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3. I paid fifteen pence for three mugs ; what should I pay for two of the same sort ? Ans. Ten pence.
Proof.—The cost of three mugs is fifteen pence; therefore the cost of one mug will be the third part of fifteen pence, or five pence; and then the cost of two mugs will be two times five pence, or ten pence.
4. If five articles cost twenty pence; what will eight articles cost ? Ans. Two shillings and eight pence.
Proof.—The cost of five articles is twenty pence; therefore the cost of one article will be the fifth of twenty pence, or four pence; and the cost of eight articles will be eight times four pence, or thirty-two pence, which is two shillings and eight pence.
Teacher. How do you find the cost of one article ?
Pupil. When I have found the cost of one article, I can then easily find the cost of eight, or of any other number, by multiplication.
5. If five lbs. of rice cost fifteen pence; how much should I pay for two lbs. ? Ans. Six pence.
6. I paid sixteen pence for four lbs. of sugar ; how much should I pay for three lbs. ? Ans. Twelve pence, or one shilling.
And so on to other problems of this sort.
II. Miscellaneous Problems. 1. I bought three lbs. of rice at two pence a lb., and also some wood for which I had to pay four pence; how much should I have to pay altogether? Ans. Ten pence.
2. I had one shilling and four pence in my pocket this morning, but out of it I paid nine pence for some paper; how much have I left ? Ans. Seven pence.
Proof.—In one shilling and four pence there are sixteen pence; then nine pence taken from sixteen pence leave seven pence.
3. How many shillings are there in two pounds ? Ans. Forty shillings.
Proof.-In one pound there are twenty shillings ; therefore in two pounds there will be twice twenty shillings, or forty shillings.
4. From one pound three shillings take away sixteen shillings. Ans. Seven shillings.
Proof.-In one pound three shillings there are twenty-three shillings; then sixteen shillings taken from twenty-three shillings leaveseven shillings.
5. A woman bought some nuts for ten pence and sold them for one shilling and two pence; how much did she gain ? Ans. Four pence.
6. A farmer's wife sold some chickens for two shillings and six pence; with this money she bought seven lbs. of sugar at four pence a lb. ; how much did she take home? Ans. Two pence.
Proof.—The cost of seven lbs. of sugar at four pence for every lb. will be seven times four pence, or twenty-eight pence; now two shillings and sixpence make thirty pence; then twenty-eight pence taken from thirty pence leave two pence.
7. A person bought three books for ten pence and sold them for five pence each ; how much did he gain? Ans. Five pence.
8. How many shillings are there in one pound seven shillings? How many pounds and shillings are there in thirty-two shillings?
And so on.
9. What two numbers multiplied together give six ? Ans. Two and three.
10. What two numbers multiplied together give ten! Ans. Two and five.
11. What are the factors of fifteen ? Ans. Three and five. 12. What numbers will exactly divide eight ? Ans. Two and four.
13. What numbers will exactly divide twenty-one ? Ans. Three and seven.
14. Name the two numbers which multiplied together will give twelve ? Ans. Two and six, three and four.
15. What is the greatest number which will divide twelve without a remainder ? Ans. Six.
16. What is the greatest number which will divide eighteen without a remainder ? Ans. Nine.
17. What number will exactly divide six as well as nine. Ans. Three. 18. What number will exactly divide ten as well as fifteen ? Ans. Five.
19. Mention all the numbers which will exactly divide eight as well twelve ? Ans. Two and four.
20. Mention all the numbers which will exactly divide twelve as well as sixteen ? Ans. Two and four.
21. What is the greatest number which will exactly divide eight as well as twelve ? Ans. Four.
22. What number will two and three both divide without a remainder ? Ans. Six, twelve, &c.
23. What is the least number which two and three will both exactly divide ? Ans. Six. (To be continued.)
MORALS TAUGAT AT HOME.—“ All your national schools, all your trade schools, all your ragged schools, all your sermons, will effect no lasting good until you begin at the beginning, and make the education of your girls a very different thing from what it is. Mind you, I do not say that your schools will not make boys cleverer, more intelligent, to have a keener view to their own interests, better workmen, more skilful mechanics, more knowing in politics—aye, or even in religious disputes, than if they had not received such instruction ; but their moral improvement,- I do not care where or what the school is, or who the master,—will not advance in the same proportion as their intellectual. Now, the truth I shall endeavour to establish is this, that while the intellectual progress of a boy chiefly depends on his application to what he learns at school, his moral education mainly depends on what he sees at home. Some of you, no doubt, will be surprised at my deliberately asserting that, while book learning depends very much, moral character in general depends very little, on the school he inay go to. The boy receives his instruction from his teacher; his education--that is, his moral habits—from his parents. This I believe to be the great difference between instruction and education; the one the boy receives from his teachers, the other from his parents. * * * * * Neither men nor children can be lectured into sobriety, piety, truthfulness, and the like. They are trained to them, not talked into them. It is a long time since the saying was uttered, “ Train up a child in the way he should go, and when he is old he will not depart from it ;' a truer and a pithier one has not been uttered since, The fact is, our virtues are habits rather than beliefs. Now, short as this saying is, it is about the most important I could utter.”—Lecture on Female Education of the Industrial Classes, by the Rev. Dr. Booth.
POLITICAL ECONOMY. TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION. SIR,—Few secular subjects are more important than Political Economy, and few, I fear, have less attention bestowed upon them in our schools. Is it not desirable that the attention of teachers should be called to this fact, and a more extended knowledge of the subject advocated ? For though Political Economy has depths beyond the reach of superficial minds, yet has it also shallows into which even children may venture. They might have clear notions imparted to them upon value, the uses of capital, the fluctuations of wages, the duty of contributing to the necessities of the state, the utter impossibility of a state of equality, and many other points of which such erroneous, and consequently mischievous, notions are too commonly entertained. The nature of savings'-banks, provident and assurance societies, and the benefits to be derived from them, might be familiarly explained and illustrated. And what would be the effect of such knowledge? It would improve the minds of the taught, and make them take greater interest in the commercial history of their country. By approaching the subject step by step, they would discourage that distaste for sober sense and dry detail which is too often the characteristic of youth, and than which nothing sooner leads to error. Useful citizens they could not well fail to be : and this is what every teacher should wish his children to become. Even if they do not possess brilliant abilities, it matters not : sparkling parts are not absolutely necessary to individuals, nor to society, though they may adorn both ; but correct views of those matters which concern our relations with each other, are like current coin, of which we have daily occasion in the ordinary occurrences of life.
Trusting that the subject will be noticed by those who are able to do justice to its importance, I remain, yours obediently, ALBERTUS.
PUBLIC EXAMINATIONS.—“While, then, I think that too much stress is at present placed upon showy exhibitions and celebrations, and that objections and dangers attend examinations, as frequently conducted, I would not recommend altogether their discontinuance. I would rather urge that the teacher, by his inflexible honesty, should make them fair representations of the actual condition of his school, without relying very much upon them as a means of stimulating the pupils to exertion ; that the pupils should be made to feel that the results of their exertion through the term, rather than a few special efforts near its close, would be brought into view; that no hypocrisy or management should ever be tolerated, in order to win the applause of the multitude; that no particular lessons should ever be assigned for the occasion ; that it should be remembered, that the moral effect of an occasional failure at examition will be more salutary upon the school than unbroken success ; and that the children are irreparably injured when they are made in any way the willing instruments of false pretension. Under such circumstances, examinations may be profitable to all concerned. If teacher and pupils have done well, they have the opportunity of showing it without violence to their own consciences. The employers, and patrons, too, have some means of forming a correct estimate of the value of their school; and all parties may be encouraged and stimulated. But above all things, LET THE TEACHER BE HONEST.”—Papers on Popular Education.
Notes of New Books.
Materials for a Grammar of the modern English Language. By George
H. Parininter, B.A. Pp. 219. Cambridge : Macmillan, 1856.
Mr. Parminter's aim is to fuse into one system the grammatical principles of the English and ancient and classical languages, for the better elucidation of the structure of English literature. This little work seems to be the offspring of notes " jotted down at various times during a period of twelve years,” which are “the memoranda of almost daily practice with private pupils and in national schools in the difficult task of teaching English.”
The fusing of the principles of languages into one system, which have little or nothing in common and are altogether incongruous with English, is a simple impossibility which Mr. Parminter has not effected. In short we have in vain sought for any useful novelty in this book. It is as little explanatory as any grammar we ever saw, and as little intelligible in style. Take, for example, the first chapter on Syntax. After describing fairly enough what syntax is, the rules begin thus :
“ RULE I. “ THE NOMINATIVE IS THE CASE OF THE AGENT TO AN ACTIVE VERB, OF
THE OBJECT TO A PASSIVE VERB, OR OF THE SUBJECT TO A MIDDLE
2. Virtue is praised.
3. They were offered a reward. Parsing and Construing. Ex. 1. Parsing : 'I,' a personal pronoun, first person, singular number,
nominative case. Construing : Agent to the active verb 'walk, and governing it ; by
Rule I., · The nominative is the case of the agent to an active verb,
and governs its verb;' as, 'I walk.' Ex. 2. Parsing : Virtue' (abstract), substantive, third person, neuter
gender, singular number, nominative case. Construing : Object to the passive verb “is praised; and governing it : by Rule I., ' The nominative is the case of the object to the passive
verb, and governs its verb;' as, ' Virtue is praised Ex. 3. Parsing : • They,' a personal pronoun, third person, plural number,
nominative case. Construing : Subject to the middle verb 'were offered, and governing
it ; by Rule I., . The nominative is the case of the subject to a
middle verb, and governs its verb;' as, · They were offered a reward. A. The nominative is generally omitted, if it be expressed before in a conjoined clause.
Éx. A righteous man lives contentedly and (...) dies hopefully : supply man or he.
B. The nominative follows intransitive verbs used inceptively.
2. There came certain ambassadors.
C. An infinitive, or other sentence, may be the nominative to a verb. Ex. 1. To have lived righteously brings peace.
2. My being present did not displease.
3. That he came at all is a marvel. D. Nominative sentences follow verbs used indeterminately. Ex. 1. It happened that many were present.
2. It pleased the Lord to bless Israel. E. The verb “be' takes two nominatives of the subject, one of which precedes, and the other follows it : these may be called Cognate nominatives.
Ex. Plato was a philosopher.
NOTE. The intransitive verbs, appear,' become, grow,' 'seem,' 'look,' and the passive forms of the transitive verbs, 'call,' name,' esteem, "reckon, and the like, follow this rule.”
The attempt to Latinize English syntax leads the author into obvious confusion here, even in the statement of his primary rule; it is most awkwardly worded. A better way to word it is thus :— The agent to an active verb, the object to a passive verb, and the subject of a middle verb, are in the nominative case, which governs the verb.' Virtue is not a neuter noun, either in English or any classical language, but feminine, if indeed it be needful to genderize English nouns not necessarily sexual, which we beg to doubt.
A mistake in this and other 'rules' laid down by Mr. Parminter consists in calling the nominative the “ agent' to the verb. Take his own example, ‘I walk ;' in what sense is 'I' agent to walking ? To us it seems a simple misapplication of the word agent. How much simpler and better is Lindley Murray's definition, that it is the subject of the verb. Substitute a neuter verb, 'I suffer :' is 'I' properly the agent here ? and must it not sorely perplex a child to have thus to misapply the term ? But this is a trifle to the attempt to give a new classical definition to a phrase which is virtually a blunder-'they were offered a reward ;' this, Mr. Parminter proposes to call a 'a middle verb.' It seems to us to be simply and purely a passive verb, the use of they, in the nominative case being an abuse of language, and if not 'bad English,' a bad idiom, and admissible only by force of usage. The sentence is an inversion of the correcter one, a reward was offered to them. As Mr. Parminter is resolved to classicalize English grammar perhaps he will be good enough to construe, they were offered' literally into Latin. If Mr. P. will buy “ Wright's Help to the Latin Grammar,” it will enable him to adapt English to Latin much more closely than he has any notion of at present.
The author attempts too much, and plunges into five cases, just as if English nouns have five cases. The only justification of the use of the term, is where nouns govern the verb or are objective to it. Lindley Murray goes a step further and allows a possessive case. He might as well have sinned like Mr. Parminter and given us an English dative. These Latin names of cases are in our humble judgment, applicable only to inflected words. Magistri needs to be distinguished in grammatical nomenclature from magister and magistro and magistrum, &c., because they are distinct words, used according to their collocation and meaning; but in English it is not so, and the invariable word 'master' with the