c. A HAMPSHIRE RECTOR.
[We shall be much obliged if our Correspondent will kindly favour us with the system of needlework, and darning and patching, to which he refers.-Ed. M. P.]
SECTIONS OF A DESK AND FORM.
SIR,-The benches and desks in a school which I have lately visited appeared to me so good, simple, and cheap in their construction, and so likely to suit country schools, that I requested the master to draw plans of them, which I enclose. The advantage of them is, that they are not easily overturned, and without being fixed stand very firmly. The desks in country schools, where the schoolroom is used for different purposes, should never be fixed; and by this simple contrivance they will stand perfectly firm without being so. The legs were made of deal; the plank of American birch, which takes a good polish and is very cheap. Every part was fastened with screws.-Yours, &c. T. A.
CANVASSING FOR QUEL'S SCHOLARS.
St. James, Devonport.
SIR,—I should be glad to know if it is customary for the Principals of the various Training Colleges to issue circulars inviting successful candidates to their respective in