manet a partibus quatuor, quarum una sit cognitionis, altera communitatis, tertia magnanimitatis, quarta moderationis; hæ in deligendo officio sæpe inter se comparentur necesse est."

SECT. I.-1. It has been said that the subjunctive is the mood of thought, and the indicative the mood of fact: illustrate this from the above passage.

2. Explain clearly, with reference to the argument of this treatise, the meaning of the following words: honestas,' officia,' 'cognitio,' 'communitas,'' magnanimitas,' moderatio.'

3. De duobus honestis utrum honestius?' What general rule does Cicero give under this head? SECT. II.-1. Who was Panæ tius? Mention some of the chief Greek, Roman, and English teachers of morals, with a very brief notice of each.

2. De officiis' has been translated on social duties.' How has it come to be necessary to insert the word social in order to define what Cicero intended? What other large branch of the subject would a treatise on duty, in the present day, comprehend?

3. Show how the matters treated in this book may best be introduced into the teaching of an ele. mentary school, and with what sort of modifications, in order to adapt them to Christian children.

PURE MATHEMATICS.

1. Of the three squares that can be inscribed in any triangle, which is the greatest?

2. If pairs of tangents be drawn, touching each pair of three given circles, their intersection shall lie in one straight line.

3. If two spherical triangles have the three sides of one equal to the three sides of the other each to each, the angles of the one triangle shall be equal to the angles of the other, each to each, and the equal angles shall be opposite to the equal sides.

6. The three sides of a spherical triangle, measured on the earth, are 29, 32, and 36 miles. Taking the earth's radius at 7500, what is the spherical excess?

10. Describe the largest rectangle in a given triangle.

11. The tangent to the cycloid at any point is the chord of the generating circle at that point.
12. Trace the curves y3=ax2, xy2+2a2y—a3x=0, r=a (1—cos 0).
13. Integrate

dx

du=

√1+x+x2

da
du=-
1+ε

duxm (log x)dx

1. Six weights in the proportions, 1, 2, 3, 4, 5, 6 are placed at the angles of a regular hexagon, each of whose sides measures 7 feet: find the position of the centre of gravity.

2. A bar of iron 20 feet long, and weighing 30lbs., rests against a smooth wall at a distance of 8 feet, and has its lower extremity attached to a hinge, about which it can revolve freely in a vertical plane perpendicular to that of the wall: find the pressure on the wall and on the hinge.

3. Apply the principle of virtual velocities to show the relation of the power to the weight in (a) the differential or compound screw; and (b) the hydrostatic press.

4. The height of a rectangular embankment to a river is 9 feet, and the weight of a cubic foot of the material is 120lbs.: what is the least thickness that will enable it to stand when the water is at the brim?

5. Two perfectly elastic spheres meet directly with equal velocities: find the relation between their magnitudes, that after collision one of them may remain at rest.

6. Show how to calculate the proper elevation of the sight on a rifle to hit an object 1750 yards off, supposing the velocity of the bullet to be 500 yards per second.

7. A clock whose pendulum should beat seconds gains 5 minutes in 24 hours: in what proportion ought the pendulum to be lengthened?

8. Find the greatest thickness that may be given to a hollow copper globe so as to allow it to float in water, the specific gravity of the copper being 9, and the outer radius of the globe 4 inches.

9. Demonstrate in what cases the image of an object reflected in a concave mirror will be erect, and in what cases inverted; in what cases magnified, and in what cases not.

10. Investigate the formulæ for finding the magnifying power of an astronomical telescope, and apply it to one the focal length of whose object-glass is 12 feet, and that of its eye-glass 1 inches.

11. Explain parallax, and show how to find the horizontal parallax of a heavenly body by observation.

12. Prove that the true difference of latitude is to the departure as the radius is to the tangent of the cause.

13. Explain what is meant by a traverse table, and show how to find the course and distance by traverse table and meridional parts.

14. Required the course and distance from lat. 50° 20′ N., long. 4° 10′ W., to lat. 13° 12' N., long. 59° 45′ W.

SCHOOL-MANAGEMENT.-Essay.

Discuss the chronological order in which the mental faculties for the most part develop themselves, and the methods for instruction best adapted to aid that development at the different stages of its

course.

MENTAL SCIENCE.
First Paper: Logic.

1. What is meant by "a term" in logic? How comes the word (term) to be so applied?

2. Give instances of terms which stand to each other in the logical relations of genus, species, difference, property, accident.

According to different ways of looking at them, genus is sometimes represented as a part of species, and sometimes species as a part of genus. Give examples, and explain.

3. What is a proposition? What is meant by its conversion? And what by opposition? Explain the different kinds of conversion and opposition.

4. What is a syllogism? Of what parts does it consist? What is meant by the 'mood' of a syllogism, and what by the figure?' Give examples.

5. State the mood and figure of the following syllogisms, pointing out the major, minor, and middle terms in each.

No white men have degenerated-
All Europeans are white men-

No Europeans have degenerated.

Every noble man is free-
Some noble men are Africans-
Some Africans are free.

How came the words 'major,' 'minor,' and 'middle,' to be so applied?

6. Explain and give formal instances of the fallacies termed "undistributed middle," "composition and division," and "ignoratio elenchi." 7. What is the difference between a logical and a material fallacy? Give an instance of each, and state how each kind of fallacy must be met.

8. What is the difference between deduction and induction? Is the syllogism a correct exposition of each process?

9. How do you reconcile the difference between the number of the parts of speech (grammar), and of the elements of a proposition (logic)? and what becomes of differences in case, mood, and tense, when grammatical sentences have to be logically analysed? Give instances.

10. How far is it correct to say that logic is a guide to truth?

11. Define exactly the faculties of the human mind of which you understand logic to be discipline, and about what objects.

MENTAL SCIENCE.

Second Paper: Mental Faculties and Moral Systems.

1. Distinguish between sensation and perception. Explain the physical process of the former. Mention some of the principal theories which have been held on the latter.

2. Give a brief classification of the laws of association. Show in what way the power of memory is affected by them. Illustrate your answer by an outline of your method in teaching history.

3. Explain the two related processes of abstraction and generalisation, and show how they are aided by the faculty of language. Can they be still further aided by the instructions of the teacher? 4. What is meant by "fundamental ideas," and "first truths"? Give your views as to the manner in which we have come by them. Is it the business of education to impart these truths, or to call them into active exercise?

reason.

5. Explain the terms-habit, faculty, emotion, appetite, passion, desire, affection, understanding, 6. Mention a few of the theories which have been held respecting the "ground of morals;" and give a brief epitome of Bishop Butler's view on the subject.

7. What is the proper function of the appetites? and how, therefore, should they be educated? 8. Which of our faculties are most influenced and cultivated by spontaneous exercise, which by the example of others, which by rules and precepts?

9. Explain what is meant by Utilitarianism, and state some of the principal fallacies which have been maintained in controversies involving the use of this term.

10. What is meant by the emotional, and what by the intellectual theory of conscience? How far does either theory bear on the cultivation of conscientiousness?

ENGLISH INTO LATIN.

Translate the following passage into Latin:

account.

"Now all punishment should be void of contumely; nor should it have reference to the advantage of him who punishes, but to that of the state. Care must also be taken lest the penalty exceed the offence; and lest, for the self-same cause, some receive stripes while others are not even called to Most of all must we discountenance anger in punishing; for in no case will a man who comes in anger to inflict punishment observe that moderation which lies between excess and defect; a virtue which the Aristotelians approve, and rightly approve, only they are inconsistent in commending* the feeling of anger, and saying that nature has given it for some good purpose; when really it ought on all occasions to be reprobated, one's chief desire being that they who preside over the state should resemble the laws, wherein the motivet to punishment is not a feeling of anger but equity.”

* Only they are inconsistent in commending, &c., modo ne laudarent, &c.
+ Wherein the motive, &c., quæ ducuntur, &c.

MUSIC.-Division I.

1. Write the ascending and descending scales of the relative minors of E and of A flat, prefixing the signatures in each case.

2. Write, in the accompanying staves, minor thirds, major thirds, fifths, and leading notes, to A, F, DI, G, AD, FD.

3. Prove the positions of the following four parts of the first line of the Hundredth Psalm to be true, i. e. in proper register or pitch, by exhibiting the identical notes on the full vocal scale below.

5. Compose your own harmony on the accompanying unfigured bass.

6. Compose basses in the major key of D and in the minor key of G, and afterwards harmonise them.

D

9. Define enharmonic modulation. Where does it occur in the following passage from Handel?

10. What is counterpoint, and what is plain and florid counterpoint?

Males.
WELSH.

1. Translate into English one of the two following passages:

"Gwae neb sydd yn dymuno dydd yr Arglwydd: beth yw hwnnw i chwi? tywyllwch, ac nid goleuni yw dydd yr Arglwydd. Megis pe ffoai gwr rhag llew, ac arth yn cyfarfod ag ef; a myned i'r ty, a phwyso ei law ar y pared, a'i frathu o sarph. Oni bydd dydd yr Arglwydd yn dywyllwch, ac nid yn oleuni? yn dywyll iawn, ac heb lewyrch ynddo?"

"Mac dawns yr Arabiaid, y Dehké, fel ei gelwir, yn gyffelyb mewn rhai pethau i dawns yr Albaniaid, ac nid ydyw y dawnswyr yn llai eu tanbeidrwydd mewn ystumiau, neu yn llai rhyfedd yn eu cyffroadau, na 'r mynyddwyr gwylltion hynny. Ffurfient gylch, gan ddal y naill y llall gerfydd y llaw, ac ymsymmud yn araf oddi amgylch ar y cyntaf, ac yna gwnaent gammau cymmysgdro, gan nyddu eu cyrph i amrywiol agweddau."

2. Parse fully one sentence in the passage which you have translated; explaining carefully the literal mutations in it.

3. Translate into Welsh:

"One of the most sacred duties we have to perform is to train up the young in the duties of religion and loyalty. We must teach them to deserve well of their country, and therefore to be themselves worthy of it; not encouraging them to self-will or obstinacy, but imbuing them with the spirit of docility and obedience; not nursing them in indolence and cowardice, but making them active, industrious, and always ready to bear arms in defence of their sovereign."

Correspondence,

[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.

THE AIM OF THE TEACHER'S STUDIES.

66

DEAR SIR,-The coarse warfare of recrimination has never done any thing for the cause of truth, and I do not intend to adopt it. I question, however, whether arguments will find much favour with your late correspondent Mac," who, in his attack on my chapter in your March number, bearing the above title, has not scrupled to make three unwarrantable and gratuitous assertions: 1. That I undervalue the

whole body of teachers in this country; 2. That I have read no other reports of her Majesty's Inspectors than those of Mr. Longueville Jones; and 3. That reports of teachers' success may be less gratifying to me than reports of their failure. I do not say that these assertions are expressed in so many terms, but I affirm that they are logical deductions from his letter. We shall now see who is right; and I hope to show that "Mac's" letter was unnecessary, uncalled for, and simply absurd.

The remark of mine which "Mac" assails is as follows: "Notwithstanding the existence of hundreds of faithful and humble-minded teachers who are labouring in the great cause of Christian training, it appears that the advancement of teachers intellectually is by no means free from drawbacks." Now, in this sentence I distinctly and candidly acknowledged the existence of hundreds of faithful and humble-minded teachers; but notwithstanding the acknowledgment, "Mac" accuses me of undervaluing the whole body of teachers, and doing them an injustice. I can only say, that I have heard of special pleading, and of what is called subtle reasoning; I have also heard of logic; but never did I read any thing so utterly illogical, so subversive of all principles of common sense, as this accusation. Can he really think?

But I must take "Mac" on his own ground. He says, that if intellectual advancement is fraught with dangerous results to a teacher, it is equally so to the learned professions. I contend that if by intellectual advancement we understand the training for a specific object carried beyond the requirements or necessities of that object (and in this sense the expression was used), the comparison "Mac" has here instituted between a teacher of the poor on the one hand and the learned professions on the other is the very worst he could have made, since it is expressly discountenanced by the reports of her Majesty's Inspectors, and is also calculated more than any other to nullify his own arguments. Every one knows that the clergyman, the barrister, the medical man, and even the tutor in a nobleman's family, have the widest fields for their talents, and ultimate objects in their peculiar walks of life commensurate with and corresponding to the knowledge and skill acquired during the periods of their special training. They can seldom become restless and dissatisfied through a discrepancy between what they have learnt and what they require in their professions. The means with them answer to the ends, and the ends to the means. This is not the case, however, with teachers who are highly trained, in other words, who have sought the highest "intellectual advancement." "For myself" (says Mr. Watkins, one of the Privy Council Inspectors), "I own that the difference between that which is required of the teacher and that which may be expected from the learner seems most discordant. The two things have no parallelism, but are like two lines continually diverging-the wider apart the further they go." (Min. 1854-5, p. 439.)

The teacher who has learnt the binomial theorem, the watersheds of all the countries in the world, the classification of clouds, the abstruse parts of algebra and trigonometry, the truths of natural philosophy, the ramifications of natural history, the wisdom of Blackstone and Hallam, and the most obscure points in history, must, if he does his duty, settle down in a remote place, "unknown to public view," to teach poor children the alphabet, monosyllables, simple addition and subtraction, and the multiplication and pence tables. There is no correspondence between his own superior "intellectual advancement" and the requirements of his ten-year-old pupils; or, to use the language of Mr. Watkins, "it is about as proportionate to its requirements as a park of artillery for the dispersion of a flock of sparrows." Hence I said that a teacher must have "the love of God and a single eye to His glory," if he would avoid becoming discontented with his position and office. We shall say more on this point towards the end of this letter; but we must first ascertain the opinions of the inspectors as to the real necessity for high training and superior intellectual ability in the present state of education.

"It is not the work of a man at all that is to be done in the education of a child up to that age (ten years), but rather of a woman; and if that which I have described is to be accepted as a permanent condition of the education of the country, these institutions for the education of masters, which have been erected at so much cost, and so long fostered by your Lordships' care, will remain without any commensurate function or adequate use. It would have been enough, and far more economical, to have provided for the establishment of a sufficient number of dames' schools throughout the country; or at best to have promoted the erection of training schools for schoolmistresses, and to have put the education of the labouring classes of both sexes into their hands."-Rev. H. Moseley, Minutes, 1854-5, p. 300.

"I fear we are getting so accustomed to this standard of school-age (ten or eleven years) as almost to regard it as the normal state, and to be passive under it, if not almost satisfied with it. Yet what is it in reality? Is it not a pretty fair assurance that all the long and imposing array of certified masters and mistresses, assistant teachers under your Lordships' minutes, pupil-teachers of both sexes and different grades, numbering now about 6000, all the instructive books, all the excellent maps, all the ingenious apparatus, if not absolutely wasted, are indeed far too costly and too cumbrous for the service in which they are engaged, and about as proportionate to its requirements as a park of artillery