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Similarly 20-15-5-no. miles per hour B gains on A ;

35-10-25= no. miles B had gained on A, when B was overtaken by fast train.

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But this time was the same as that which the fast train took to overtake B, that is :

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After the starting of the fast train, B gains on A 35-10 miles, at the rate of 20-15 miles an hour; therefore

take B.

35-10 20-15

5 hours, is the time required to over

Hence the whole distance B travels from the station is 30+ 5 × 20 = 130 miles, which the fast train performs in 5 hours, being 26 miles an hour.

This question was also answered by J. Sheppard, J. Buckmaster, J. Walters, Georgius B., J. Stephens, and the Proposer.

QUEST. 16.-Proposed by Mr. J. S. Davies.

The weight of a piece of cheese in the form of a segment of a circle is 6 lb., and the length of the arc is of the complete circumference. Required, the weight of the whole cheese.

Answered by J. Sheppard.

The circle, forming the cheese, will evidently consist of a regular pentagon inscribed in it, and five equal segments, such as the one described in the question.

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Now the thickness of the circle being uniform, the areas of any portions necessarily vary as their weights.

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This question was also answered by Sigma, J. Waters, B. J. Jeffrey, J. Stephens, J. Buttrey, W. Pringle, and the Proposer.

QUES. 17.-Proposed by Mr. Smith.

There are three towns, A, B, and C; the road from B to A forms a right angle with that from B to C. Now a person has to go from B to A, but after travelling a certain distance towards A he takes the nearest way leading to the road from C to A; but when he comes to this road he is three miles from A and seven from C. He then proceeds to A, and when he arrives there, he finds that he has gone over of the distance from B to C more than he would have done had he taken the direct road from B to A. Required, the distances of the places.

Answered by Sigma, and similarly by Mr. Buttrey.

Let B C, B A, and C A be the three roads, and B E D A the course travelled. By the question C D=7 and D A=3. Put x for E A, then D E√x2-9, and by the similar triangles A B C and A D E, we have

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This question was also answered by J. Sheppard, J. Stephens, J. H., Georgius B., J. Jeffrey, J. Walters, J. Rome, J. Ward, S. Cheadle, and the proposer.

NEW QUESTIONS,

TO BE ANSWERED IN OUR NUMBER FOR FEBRUARY.

QUES. 18.-Proposed by Sigma.

A piece of mahogany, which formed a portion of a circular table, has an arc of 60 degrees at one end, and an arc of 30 degrees at the other, the deficient segments containing each 135 degrees; it is required to cut it into two equal parts, by a line drawn perpendicular to the diameter which bisects the two arcs.

QUES. 19.-Proposed by Mr. Baker, Civil Engineer.

In a rectangular pleasure-ground, A B C D, the following dimensions could only be taken on account of obstructions, viz. the portion A H of the diagonal A C measured from A to the perpendicular, let fall thereon from the corner B; and the prolongation, H I, of this perpendicular to the side D C; to determine the area of the pleasure-ground.

QUES. 20.-Proposed by Mr. Walters, jun., London.

The circumference of a given circle is c, required an expression for the area of a circle circumscribing a square, which contains the same area as the given circle.

Intelligence.

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WINCHESTER TRAINING SCHOOL. -On Thursday last the half-yearly examination of the pupils of the Diocesan Training School for Masters, twenty-five in number, took place at the Episcopal Palace of Wolvesey, which, as our readers know, has now for more than a twelvemonth been generously appropriated by our respected Bishop to the important Diocesan object of training masters. There were present on the occasion, Mrs. H. Mann and the Misses Mann, Mrs. H. Garnier, Mrs. Bishop, and Miss Onslow; the Very Rev. the Dean, Archdeacon Hoare, the Warden, Hon. and Rev. Lowther Barrington, Canon Woodrooffe, Rev. Dr. Moberly, the Rev. Thomas Jackson, the Principal of the National Society's Training College of Battersea, J. M. Elwes, Esq., Rev. Messrs. Pigou, T. Garnier, Wilson, Buttemer, Cubitt, Salter, Midwinter, Wright, Haygarth, Adams, C. Walters, Williams, Poore, J. D. Walford, Esq., the Principal of the Diocesan School of Southampton, and the Secretary, Rev. Canon Jacob. The examination commenced with reading a chapter of the Scriptures, after which the Principal of the Battersea Training College questioned the pupils in the history and doctrines of the Bible, passing on to ecclesiastical history and the constitution of the Church. No occasion was lost of giving a practical turn to the examination, by the deduction of lessons applicable to future teachers of youth. The Rev. Examiner dwelt with peculiar interest on the period of the Reformation, both foreign and English, its rise and progress, and the characters which were conspicuous in it, particularly on that of Luther, interspersing brief remarks, the results of foreign travel in places the scenes of the Reformation, and reminding the pupils that next year would be the tri-centenary of the translation of the Book of Common Prayer into the vernacular tongue., Nearly two hours were occupied in a most varied examination, embracing

the geography, chronology and general knowledge of the Scriptures, highly instructive and interesting to the auditory, and full of searching power as to the real attainments of the pupils. Rev. Dr. Moberly followed, and examined the pupils in English History, from the accession of the House of Tudor to the accession of the House of Hanover; and at no former period of these examinations had the well practised skill of the Head Master of Winchester College been more ably exercised than on the present occasion. The celebrated men, their genealogies, and the chief events of the several reigns, were presented to view with an easy familiarity and singular exactness. The evenness of the answering was very satisfactory, each pupil taking his turn, and rarely leaving the questions unanswered. Recitations in Shakspeare followed. As the object of these exercises is elocution and not display, a quiet, distinct, and intelligent enunciation was the point aimed at; and it is not too much to say that in most cases it was acquired. On the conclusion of this part of the examination, which had occupied nearly four hours, the Rev. Principal of the Battersea Training College asked permission of the Dean to address the pupils. He said he had watched the examination with peculiar interest; the pupils had acquitted themselves best in the best subjects. He did not expect or desire they should be Shaksperians: the subjects with which they would hereafter have to deal were the poor man's child: let them ever after picture to themselves that child in his rustic smock, in all his simplicity and need. They would have to awaken spiritual consciousness, guide and direct, and bring out the powers of the understanding controlling that which most of all in our compound being has most experienced the effects of the fall-the human will, and all this in the fear of God; an instilling that prime element of wisdom, without which all knowledge would be folly.

From the difficulty of the task, he argued the necessity of dependence upon the Divine blessing, and of personal devotion and prayer. Consistency of conduct also was most important. Many a child would take his tone from the National Schoolmaster. It would be natural to think, "if the master did so and so, there would be no harm in the child's doing so also." In conclusion he remarked, "Your office then is only next to the pastor's-it is full of the power of mischief, but, by God's grace, it is fraught with immense good. You are to be the teachers of unborn generations. How ought you to magnify your office in all personal humility. I love to think

of

you as about to be engaged in so high a calling. I share your sympathies. I embrace you in my heart, and wish you, in God's name, every blessing." The rev. gentleman thanked several of the pupils for their accurate answers. Burr, Mason, Havill, Gedge, West, Renwick, Stroud, and A. Smith were particularised. The Venerable the Archdeacon of Surrey made some useful remarks on the answers in writing to his questions of one of the pupils (Burr), on the six first chapters of St. John's Gospel, in Greek, and some of the others in Latin, pointing out the object of these studies to be not the acquisition of a dead language, but the means of gaining a closer insight into their own, and of teaching it accurately to others. The secre

tary read the reports of an examination in writing, held last week, by the Rev. R. Dawes, on Popular Astronomy, and the Geography of Europe; and by J. D. Walford, Esq., in Arithmetic, Algebra, Geometry, Mensuration and Trigonometry. Both these gentlemen concurred in "forming a very favourable impression of the improvement of the young men during the last year," attributing much of the increased accuracy, and the attainment of a higher standard in the scientific department of study, to the appointment of a Second Master, Mr. Gyles, and to his great skill and ability in teaching. The zeal and energy both of the

Principal and of the Second Master have been most commendable. We have again to record the liberality of our respected Dean in noticing the most distinguished of the training pupils at this examination, as he has often done on so many previous like examinations, as he has often done on so many previous like occasions. Three elegantly bound books were presented to Burr and Mason in the first class, and to Stroud in the second, as marks of commendation. The two former of these pupils are about to be engaged in our city as parochial schoolmasters, and those who observed their examinations cannot doubt that, under the guidance of their respective pastors, as they have all the elements of the master, they will prove themselves very efficient in their most important vocation. The prize for music, given by Mr. Long, was awarded to R. West.Hampshire Chronicle.

The Examination Papers will be found in another part of this Number.

[The following masters have been engaged from this useful Training School since Michaelmas, 1848Richard West, St. Thomas's School, Winchester; William Mason, St. Michael's School, Winchester; William Furniss, Headley School, near Liphook; John Pople, Pewsey School, Wilts; John Havill, North Petherton School, near Bridgewater; Charles Gedge, Brighstone School, Isle of Wight; William Shepherd, Winterslow School, Wilts; James Stone, Lyme Regis School, Dorsetshire; Edward Lucas, Hurn School, near Christchurch; James Fordham Burr, St. Maurice School, Winchester; Edward Kohlhoff Baker, King's Worthy School, near Winchester; Benjamin Cæsar, Wymering School, near Portsmouth; William Earwaker, Dummer School, near Andover. Six of these pupils have not yet entered upon their duties as schoolmasters.]

EVENING CLASSES FOR YOUNG MEN. -The experiment, to which we alluded in a former number, has been tried with great success in four classes in Shoreditch, (in Hebrew,

English, Mechanics, and Philosophy); and in three in Bishopsgate, (in Drawing, Greek, and Latin).

The committee, under the sanction of the Bishop of London and Bishop of Winchester, will, after Christmas, be prepared to continue these, and to open other classes elsewhere, provided there are for any one subject twenty applicants, who will bring a note of introduction, promise to attend regularly, and pay 2s. 6d. for the Lent Term, i. e. for one evening a week from 11th January to 28th March, 1849. It is proposed to divide the year of study into three terms-Lent, Trinity, and Michaelmas; and these will probably extend from October to July, with short vacations at Christmas and Easter. A record of the attendance of pupils will be kept in each class. Voluntary examinations may hereafter be adopted, at which prizes may be awarded. Certificates of regular attendance can be obtained; and these may be found very useful in after-life, as indicative of steadiness of conduct, and of a wise application of leisure time. Young men are invited to specify (without delay) the subject on which they desire to receive instruction, to the Rev. C. Mackenzie, Hon. Sec. ; or to one of the Local Secretaries, viz♪:

Bermondsey, Rev. R. M. Martin.
Bethnal Green, Rev. D. Fenn.
Bishopsgate, Rev. Timothy Jones.
Dalston, Rev. J. R. Thomson.
St. Giles, Rev. G. Rust.
Hackney, Rev. C. J. Daniel.
Kennington, Rev. C. Lane.
Lambeth, Rev. C. B. Dalton and
Rev. James Gilman.

London Wall, &c., Rev. H. Christmas.
Newgate Street, &c., Rev. M. Gibbs.
Paddington, Rev. H. J. Phillips.
Peckham, Rev. E. Lilley.
Rotherhithe, Rev. W. Hutchinson.
Shoreditch, Rev. W. H. Jones.
Walworth and Camberwell, Rev. F.
Statham.

The class teachers are, for the most part, clergymen, who will give their services gratuitously; but if this effort is to meet the pressing exigencies of the day, it must be

liberally supported by laymen, and particularly by those who have young men in their employ.

[Surely there are many towns in the country to which this plan is adapted, and in which it might be most advantageously introduced.EDITOR.]

THE EDUCATION QUESTION.— A meeting was held at Chichester, on Tuesday, Dec. 19, for the purpose of taking into consideration the correspondence which has recently taken place between the Committee of Privy Council on Education and the Archbishop of Canterbury, on the part of the National Society, and to adopt such measures with reference to it as might be deemed desirable.-The Ven. Archdeacon Manning presided, and was supported by the Lord Bishop of Glasgow, the Hon. and Rev. J. H. Nelson, the Archdeacon of Chichester, and many other influential clergymen of the diocese.The Archdeacon of Chichester, in opening the proceedings, remarked that the clergy had assembled that day, according to the tenor of a requisition forwarded to him, to consider the subject of a correspondence which had lately passed between the Committee of Privy Council on Education and the National Society; and also to consider the subject of education generally. He conceived that their object was to promote the education of the people of England, and with a view to that, to remove obstacles which at the present moment presented themselves in the way of that work-obstacles which, he contended, had not originated with the Church (hear, hear). It was also of the greatest moment that it should be thoroughly understood that it had been the great object of the clergy to avail themselves of the zeal and cooperation of their lay brethren, in the important work of education. A notion has been propagated, that in desiring that the education of the people should be under the guidance of the Church of England, the clergy wished that it should be entirely in their own hands, to the exclusion of the laity; and from an imperfect manner of speaking, the phrase " Education by the Church" had become conven

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