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QUERIES.

8. Proposed by J. A. J.-(1.) Solve the equation {√a+x-√a} {√ a − x + √ a} = cx.

(2.) A perfectly flexible rope, whose diameter is 3 inches, when closely coiled on a ship's deck.

forms 40 complete coils; required its length (22)

9. Proposed by s.- —(1). ABC is any triangle; Aa, Bb, Ce are drawn perpendicular to, and As Bb', Ce' bisecting, BC, CA, AB, respectively; a circle is drawn through a, a′, b, b', c, c'. Shew that one of the arcs aa', bb', cc' is equal to the sum of the other two, or having regard to the algebraical sign aa' + bb'+ cc' = 0.

=

(2). If d, da, da, be the depths at which the lower surface of a cylinder will float in equilibrium in a fluid when bearing the weights P1, P2, P, respectively; shew that

3

P1 (d2 — d3) + P2 (dz — d1) + P3 (d, — d2) = 0.

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S, and sin. A: sin. B::

10. Proposed by D. M. A.-Given the sum of any two angles A and B, mn; shew that A and B are found from their sines being equal to m and n respectively multiplied by

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L

2

H

2

E

IH AH AC LC CH

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Let CE be parallel to HI

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HI

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Then the angles marked 1, 2, 3, 4, are

equal to each other.

To find sine (a + 6 + 2) in terms of

a, B, and 2.

Sin. (a+6+) ==

AC

=

ᎠᏴ AD

IH+LC + FD
AD

IH LC FD
+ +
AD AC AD

FD DC

X + X
X + X
AH AC AD CH AC AD DC AD

sin. a cos. ß cos. + cos. a sin. 6 cos. y + cos. (a + B) sin. 2.

But cos. (+6) =cos. cos. G sin. a sin. ẞ .. Sin. (a + B + 2)
sin, a sin. 6 sin. y.

sin. cos. cos. y + sin. ß cos. cos. y + sin, y cos. a cos. 6

Education at Home.

EDUCATION IN PARLIAMENT.

28th June.-MR J. D. MORELL.-The Marquis of Westmeath asked the Lord President if his lordship

were aware that Mr J. D. Morell, late one of Her Majesty's inspectors of Roman Catholic schools, who was dismissed from that office on the 4th day of March 1864, had been appointed as inspector of Roman Catholic schools by the Royal Commissioners of the Patriotic Fund, with the sanction of

the Committee of the Council on Education. The Earl of Granville was understood to say that the Government had nothing to do with the appointment.

30th June-THE OPENING OF THE BRITISH MUSEUM IN THE EVENING.-Lord Ebury presented a petition from the Early Closing Association in reference to the opening of the British Museum, and other national collections, three evenings in the week, between the hours of seven and ten o'clock. He also desired to know if the Government could hold out any hope of this very reasonable request being complied with. Earl Granville said that what was suggested had been very successfully carried out at South Kensington Museum; but it was found that special arrangements were required to enable that and similar institutions to be opened in the evening. He was not then able to say whether the National Gallery could be opened in the evening. The late Mr Braidwood was of opinion that it would entail great risk of fire to open the British Museum in the evening; and the trustees were of opinion that, considering the value of the collection, it was not desirable to run the risk. Earl Stanhope said that there was not only the question of risk, but also that of expense, to be considered before the British Museum could be opened in the evening. In that ease it would be necessary to have a double staff of

officers.

HOUSE OF COMMONS.-19th June.-THE NATIONAL GALLERY. On the item of £20,000 for the purchase of land for the enlargement of the National Gallery, Mr Cowper described the shifts to which the Trustees had been put to find room for their treasures and the risk they had actually run of losing the Turner bequest from that cause. Not only was there an insufficient amount of wall space, but the rooms of the gallery were too small for the crowds that frequented them. The number of visitors last year was 630,000; the number on Whitsunday alone was 10,000. He believed that the maximum cost would not exceed £100,000, and he proposed that a general plan should be prepared which might be carried out from time to time as circumstances required. Lord

Elcho considered that the cost of a National Gallery on its present site would be double that of one at Burlington House; and he strongly objected to a scheme of mere patchwork like that of the Government. Mr Tite also insisted on the propriety of having the plans at once settled. Sir G. Bowyer protested against the destruction of Burlington buildings in London, or indeed in Europe. Mr Locke spoke to much the saine effect. Mr H. Seymour, though intending to vote for the motion, was also dissatisfied. Mr Gregory trusted that the present gallery would be rebuilt de novo. Mr Cowper assured the committee that there was no intention to destroy Burlington House; and, after a little further conversation, the vote was agreed to.

House, which he said was one of the handsomest

20th June - UNIVERSITY FOR IRELAND.-The subject which stood first for discussion, and which brought together a House creditable in point of numbers, and by no means consisting in the bulk of Irish members, was a motion of the O'Donoghue, in which he insinuated rather than asked that a charter should be granted to the Roman Catholic university now in operation in Dublin. Those who have read some of the demonstrative addresses which have been attributed to this honourable gentleman, to popular assemblies in Ireland, would scarcely have recognised the fiery demagogue whom their imaginations may have conceived, in the quiet, calm, almost sententious gentleman, who delivered a temperate, fair, and conciliatory speech, in which even justice to Ireland was acknowledged and appreciated. Nothing could have been better in taste than his speech, and it made exactly the impression on the House which a practical member could desire. The response of Sir George Grey on the part of the Government, which, while refusing the special charter asked for, indicated an intention of including the Catholic college within the academical system of the Queen's University, was received in solemn silence by the majority of the Irish members, although the plan was afterwards very frankly accepted by Mr Monsell, and he may be taken to be a representative Roman Catholic. It was amidst the undisguised stares of astonishment of the House, and of the Irish members in particular, that Mr Whiteside, in his most elaborate, because somewhat subdued, style, argued in favour of that mixed education in Ireland which he has so often denounced, and complained, with a sort of ironical pathos, of a policy of Archbishop Cullen's which was intended to prevent ultr: Protestant and ultra-Catholic from mingling in one harmonious educational fold. This was a novel

tions. It is also advantageous to the students, because it offers the benefit of the Andrews Fund to seven students annually instead of to two; and it does this without greatly diminishing the value of each prize. Under the new system, it is possible for a student to

old Andrews scholarship, as, besides an annual payment out of the Andrews Fund, free tickets are offered for three of the college classes.

view of matters on the part of the right hon. gentleman, and Mr Monsell did not fail to comment upon it accordingly. The discussion waned down to Mr Newdegate, who protested in his most protesting fashion, and so was thought worthy of being followed by Mr Gladstone, who had sat through the obtain a prize considerably more valuable than the debate evidently with the intention of speaking, and who also protested against Mr Newdegate's attack on the nerves of his conscience. Nothing could be more pronounced than the declarations of Mr Gladstone in the direction of neutralising Ireland as a difficulty of the Government; and his manifesto was more distinct and more earnest than that of Sir G. Grey, though the latter was obviously intended to produce a special effect. The result of the Ministerial tactique was seen immediately in the withdrawal of the motion, and probably will be recognised in Ireland in the midst of a certain proximate event.

UNIVERSITY INTELLIGENCE. CAMBRIDGE-CHRIST'S COLLEGE. THE TANCRED DIVINITY SCHOLARSHIPS.-These scholarships were founded in 1721, by Christopher Tancred, of Whixley Hall, in the county of York, with kindred (but medical) scholarships at Caius. The value of the scholarships is £100 per annum, and they are tenable from election until taking the degree of Bachelor of Arts, and for three years afterwards. This fact, together with the prestige attaching to election, owing to the invariably keen competition, invests them with much interest. The successful candidates on the present occasion were—C. Phelips, from Sherborne School; and George Bruce Rhind, from King's College School, London. There were 26 candidates.

THE number of matriculations at the University in the academical year which is just closing, viz., 530, is the largest on record. It exceeds by 11 that in 1864, which was of itself unprecedentedly large. Some difficulty was experienced last October in finding accommodation for the students.

UNIVERSITY COLLEGE, LONDON.-The ceremony of distributing the prizes in connection with the Faculty of Arts and Laws, took place on 1st July, Mr Grant Duff, M.P., in the chair. The Dean (Profes sor Seeley) read the report, from which it appeared that the number of students in the classes of the

faculty during the session was 217, being an advance of twelve upon the last session. The number of new students was 132. During last year a change was made in the application of the Andrews Fund, which it is hoped will be advantageous to the college, for as it offers prizes to students not when they leave, but when they come and while they stay, it both attracts to the college promising students, and secures to the college the credit arising from their success at the London University, and in the other public competi

THE Professorship of Natural Philosophy and Astronomy at University College, London, is vacant, and the council intend to appoint a Professor of Experimental and Mathematical Natural Philosophy, or (if they deem it expedient) two Professors, the one of Experimenta!, and the other of Mathematical Natural Philosophy.

NEW TRAINING COLLEGE.-The Training Col lege at Peterborough was opened on Wednesday June 21. There was a full morning service in the cathedral, when the Archbishop of York preached from St Luke ii. 48, 49. After the service, the archbishop, bishops, the college committee, the cathedral clergy, and the parochial clergy, walked in proces. sion to the college grounds, where the dedication was declared by the Bishop of Peterborough. The com pany then adjourned to a marquee for luncheon, at which the Bishop of Peterborough presided, when Mr Ward-Hunt, M.P., proposed the health of the bishops and clergy of Peterborongh, Lincoln, and Ely, for which the Bishop of Lincoln returned thanks. The Chairman then proposed the preacher's health, to which the Archbishop replied, and gave the toast of the day, "Prosperity to the new College."

TAUNTON DEANERY SCHOOL UNION.-The an nual meeting was recently held at St Mary's Schoolroom, Taunton, under the presidency of the Ven. the Archdeacon of Taunton. The chairman opened the meeting by stating that the principle of competition and emulation was a wholesome one, and that it was honourable to have ruu in the race, though it was not read a paper "On our Parish Schools." He hoped possible that all could win. The Rev. Eccles Carter that ancient models would still be adhered to, and that moral and religious training would ever be made matters of primary importance. The district inspec tors of schools-Rev. G. R. Lawson, Rev. W. H. their examination in Scriptural knowledge, prayerWalrond, Rev. A. C. Ainslie-stated the result of book, catechism, and arithmetic. Out of 197 scholars certificate, and only 9 had failed altogether. Prizes presented for examination, 41 had gained a first class chairman to the successful teachers and scholars, with in books and money were then distributed by the a few words of suitable encouragement to each.

WORKING MEN'S COLLEGE.-The Council of the Working Men's College, in Great Ormond Street,

2

have issued their annual report. The record of the state of the classes shews a steady increase. The number of students of all kinds entered the first term of the eleventh year is 524, who receive instruction in 17 classes. The progress of the Institution has compelled the council to consider how further accommodation can be provided. All the classes were crippled for want of room for their work. The council, after giving the subject the best consideration, feel themselves compelled to face the demand for fresh buildings, and "have been driven to the necessity" | of appealing to the public for aid. It is proposed to raise the sum of £1000 for the extension of the pre-meet to-day shall not only tread in my footsteps, but sent building; and subscriptions, it is announced, will be received by the Treasurer or the Secretary of the College, in Great Ormond Street.

factorily as I have done. I have expressed to you verbally my conviction that what I have done is simply the discharge of a debt, and, accordingly, that I take no credit or merit in discharging it. I may truly say, that all the education which I received was imparted in the Parish School of Auchtermuchty, and that, under God, my present position may be ascribed to the benefit of that education. It is natural for me to desire that the advantages which I enjoyed should be extended to the rising generation; and although I have been fortunate and successful, it is my anxious wish that many of our young friends with whom we

SCOTLAND.

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PRIZES IN PARISH SCHOOLS IN SCOTLAND.-Auchtermuchty Parish School.—By an oversight, notice of a very interesting occurrence, which took place at the Examination of the Auchtermuchty Parish School, April 6, was omitted. The interest of the occurrence, however, has not passed away; and therefore we make no apology for copying the following extract from a local journal, hoping that the example of Mr Marshall will be followed throughout the country: "On Thursday last the Presbyterial examination took place in presence of the members of committee, when, as usual, the scholars, amounting to 123 present, made an appearance in the highest degree creditable to themselves and to their excellent teacher, Mr Borrowman. In addition to the members of Presbytery, we were happy to notice the presence of the ⚫ Rev. Messrs Wise and Sidey, the Provost and Magistrates, and many of the leading ladies and gentlemen of Auchtermuchty. The Rev. James Macnair, at the close of the examination, introduced Mr Marshall, who had a statement to make which would doubtless be listened to with the deepest interest by all present. "Mr MARSHALL then rose and spoke as followsaddressing himself to Mr Macnair, Mr Walker, and Mr Borrowman, trustees under a deed explained in the remarks made :-You are aware, from our previous correspondence and communings, that it has been my desire to discharge what I feel to be a duty, yet what I regard at the same time to be a privilege, of providing permanently, though in a small way, for the promotion of the cause of education in this my native parish, and for the encouragement of the young in attendance at this parish school. And I am glad to have the present opportunity of publicly announcing the completion of my arrangements. Before adverting more particularly to these, I must tender you my sincere and heartfelt thanks for the readiness and cordiality with which you have co-operated with me in perfecting these arrangements. But for your assistance, I could not have completed these so satis

go greatly a-head of me. What I have done in that view, is in any sense little or nothing to boast of. By the deed which I shall immediately hand to you, I have secured in perpetuity an annual sum of £5 to be applied for three scholarships-the first, of £2, 10s. ; the second, of £1, 10s. ; and the third, of £1. In conjunction with these scholarships, I have provided three silver medals to be held by the successful competitors during their sessional term. I will now simply read the preamble of the deed securing these scholarships, which will sufficiently explain my objects and purposes, and the security which I have provided for the accomplishment of these:—'I, John Marshall, Solicitor in the Supreme Courts of Scotland, in consideration of my regard for my native parish of Auchtermuchty, and with a view to the furtherance of the cause of education among the scholars in attendance at the Parish School, do hereby assign and transfer to the Rev. James Macnair, minister of the parish, Henry West Walker, Esquire, town-clerk, and to Mr William Donaldson Borrowman, parochial schoolmaster of Auchtermuchty, and to their respective successors in these offices, in trust for the "Marshall Scholarships" in connection with the parish school aforesaid, One hundred pounds £12, 10s. preference stock, eighteen hundred and sixty-three, and in the undertaking called, "The North British Railway Company." That deed, gentlemen, I now deliver to you, and at the same time I hand over to you the three relative medals. I doubt not all concerned, present and prospective, will cordially approve of the trustees whom I have selected. We all know the present trustees, and we all know that they are truly the right men in the right place.' And we are entitled to assume that their successors in office will be no less worthy than their predecessors. The future trustees must necessarily be, from their position, men of intelligence, and well qualified for the discharge of the offices assigned to them. Apart from the worthiness and fitness of the present trustees, I selected them from the circumstance that, as officials, they can never die; and, consequently, that while all of us must heartily desire that their term of life will be largely extended, their death will create no difficulty whatever as regards the execution of the trust. I shall take the further opportunity which is to be offered to

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DEPARTMENT OF SCIENCE AND ART. ART SCHOOLS.-The Committee of Council on Education have published a Minute relative to Art Schools. On the 1st June, the consideration of the Memorial from various Schools of Art was resumed, and the Council agreed to modify the arrangements, consenting to resume the payments of building grants and grants for examples, but declining to revert to the system of payment by certificates. It is not considered that Art-teachers come within the provisions of the Superannuation Act, 22 Vic. c. 28, but they will increase the amount of the payment proposed in the schedule appended to the Minute of February 9, in the hope that certificated Art-teachers will earn payments equivalent to the value of their certificates. The schedule referred to is cancelled, and another, which is given in return, is substituted for it.

FEMALE SCHOOL OF ART.-A public meeting was held, 24th June, in the Museum of Geology, Jermyn Street, for the purpose of distributing medals and prizes to the pupils of the Female School of Art,

which is under the special patronage of the Queen and the Princess of Wales. In the absence of Earl Granville, owing to a recent domestic affliction, the chair was taken by Mr Bruce, Vice-President of the Committe of Council on Education. The right hon. gentleman, after referring to the progress which had taken place since the Great Exhibition of 1851, and the improved taste which had sprung up since the establishment of schools of art and design, concluded by saying that art, like everything else, could be most successfully promoted, not by the assistance of the State, but by the energetic action of individuals.

THE Times announces a mathematical discovery. Professor Sylvester has just discovered the proof of Sir Isaac Newton's rule for ascertaining the imaginary roots of Equations. According to the Reader

A proof for a few clementary cases was given by Professor Sylvester in a paper published in this year's volume of the Philosophical Transactions. He has recently discovered a complete one, founded on the ordinary principles of elementary algebra; and more than this, a theorem, which stands in precisely the same relation to Newton's rule as Fourier's theorem does to Descartes' rule, the rule being deducible from the theorem as a particular case. But this is not all;

this general theorem is itself only a particular case of a still more comprehensive one.

This rule has been a Gordian knot among alge. braists for the last century and a half. The rule itself used to be given in an imperfect form in ordinary Algebras, such as Wood's. But, the proof being wanting, authors became ashamed at length of advancing a proposition the evidence for which rested on no other foundation than belief in Newton's sagacity. It was supposed that no one hitherto had succeeded in demonstrating this rule; but the honour of having done so more than twenty years ago is claimed by Mr J. R. Young, certainly one of the greatest of living mathematicians, and formerly Professor of Mathematics at Belfast. Mr Young has sent his demonstration for publication to the Philosophical Magazine.

SOCIAL SCIENCE ASSOCIATION.-The ninth annual meeting of the Association for the Promotion of Social Science is fixed to be held at Sheffield, from the 4th to the 11th of October next, under the presidency of Lord Brougham. In the "Education" de"What better partment the questions will be: provision ought to be made for the education of girls of the upper and middle classes? What further regulations of the labour of children are required to promote their education? Does or does not the present mode of Government payment for particular subjects promote the efficiency of education in primary schools?" A section of Art has been added to this department for the consideration of the fol

lowing and other questions: "What improvements

can be made in the schools, museums, and exhibi

tions of art, with a view to the development of the public taste, and the prosperity of our manufac

tures ?"

LORD DERBY, we understand, has cleared by his translation of the Iliad such a sum as, having been invested by him for the purpose, will bring in about £50 a-year, with which he has founded a prize for general good conduct at the Wellington College.

APPOINTMENTS.

22d June. The Queen has been pleased to appoint Wm. Good, Esq., Barrister-at-Law, to be one of the Inspectors for the purposes of the Charitable Trusts Act, in room of John Simons, Esq., deceased.

The Rev. Dr Collis has appointed Mr Henry Chenevix, B.A., late Scholar of Worcester, Oxford, and Mr J. Bowstead Wilson, B.A., Scholar of Pembroke, Cambridge, to vacant Masterships at Broomsgrove School.

Mr William Coxe, of Balliol College, Oxford, and the British Museum, and son of the Rev. H. O. Coxe, M.A., Librarian of the Bodleian, has been appointed Professor of Sanskrit at King's College, London.

The Rev. Arthur Calvert, M.A., late Fellow of St John's, has been appointed to the Head Mastership of Crediton Grammar School, Devon.

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