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8. Proposed by J. A. J.-(1.) Solve the equation (Vati - Va {va - x + Va} = .

(2.) A perfectly flexible rope, whose diameter is 34 inches, when closely coiled on a ship's deck,


forms 40 complete coils ; required its length (n=27)

9. Proposed by A.-(1). ABC is any triangle; Aa, Bb, Cc are drawn perpendicular to, and As', BO', Cc' bisecting, BC, CA, AB, respectively ; 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 siga aa' + 6b' + cc' = 0.


(2). If du, d., d., 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

P, (do - - d.) + P2 (dz d.) + Pg (d, da) = 0. 10. Proposed by D. M. A.-Given the sum of any two angles A and B, S, and sin. A : sin. B :: min; shew that A and B are found from their sines being equal to m and n respectively multiplied by

sin s the common factor

Nm" + 2mn cos. S + na

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sin. < cos. ß cos. q + cos. a sin. ß cos. y t. cos. (a + b) sin. y.

But cos. (a + b) = cos, a cos. ß - sin, a sin. B .:: Sin. (v + B + y)
sin, a cos. ß cos. g + sin. ß cos. e cos.y + sin. y cos. e cos. 6 — sin, a sin. 6 sin.

Education at Home.

EDUCATION IN PARLIAMENT. Elcho considered that the cost of a National Gallery 28th June.—MR J. D. Morell.—The Marquis of

on its present site would be double that of one at Westmeath asked the Lord President if his lordship Burlington House; and he strongly objected to a were aware that Mr J. D. Morell, late one of her scheme of mere patchwork like that of the GovernMajesty's inspectors of Roman Catholic schools, who

ment. Mr Tite also insisted on the propriety of was dismissed from that office on the 4th day of having the plans at once settled. Sir G. Bowyer March 1864, had been appointed as inspector of protested against the destruction of Burlington Roman Catholic schools by the Royal Commis buildings in London, or indeed in Europe. Mr

House, which he said was one of the handsomest sioners of the Patriotic Fund, with the sanction of Locke spoke to much the saine effect. Mr H. Seythe Committee of the Council on Education. The Earl of Granville was understood to say that the Go

mour, though intending to vote for the motion, was

also dissatisfied. Mr Gregory trusted that the preTernment had nothing to do with the appointment.

sent gallery would be rebuilt de novo. Mr Cowper 30th June.—THE OPENING OF The British Mu- assured the committee that there was no intention SEUM IN THE EVENING.–Lord Ebury presented a

to destroy Burlington House ; and, after a little fur. petition from the Early Closing Association in re

ther conversation, the vote was agreed to. ference to the opening of the British Museum, and other national collections, three evenings in the

20th June - UNIVERSITY FOR IRELAND.-The week, between the hours of seven and ten o'clock. subject which stood first for discussion, and which He also desired to know if the Government could brought together a House creditable in point of hold out any hope of this very reasonable request numbers, and by no means consisting in the bulk of being complied with. Earl Granville said that what Irish members. was a motion of the O'Donoghue, in was suggested had been very successfully carried which he insinuated rather than asked that a char. out at South Kensington Museum ; but it was found ter should be granted to the Roman Catholic univer. that special arrangements were required to enable sity now in operation in Dublin. Those who have that and similar institutions to be opened in the read some of the demonstrative addresses which evening. He was not then able to say whether the have been attributed to this honourable gentleman, National Gallery could be opened in the evening.

to popular assemblies in Ireland, would scarcely The late Mr Braidwood was of opinion that it would have recognised the fiery demagogue whom their entail great risk of fire to open the Rritish Museum imaginations may have conceived, in the quiet, calm, in the evening; and the trustees were of opinion almost sententious gentleman, who delivered a temthat, considering the value of the collection, it was

perate, fair, and conciliatory speech, in which even not desirable to run the risk. Earl Stanhope said justice to Ireland was acknowledged and appreciated. that there was not only the question of risk, but also Nothing could have been better in taste than his that of expense, to be considered before the British speech, and it made exactly the impression on the Museum could be opened in the evening. In that House which a practical member could desire. The ease it would be necessary to have a double staff of response of Sir George Grey on the part of the Goofficers.

vernment, which, while refusing the special charter

asked for, indicated an intention of including the HOUSE OF COMMONS.—19th June.—THE NATIONAL Catholic college within the academical system of the GALLERY.—On the item of £20,000 for the purchase Queen's University, was received in solemn silence of land for the enlargement of the National Gallery, by the majority of the Irishi members, although the Mr Cowper described the shifts to which the Trustees plan was afterwards very frankly accepted by Mr had been put to find room for their treasures and Monsell, and he may be taken to be a representative the risk they had actually run of losing the Turner Roman Catholic. It was amidst the undisguised bequest from that cause. Not only was there an stares of astonishment of the House, and of the Irish insufficient amount of wall space, but the rooms of members in particular, that Mr Whiteside, in his the gallery were too small for the crowds that fre- most elaborate, because somewhat subdued, style, quented them. The number of visitors last year argued in favour of that mixed education in Ireland was 630,000; the number on Whitsunday alone was which he has so often denounced, and complained, 10,000. He believed hat the marimum cost would with a sort of ironical pathos, of a policy of Archnot exceed £100,000, and he proposed that a general bishop Cullen's which was intended to prevent ultri plan should be prepared which might be carried out | Protestant and ultra-Catholic from mingling in one from time to time as circumstances required. Lord | harmonious educational fold. This was a novel

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view of matters on the part of the right hon. gentle- tions. It is also advantageous to the students, because man, and Mr Monsell did not fail to comment upon it offers the benefit of the Andraws Fund to seven it accordingly. The discussion waned down to Mr students annually instead of to two; and it does this Newdegate, who protested in his most protesting without greatly diminishing the value of each prize. fashion, and so was thought worthy of being fol- Under the new system, it is possible for a student to lowed by Mr Gladstone, who had sat through the obtain a prize considerably more valuable than the debate evidently with the intention of speaking, and old Andrews scholarship, as, besides an annual pay. who also protested against Mr Newdegate's attack ment out of the Andrews Fund, free tickets are on the nerves of his conscience. Nothing could be offered for three of the college classes. more pronounced than the declarations of Mr Glad. stone in the direction of neutralising Ireland as a

The Professorship of Natural Philosophy and

Astronomy at University College, London, is vacant, difficulty of the Government; and his manifesto was more distinct and more earnest than that of Sir G. and the council intend to appoint a Professor of EsGrey, though the latter was obviously intended to perimental and Mathematical Natural Philosophy, or produce a special effect. The result of the Minis- (if they deem it expedient) iwo Professors, the one of terial tactique was seen immediately in the with. Experimental, and the other of Mathematical Natural drawal of the motion, and probably will be


recognised in Ireland in the midst of a certain proximate

New TRAINING COLLEGE.—The Training Col. event.

lege at Peterborough was opened on Wednesday

June 21. There was a full morning service in the UNIVERSITY INTELLIGENCE.

cathedral, when the Archbishop of York preached CAMBRIDGE —Christ's College.—The TANCRED from St Luke ii. 48, 49. After the service, the arch. Divinity SCHOLARSHIPS.—These scholarships were bishop, bishops, the college committee, the cathedral founded in 1721, by Christopher Tancred, of Whix- clergy, and the parochial clergy, walked in procesley Hall, in the county of York, with kindred (but sion to the college grounds, where the dedication was medical) scholarships at Caius. The value of the declared by the Bishop of Peterborough. The com. scholarships is £100 per annum, and they are ten

pany then adjourned to a marquee for luncheon, at able from election until taking the degree of Bache- which the Bishop of Peterborough presided, when Mr lor of Arts, and for three years afterwards. This Ward-Hunt, M.P., proposed the health of the bishops fact, together with the prestige attaching to election, and clergy of Peterborongh, Lincoln, and Ely,

for owing to the invariably keen competition, invests which the Bishop of Lincoln returned thanks. The them with much interest. The successful candidates Chairman then proposed the preacher's health, to on the present occasion were–C. Phelips, from Sher which the Arclibishop replied, and gave the toast of borne School ; and George Bruce Rhind, from King's the day, “ Prosperity to the new College." College School, London. There were 26 candidates.

TAUNTON DEANERY SCHOOL UNION.— The an. The number of matriculations at the University in nual meeting was recently held at St Mary's Schoolthe academical year which is just closing, viz., 530, room, Taunton, under the presidency of the Ven, the is the largest on record. It exceeds by 11 that in Archdeacon of Taunton. The chairman opened the 1864, which was of itself unprecedentedly large. meeting by stating that the principle of competition Some difficulty was experienced last October in find and emulation was a wholesome one, and that it was ing accommodation for the students.

honourable to have ruu in the race, though it was not

possible that all could win. The Rev. Eccles Carter University College, London.—The ceremony read a paper “On our Parish Schools.” He hoped of distributing the prizes in connection with the Fa- that ancient models would still be adhered to, and that culty of Arts and Laws, took place on 1st July, Mr moral and religious training would ever be made Grant Duff, M.P., in the chair. The Dean (Profes: matters of primary importance. The district inspecsor Seeley) read the report, from which it appeared that the number of students in the classes of the Walrond, Rev. A. C. Ainslie-stated the result of

tors of schools—Rev. G. R. Lawson, Rev. W. H. faculty during the session was 217, being an advance their examination in Scriptural knowledge, prayer. of twelve upon the last session. The number of new book, catechism, and arithmetic. Out of 197 scholars students was 132. During last year a change was made in the application of the Andrews Fund, which certificate, and only 9 had failed altogether. Prizes

presented for examination, 41 had gained a first class it is hoped will be advantageous to the college, for as

in books and money were then distributed by the it offers prizes to students not when they leave, but chairman to the successful teachers and scholars, with when they come and while they stay, it both attracts

a few words of suitable encouragement to each. to the college promising students, and secures to the college the credit arising from their success at the WORKING Men's COLLEGE.-The Council of the London University, and in tlie other public competi- | Working Men's College, in Great Ormond Street,

have issued their annual report. The record of the factorily as I have done. I have expressed to you state of the classes shews a steady increase. The verbally my conviction that what I have done is number of students of all kinds entered the first term simply the discharge of a debt, and, accordingly, that of the eleventh year is 524, who receive instruction I take no credit or merit in discharging it. I may in 17 classes. The progress of the Institution has truly say, that all the education which I received was compelled the council to consider how further accom- imparted in the Parish School of Auchtermuchty, and modation can be provided. All the classes were that, under God, my present position may be ascribed crippled for want of room for their work. The coun- to the benefit of that education. It is natural for me cil, after giving the subject the best consideration, feel to desire that the advantages which I enjoyed should themselves compelled to face the demand for fresh be extended to the rising generation ; and although I buildings, and “have been driven to the necessity" have been fortunate and successful, it is my anxious of appealing to the public for aid. It is proposed to wish that many of our young friends with whom we 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 go greatly a-head of me. What I have done in that be received by the Treasurer or the Secretary of the view, is in any sense little or nothing to boast of. By College, in Great Ormond Street. the deed which I shall immediately band to you,

I have secured in perpetuity an annual sum of £5 to be

applied for three scholarships—the first, of £2, 10s. ; SCOTLAND.

the second, of £1, 10s.; and the third, of £l. In Peizes IN PARISH SCHOOLS IN SCOTLAND.-Auch- conjunction with these scholarships, I have provided lermuchty Parish School.-By an oversight, notice of three silver medals to be held by the successful coma very interesting occurrence, which took place at the petitors during their sessional term. I will now simply Examination of the Auchtermuchty Parish School, read the preamble of the deed securing these scholarApril 6, was omitted. The interest of the occurrence, ships, which will sufficiently explain my objects and however, has not passed away; and therefore we purposes, and the security which I have provided for make no apology for copying the following extract the accomplishment of these :—I, John Marshall, from a local journal, hoping that the example of Mr Solicitor in the Supreme Courts of Scotland, in conMarshall will be followed throughout the country :- sideration of my regard for my native parish of Auch

"On Thursday last the Presbyterial examination termuchty, and with a view to the furtherance of the took place in presence of the members of committee, cause of education among the scholars in attendance when, as usual, the scholars, amounting to 123 pre- at the Parish School, do hereby assign and transfer to sent, made an appearance in the highest degree the Rev. James Macnair, minister of the parish, creditable to themselves and to their excellent teacher, Henry West Walker, Esquire, town-clerk, and to Mr Mr Borrowman. In addition to the members of Pres. William Donaldson Borrowman, parochial schoolbytery, we were happy to notice the presence of the master of Auchtermuchty, and to their respective Rev. Messrs Wise and Sidey, the Provost and Magis- successors in these offices, in trust for the “ Marshall trates, and many of the leading ladies and gentlemen Scholarships” in connection with the parish school of Auchtermuchty. The Rev. James Macpair, at the aforesaid, One hundred pounds £12, 10s. preference close of the examination, introduced Mr Marshall, who stock, eighteen hundred and sixty-three, and in the had a statement to make which would doubtless be undertaking called, “ The North British Railway listened to with the deepest interest by all present. Company." That deed, gentlemen, I now deliver

“Mr MARSHALL then rose and spoke as follows to you, and at the same time I hand over to you the addressing himself to Mr Macpair, Mr Walker, and three relative medals. I doubt not all concerned, Mr Borrowman, trustees under a deed explained in present and prospective, will cordially approve of the the remarks made :-You are aware, from our pre- trustees whom I have selected. We all know the vious correspondence and communings, that it has present trustees, and we all know that they are truly been my desire to discharge what I feel to be a duty, 'the right men in the right place.' And we are enyet what I regard at the same time to be a privilege, titled to assume that their successors in office will be of providing permanently, though in a small way, for no less worthy than their predecessors. The future the promotion of the cause of education in this my trustees must necessarily be, from their position, men native parish, and for the encouragement of the young of intelligence, and well qualified for the discharge of in attendance at this parish school. And I am glad the offices assigned to them. Apart from the worthi. to have the present opportunity of publicly announc- ness and fitness of the present trustees, I selected them ing the completion of my arrangements. Before ad-from the circunstance that, as officials, they can never verting more particularly to these, I must tender you die ; and, consequently, that while all of us must my sincere and heartfelt thanks for the readiness and heartily desire that their term of life will be largely cordiality with which you have co-operated with me extended, their death will create no difficulty whatin perfecting these arrangements.

But for your

ever as regards the execution of the trust. I shall assistance, I could not have completed these so satis- take the further opportunity which is to be offered to

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me of addressing the scholars generally. Meanwhile, this general theorem is itself only a particular case I have simply to express my anxious and ardent hope of a still more comprehensive one. that God will bless the means which I have employed

This rule has been a Gordian knot among alge. to secure the ject which I have in view; and that braists for the last century and a half. The role while, as I have already said, I neither desire nor itself used to be given in an imperfect form in ordideserve any thanks for what I have done, I do ear- nary Algebras, such as Wood's. But, the proof being nestly hope that He, by the aid of his Holy Spirit, wanting, authors became ashamed at length of adwill stir up others connected with this parish, equally vancing a proposition the evidence for which rested on able with myself, to 'go and do likewise.""

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 DEPARTMENT OF SCIENCE AND ART.

done so more than twenty years ago is claimed by

Mr J. R. Young, certainly one of the greatest of Art Schools.-The Committee of Council on

living mathematicians, and formerly Professor of Education have published a Minute relative to Art Mathematics at Belfast. Mr Young has sent his Schools. On the Ist June, the consideration of the demonstration for publication to the Philosophica! Memorial from various Schools of Art was resumed, Magazine. and the Council agreed to modify the arrangements, consenting to resume the payments of building grants

Social Science Association. The ninth annual and grants for examples, but declining to revert to meeting of the Association for the Promotion of the system of payment by certificates. It is not con- Social Science is fixed to be held at Sheffield, from sidered that Art-teachers come within the provisions the 4th to the 1lth of October next, under the presiof the Superannuation Act, 22 Vic. c. 28, but they dency of Lord Brougham. In the “Education" dewill increase the amount of the payment proposed partment the questions will be: “What better in the schedule appended to the Minute of February 9, provision ought to be made for the education of in the hope that certificated Art-teachers will earn girls of the upper and middle classes ? What forpayments equivalent to the value of their certificates. ther regulations of the labour of children are required The schedule referred to is cancelled, and another, to promote their education ? Does or does not the which is given in return, is substituted for it.

present mode of Government payment for particular

subjects promote the efficiency of education in priFemale School of Art.- A public meeting was

mary schools ?" A section of Art has been added held, 24th June, in the Museum of Geology, Jermyn to this department for the consideration of the folStreet, for the purpose of distributing medals and lowing and other questions: “What improvements prizes to the pupils of the Female School of Art, tions of art, with a view to the development of the

can be made in the schools, museums, and exhibiwhich is under the special patronage of the Queen and the Princess of Wales. In the absence of Earl public taste, and the prosperity of our manufac

tures?" Granville, owing to a recent domestic affliction, the chair was taken by Mr Bruce, Vice-President of the Lord Derby, we understand, has cleared by his Committe of Council on Education. The right hon. translation of the Iliad such a sum as, having been gentleman, after referring to the progress which had invested by him for the purpose, will bring in about taken place since the Great Exhibition of 1851, and £50 a-year, with which he has founded a prize for the improved taste which had sprung up since the general good conduct at the Wellington College. establishment of schools of art and design, concluded by saying that art, like everything else, could be most

APPOINTMENTS. successfully promoted, not by the assistance of the 22d June.—The Queen has been pleased to appoint State, but by the energetic action of individuals. Wm. Good, Esq., Barrister-at-Law, to be one of the

Inspectors for the purposes of the Charitable Trusts The Times announces a mathematical discovery. | Act, in room of John Simons, Esq., deceased. Professor Sylvester has just discovered the proof of The Rev. Dr Collis has appointed Mr Henry Sir Isaac Newton's rule for ascertaining the imagin- Chenevix, B.A., late Scholar of Worcester, Oxford, ary roots of Equations. According to the Reader, and Mr J. Bowstead Wilson, B.A., Scholar of Pem

A proof for a few clementary cases was given by broke, Cambridge, to vacant Masterships at BroomsProfessor Sylvester in a paper published in this year's grove School. volume of the Philosophical Transactions. He has Mr William Coxe, of Balliol College, Oxford, and recently discovered a complete one, founded on the the British Museum, and son of the Rev. H. 0. Coxe, ordinary principles of elementary algebra ; and more M.A., Librarian of the Bodleian, has been appointed than this, a theorem, which stands in precisely the Professor of Sanskrit at King's College, London. same relation to Newton's rule as Fourier's theorem The Rev. Arthur Calvert, M.A., late Fellow of St does 10 Descartes' rule, the rule being deducible from John's, has been appointed to the Head Mastership the theorem as a particular case. But this is not all; 1 of Crediton Grammar School, Devon.

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