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Jes.

Trin.

NEW BRUNSWICK.

Johnson and Sikes, to scholarships of the value of Regius PROFESSOR OF PHYSIC. The University of New Brunswick, established 301. per annum.

Examined and approved : under an Act which received her Majesty's! The above are tenable during the undergraduate

Withers ... ... Corpus assent in January 1860, is now in successful course, | Baker and Whitaker were elected to scholarships

Professor or POLITICAL Economy. operation. The University is under the Govern value each 401. per annum. tenable till scholarship ex- Examined and approved i ment of a Senate, appointed by the Governor in amination in the Easter Term of 1862.

De Robeck ... Trinity | Hampton ... Queen's Council, and comprises what was formerly known Mr. Francis Pattrick, B.A., Fellow of Magdalen

Walker ....... 'Trinity. as King's College, but now absorbed into the College, Cambridge, eighth wrangler, 1861, has been New University. The Encænia, or festival in appointed First Mathematical Master in Ipswich honour of the founders and benefactors of the School, vice Rev. J. Mowat, appointed Classical | REFORMATORY Schools. --The annual report University, was celebrated in June last, in pre- | Lecturer of Sidney College.

of the Inspector of Reformatories, Mr. Sydney sence of the Governor and the various Colonial

Oct. 14.

Turner, states the number of inmates under authorities.

The following have been elected scholars of Jesus detention in these establishments in Great Britain
Nova Scotia.
College :-Classical--Fisher, from Blackheath Pro-

-3222 at the end of 1859—was 3712 at the end ACADIA COLLEGE, Nova Scotia.-We see by prietary School; Fennell, from Rossal School.

1:1 of 1860. The increase may seem surprising in

Blackheath Proprietary the “ Christian Messenger” of Halifax, that the Mathematical-Dale, from

the face of a diminution in the number of juvenile friends and supporters of Acadia College are anxi- / School.

criminals committed to prison Oct. 15.

a decrease amountous to place its finances on a more sure footing than

ing in England to 10 per cent last year, while in they are at present, to elevate its literary stan

SIDNEY Sussex COLLEGE.

the last five years the commitments have been dard, and to create four Professorships. With this 1 An examination for scholarships and exhibitions object it is proposed to raise 15,0001. in all, as

reduced from 13,981 to 8029. At the same time, took place at this College yesterday. The successful

besides that the chances of escape have greatly an endowment fund. The amount already in. I candidates were as follows: vested, pledged, and to be collected, is 50001.,

J. Ashton, of University College, London, to the lessened, the sentences under the Criminal Justice
Taylor Exhibition of 601. a-year.

| Act are short, and regular offenders are soon at which leaves 10,0001, still to be provided; half of Í. Masheder: J. J. Benstead, of Oundle School ; | large again. There is, too, owing to the cessation that sum (5C007.) a gentleman interested in the T. D. Gray, of Marischal College, Aberdeen; and A. of transportation, a steady increase in the number matter proposes to raise by appealing to the S. Davis, of Leeds Grammar School-each to Exhi- of liberated criminals, many of them the trainers generosity, wealth, and intelligence of the Baptist bitions of 301.

of young thieves; and considering how deeply the body of the three Provinces, and calling on fifty! C. W. Holdich, of Oakam School, to a Johnson

interests of society are concerned in making it as persons to subscribe 1001, each. The duty of Exhibition. collecting the other 50002. to devolve on the N.B. The Classical Foundation Scholarship was

difficult and dangerous as possible to follow crime

as a trade or calling, Mr. Turner heartily trusts Governors and friends of the College. The pro- | not adjudged.

that an effort will be made to adopt the principles poser of the scheme is sanguine of success.

Oct. 18.
SECOND PREVIOUS EXAMINATION.

of the Irish system, and make the ticket-of-leave =| EXAMINED IN THE ORDINARY SUBJECTS AND a more effective security of good conduct, or for UNIVERSITY INTELLIGENCE,

APPROVED.

the re-apprehension and continued detention of Adcock Sid. Lawson

Trin.

those who return to crime; the difficulties would Bonser

Trin.
Lee

Emm. I probably not be so great in practice as in theory.
OXFORD, Oct. 10.

Carroll

Trin.
Lock

Trin. | He also pleads for a better regulation of common Mr. T. H. Sweet Escott, from the Somersetshire Churchill Trin. Marshall Trin. H. lodging-houses as well as marine-store shops, both College, Bath; Mr. W. Sells, from Windermere Col. | Davies

Cath. Parsons

Clare. of them frequently the means of making the delege; Mr. Herbert H. Morris, from the Naval School, Edwards, N. W. Trin. Peareth

Cath. I predations of the young thief possible and profitNew.cross; and Mr. George O. Balleine, from Gardner

Trin, H. Procter

Christ's. able. But the truth is, that the Reformatories Victona College, Jersey, were this day elected Scho- | Graham

Roberts

Trin.

become so full through the system being adopted urs of Queen's College. At the same time Mr. H. Guest, A. E. Pet. Roose

Jeg.

of sending to them mere children on the first Hogarth, from Appleby School, and Mr. H. W. Guest, A, F.

Sevier

Trin,

conviction, when they are fitter for industrial Barber, Commoder of Queen's College, were elected Hervey

Trin, Steele

Job. Lihibitioners-the former on the Hastings foundation.

Hope-Grant Trin. Taylor

Cath.

schools ; and it is hoped that under the new Act Hughes

Jes.
Ward

of this session these will be established in larger

Joh.
Oct. 11.
There will be an election to two Scholarships at

Langham

Trin
Ward

Queen's. numbers; for with good management, and a suffiBalliol College, each worth about 751. a-year, and

Joh. Webster

Pet. cient number of half-criminal children committed tetable for five years, on the 29th day of November

Latham
Trin. Yearsley

Trin.

to them, the allowance from the Treasury will next. Candidates (who must be under 19 years of EXAMINED IN THE ADDITIONAL SUBJECTS AND

probably be enough to support them. With regard age on the day of election) are required to call on the

to results, we learn that above 1000 boys were

APPROVED. Master of Balliol on the evening of Saturday, Novem - Ainslie

| discharged from reformatories in England up to ber 23, with certificates of baptism and of the date of

Pemb. | Mayo

Trin,

the end of 1859, and more than 600 are known to their birth, and testimonials from

Bonser

Trin.
Mitton

Cath.
their college or

be doing well, and not 120 have been again conChurchill Trin. Parsons

Clare.

victed of crime. The number of girls who are Trin.

Christ's.

Procter
Oct. 18.

W. Trin.
The annual election of two scholars will take place Geach

Stephenson Joh.

reformed is always less, but 40 out of the 108 are at Oriel College, on Friday, December 6. The Scholar- Goodacre

Trin. Tarleton

Joh. doing well, and only 13 have been again convicted.

Pemb. ships will be tepable for five years, and their value, Hanbury

Tomlinson

Clare. | The relapses into crime are most numerous among during residence, in addition to rooms rent free, will | Hervey

Clare. Webster

Pet. those who, on discharge, return to their friends, De £60 per annum. No one will be eligible who shall | Lee

Trin. Wright

Trin. which generally is a return to the influences which Dave attained the age of 20 years, or who, being a

Emm. Yearsley

Trin.

led to their depraved condition ; but this may be member of the University, shall have exceeded two

Oct. 22.

avoided by placing them out on ticket-of-leave for Fears from his matriculation. Candidates must pre

The Carus Greek Testament prize has been a ljudged the last year or more, accustoming them to selfas of good conduct, and certificates of to H. Bothamley, B.A., of Trinity College.

government in partial liberty, and making the aptism, to the Provost of Oriel! The Examiners are of opinion that:R.C. Raban, B.A., restoration to freedom gradual. In this and every of Emmanuel College, has acquitted himself with great

respect, the work of reforming is better accomAloition on Bishop Robinson's Foundation. / credit.

plished in a small than in a large and centralised members of the College, will also be filled | CAMBRIDGE UNIVERSITY LOCA.L EXAMINATIONS establishment. The inmates of reformatories are

1861.

very different from what they were three or four ship on the foundation of the Rev. John The examinations will be held this year at the fol

1 years ago. It is true that in London, where the an exhibition on the foundation of the lowingplaces:-Brighton, Bristo 1, Cambridge, Exeter, Profor

reformatory process has been least applied, there Lucy, will be filled up at Magdalen Hall, Liverpool, Wolverhampton, London, Northampton,

Jis still a fair supply of lads who have been several be Ist of November. The value of the Norwich, Plymouth, and Sheffield. The examinations

per annum; that of the exhibition will commence in each place on Monday, the 16th of times convicted, and with whom the old system . Both are declared open for this turn, | December, at 2 o'clock, and will be continued from of repeated commitments to gaol has been pere for three years. Gentlemen who de day to day until they are completed.

severed in till thievish habits and prison tastes and o be candidates are requested to call on the

qualities have become thoroughly engrained; "but cipal on Monday. the 28th of October, with testi

Oct. 23.

elsewhere,” says Mr. Turner, "such lads are rarely S of good conduct from their colleges or schools.

EXAMINATION FOR I 'ROFESSORIAL

| met with, and in the Metropolis they would soon CERTIFICA' TES.

disappear before such continuous and consistent CAMBRIDGE, OCT. 10. DOWNING PROFESSOR OF MEDICINE.

action on the part of the Magistrates and the Police Exainined and approved :

as have been brought to bear in Liverpool and ng Scholars of Trinity College were this Gardner* ... Downing | Marsden eeted Fellows of that Society:-S. Taylor, B.A.;

..

Leeds and Manchester.”
Tooth* ... Downing (arsh

Trinity
Barnes
Oct. 11.

... St. John's Myers

Queen's following have been elected Scholars of Queen's

CRYSTAL PALACE SCHOOL OF ART.
Dickins on ... St. John's | Pierce

Corpus
Duon ... Corpus Tate

... Queen's

SCIENCE, AND LITERATURE.
Hand Merriman, to scholarships of the value
Taylor-Jones Queen's

The establishment of Classes and Lectures, * Passed with 8 rcat credit.

I which should in a proper manner utilize, for

Lane

school.

Cope

sent testimonials of good conduct, and
time of birth an
on Saturday, November 30.

ap on the 6th of December.

A scholarship on the ! Meeke, and an exhibition

Rer. William Lucy, will on Friday, the 1st of NO scholarship is £37 per annum; £97 per annum. Both are dec and are tenable for three years.

aPrincipal on Monday, the

monials of g

The following Scholars o

Qneen's

L. Trotter, B.A.; E. Kirby, B.A.

College

Buswell and Merriman, to de, of 401. per annum.

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educational purposes, the vast and unequalled re- he would keep the papers with their marks, and
sources of the Crystal Palace, commenced last he hoped to meet them another year, and would > a, then P = iQ
year, and has been attended with satisfactory be glad to witness their progress. Remember,
results. The Classes established were those for said he, though you may not all be Bambridges 4. When the distance between the wires is
ladies, and all the plans were carefully laid accord and Whitfields in attainments (alluding to the two equal to the diameter of the coin, (8 = a),
ingly; but it is understood that the operation of head boys in the examination), you may all be as
the movement is not to be restricted to this, but to good; and the value of a school is not to be
receive every practicable development. The ser measured by the ability of those it sends out, but
vices of Professors of reputation in each study by its sending out boys that will do their duty
were retained, and in every feature of the organi. faithfully. With them now, he said, rested the cr P= Q = 1 nearly.
zation the greatest care was exercised by the Com-reputation of the school; and not only did he hope
mittee that a high character should be maintained they would grow up to be good specimens of wbat

5. Next, suppose the distance between the in the instruction and in the Lectures; and that the school could produce, but that they might be vir

and in the Lectures; and that the school could produce, out that they might be wires less than the diameter of the coin (8 cal the privacy and comfort of the studios and rooms successful in life, and able themselves to be patrons in the

Is in the Question: then, putting 8 = a . cos B, it is provided should be equal to the advantages in and supporters of the school, when I, he added,

evident that if O B the coin must strike the other respects. The regulations and announce. who am growing grey, and Mr. Hawtrey, who

grating. ment for the new Term, which commences on the loves you so well, and whom you love so well, will

And for every value of o between (B, žr), the 1st of November next, and continues till July 31st, have passed away.

probability that the projected ellipse will cross 1862, have just been issued. The classes for Wa.

one of the wires is ter Colour Painting, &c., are taught by Mr. E. A. Goodall; those for Figure Drawing and Modelling, 1 MATHEMATICAL QUESTIONS AND by Mr. W, K. Shenton, and for these the magni.

SOLUTIONS. ficent Art Collections of the Palace are all available. English is taught by the Rev. Philip Smith, B.A.;

x.dø + 28, where sin a , sin 0 = sin B and Professor Mariette, of King's College, London, 1165 (Proposed by Exbumatus.) - A coin takes the French. Dr. Kinkel instructs in German, is dropped over a grating composed of parallel and no doubt will also give some of his famous equidistant wires in a horizontal plane.' What For this expression I refer to the second part lectures on the History of Art, delivered with such is the chance that it will go through without of my solution of Question 1226, (col. 3, line 14), success at the South Kensington Museum. Italian striking, supposing the distance apart of the wires is by Signor Volpe, and Latin, as well as History, to be less than the diameter of the coin. where the term 24 has been inadvertently omitted. by the Rev. C. Boutell; Herr A. Sonnenschein is the Professor of Physical Geography; Dr. SOLUTION BY W.J. MILLER, B.A.,

Hence Dresser, of Botany; Dr. E. Lankester, of Physi.

HUDDERSFIELD College. ology; and Dr. D. S. Price, the Director of the Technological Museum, of Chemistry and its

1. FIRST SOLUTION.- Let a be the radius of applications. For the Pianoforte, there are Messrs.

'the coin, 28 the distance of the wires, and the P= f sin 6.do + fa, sin 8. do + Benedict, Lindsay Sloper, and Prout; Singing,

inclination with which the coin reaches the plane
of the grating; then the orthogonal projection of

B the great Garcia, Mrs. Street, and Miss Whyte;

. for Part-singing, Mr. Henry Leslie and Mr. J.G.

the coin on this plane will be the ellipse whose Calcott; while M. Louis d'Egville teaches the

semiaxes are (a, a. cos 0). Dancing. The first courses of Lectures will be by

2. Imagine a sphere to be described about the Dr. Dresser and Dr. Lankester, and will compoint where the coin meets the plane of the wires,

1 x.sin 8.de.do; as centre; then the normal to the coin, through mence on the 17th instant. Dr. Dresser's will be on the “Arts of Decorative Design, and their

this point, will traverse every part of the hemirelation to Botany," and will be specially addressed

spheric surface above the grating, whilst the coin to those who may be preparing to exhibit in com.

takes every possible position ; and, whilst the whence, putting cos = cos B. sin y, we obtain petition in the International Exhibition of 1862. |

coin takes every position between the inclinations Dr. Lapkester's will be on the " Physiology of the (0, 8+ do) the normal will traverse a zone whose Nervous System, in relation to Health and Edu

ratio to the entire hemispheric surface, that is, to

the total number of positions, is (sin 0 . do). / cation."

f/cot t-cosy. Jog cotid Hence, supposing every possible position of the

col p. sec B + tanaB PHARMACEUTICAL SOCIETY OF GREAT BRITAIN.

/ --The first two Jacob Bell Memorial Scholar

coin to be equally probable, the probability of an

' ships, value £30. a-year each, with free Laboratory

inclination between (0, 0+do) is (sin 0.do). 6. To find the value of this definite integral, Instruction, have been awarded by the Council to

"Y 3. Now suppose, first, that the distance be- put it into the form Thomas W. H. Tolbort, pupil of Mr. Froud, che.

tween the wires is not less than the diameter of the mist, Dorchester; and William A. Tilden, pupil

coin (8 >=a); then, by the first part of my solu. of Mr. Allchim, chemist, Barnsbury Road. "Bo.

"tion of Question 1226 (“ Educational Times" for tanical Prize Medals for the best Herbaria, October, 1861, p. 165, col. 3, line 1), the pro

-fcosa vidit

(cos - sec ) to James Browne and Joseph H. Richardson. bability that the projected ellipse will cross one

sec B-sino Sessional Prize Medals, to Thos. J. Hasselby,

of the wires is for Chemistry and Pharmacy; and Frank H.

[ tan B Lescher, for Botany and Materia Medica.

MR. COBDEN'S ADVICE To Boys.- The Wind 2 sor and Eton Express reports a speech addressed / X. do, where x, or a (1-sina 0. sino 0) then to the boys of St. Mark's School, at St. Leonard's, by Mr. Cobden, on the occasion of the usual distribution of prizes. Mr. Cobden warned the boys is the distance of the projected centre from the

2. cosa .dk that to whom much was given, of them much nearest wire. Hence, putting P, Q for the re

(I-sin 8); would be required.

2 He had lived most of his life spective probabilities that the coin will, or will

J seco B – sind in the North of England-in Lancashire, where, not, strike the wires, we sball have he said, they make the clothes they and half the world wear; and there men often rose from very small beginnings. He instanced one case especially—that of his friend who invented the engines P = 20

- sin? 0. sino) sin 9. de. do

(cos f-sec ) log cotit. which drew them along the railways. When he was making his first attempts he could neither read nor write. What a chance it would have been for him to have had the help of such an edu

and, putting cot }} = €", 2 co8 2 = 0, we have cation as they were now receiving. Alluding to the prizes that had been given, he told those who

(sec $-cos ) log cot fo.do had not been successful to-day that they migbt

f/sec * -cos still bope, and try for another time. Some found

y log cot d it harder to learn than others, but they must go

Seca B-sin

cota B on. It was so with woods : all were not of the same kind ; some burnt readily, others wanted more blowing and stirring, but both made a good The value of this definite integral is found in at last. Let those who dont find it so easy my solution of Question 1160, (“Educational |

2 (2-0) to learn as others still persevere. He told them | Times” for August, 1861). When

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SOLUTION BY THE PROPOSER. :: Q = 1 - CT, P = , as found in (3).

CASE 1.-Suppse a, b, c to be so

posited in the sides of A ABC, that 10. The results obtained, in three particular 15 = 4 13 52

Ac . Ba .cl=CB. aC, A. Draw cases, which involve all the different forms of the of 7. When the distance between the wires is problem, may be stated as follows :

Bb, Ce intersecting in P, and join

AP, Pa. Then it is required to equal to the radius of the coin, then c = -), ( When the distance between the wires is = the

prove that APa is a right line. radius of the coin, then PE V3+1 - 6 SITI

Ho Draw AD, ad I Cc, and AE, ae I P:Q = 22: 1. T

|Bb, and join DE, de.
When the distance between the wires is = the Then, by well known properties we have
diameter of the coin, then

AccB * A APc: A CPB,
P:Q = 11: 3.
When the distance between the wires is = the

Ba : aC = A BPa : AaPC,
20003911104,
circumference of the coin, then

CB : A = A CPb: A IPA, b. when a = 28, then P=V

! P:Q=1:3.

AAPc: APC=Pc. AD: PC.ad, 11. In the preceding solutions, the probability

APBA : AOPA-PB. ae : Pb.AE, ( 8) 1990 ad A10 1 97 P=19566 = Q= '0434 = nearly. has been calculated upon the supposition that

ACP: ACPB PC.PL : Pc, PB; whatever rotatory motion the coin may have when

is compounding we get 8. SECOND SOLUTION.-As in the former solu. it reaches the grating will equally affect the tion, let e be the inclination with which the coin

chances for and against striking the wires : so Ac. Ba . Cb: cBaC.bA=AD. ae : AE . ad. reaches the plane of the wires, x ( = a.cos x, that the probability may be considered the same

Now (byp.) Ac. Ba . Cb=cB. aC.bA, suppose) the distance of the centre of the pro-as | as if the coin were constrained to move parallel

..CD.ae=AE, ad,

aug Jected ellipse from the nearest wire, o the inclinato itself during the very small space of time which tion of the minor axis to this wire, or of the major intervenes between its reaching and quitting the

i.e. AD: AE=ad : ae. axis to the line (x), 0 = a.cos B, and cos p =

But L DAE= dae, each being the supplement, cos B. siny. Then, when the ellipse just touches

NOTE.-Mr. Watson's solution (“ Educational of LDPE or dPe; .. Euc. vi. 6, the AS ADE, the wire, o is the inclination of the major axis to

| Times” for October, 1861) of this Question is ade are equiangular ; hence as PDE, Pde are the I from the centre on the tangent,

| incorrect. He has taken the number of positions equiangular also, and
1 for a given elevation (o) as proportional to cos ;

ad=DE 1.= a.coso y = a" (1-sino 0 .sino),

= PD: Pd ; or, sin e. sin o = sin %.

it is shown in (2) that this number varies as sin ; i.e. the right-angled As ADP, ad P are equianguHence, when 8 < a, the coin will not strike the and his solution may then be put into the form in lar,..2 DPA=L dPa. Hence A Pa is a right line. wires, if e, x, o, taken in order, lie between the(8), (9). respective limits (Y, A), (P, B), (B, $T), where

Case 2.- Let ABCDE sin y. sin 0 = sin x. Also the probability of an

be a pentangular figure, and inclination between (e, 0 + de) is proportional to 1173 (Proposed by W. J. Miller, B.A.) --In a

through P draw lines from the number of positions of the normal between

the angular points A, B, E I given triangle place a given circle, so that the of these limits, that is, to (sin 0.de), as shown in / area of the triangle polar to the given triangle,

to meet the sides opposite (2); and (dx : 8), (do : 1T) are the respective relatively to the given circle, may be a minimum.

in a, b, e, and in AB take probabilities that x will be between (r, x+d.x), Also, find the locus of the centre of the circle,

any point d, not in a right and between (,+ lo). | when the area of the polar triangle is constant,

line with D, P; and supWe have, then, when & <a,

pose EA divided at c so

that Ad. Be . Ca. Db: dB. eC, aD.6E = CA

SOLUTION BY THE PROPOSER. Juado o

|: Ec; then gie 2200 200

Ad. Be . Ca. Db . Ec = dB, eC. aD,BE.CA;
A

Let A'B'C' be the
A polar to the given

li.e. the points d, e, a, b, c are so posited in the A ABC, relatively to

sides, that Ad. Be. Ca. Db . Ec = dB.C.ad B ogol2012

the circle whose cen- ::

1.6E.CA, and yet the line joining D, d does not tre is O, and radius r;

I pass through P, as do the lines joining Aa, Bb, then if OA', OB'n,

Ee. And thus it may be proved of every odd-sided 2 (1 – cosec? p. sin x)*sin zdody

OC'p be drawn, these
lines will be respec-

| Note.-In the enunciation of this Question B B

Vetively I to BC, CA, read “otherwise than ex absurdo,” for “by direct

AB, and y'=OA'. Om methods."
=OB' . On = OC'. Op. HOMENS

P.S.-It is rather remarkable that the proof of
Now A A'OB' : A ABC :: OA'.OB': AC.BC the converse in the case of every odd sided figure
B. cost-cos o log cot } 4); ..
TO :: got: AC. BC. Om . On ;

except the A is quite easy when compared with I hence. putting A, A., A.. A.. A. for the double that as regards the A, in which case it cannot be areas of the As ABC, BOC, AOC, AOB, A'B'C',

Apple applied, and by no means do I consider my solu

tion of the converse case, as regards the A, prewe shall have

ferable to that by Professor Davies, but I beA: 2 A’OB' :: A,A,A, : Agr4; lieve it to be quite new. cota -cos :Q=

, log cot }
(

A : 2 A'OC' :: A,0,0, : Agr4;
cota 1. sec B + tan- B
A : 2 B'OC' :: A,A,A, : A,n;

1212 (Proposed by Zero.)-In any Geome9. The same result has been thus obtained, in W A :A: A,A,A, : Art;

trieal Progression, the sum of the first and last

terms is greater than the sum of any other two (5) and (8), from two different methods, and the I TO WA MA.

terms equidistant from the extremes. value of the definite integral for a Q is found in

!

S (6), where it is shown that, when ö<a, it gives

A , A,A, S

,

SOLUTION BY MR. S. Watson. But A,A,A, is a maximum when A, =A,=A, P= + sin B. F(B); and when 8 =a. B=0.1 = A;A (or A'B'C') is a minimum when O is Let the geometrical progression be 2 b 400 go! ( SE at the centroid of the given A ABC. 'i

M a, ar, ar?, ........ax"-?; Shell PP, Q = 1-5.

When the area of the polar A A'B'C is constant,

then Om.On. Op will be constant, and the locus then we have to prove that When 8 > a, the probability (Q) of not striking of O will be a cubic hyperbola,

|a + ax? - 1 > arm + ax” -m-1 ..........(1), will be as in (8), from x = 0 to x = a, or $ = ** to o=0; but if x be between (a, 8), the proba

m being any whole number between 1 and n - 2. bility of which is (8-a): 8, the coin cannot strike 1180

Omitting the common factor a, (1) may be

(Proposed by Mr. W. Hopps.)- If written either the wires. Hence, when 8 > a,

points be so posited in the sides of an odd-sided
figure, that the compounds of the alternate seg 1-2 > 2.9-m-1 (1-2") .......... (2),
ments of the sides be equal; prove that, in the

case of the A, the lines drawn from the angular or (x^_) "- -- > -1 ........ (3). d d 1-(sec ¢-coso) log cot ? points to the points in the sides opposite intersect

in the same point; but that in the case of any / When æs 1. equation (2) divided by 1-2 gives other odd-sided figure such is not necessarily the

e case,

nd loen-m-1, an obvious truth; :

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and when x > 1, (3) divided by x"" - 1 gives

1 1232 (Proposed by Cantab.)- Given of a This liberal offer was unanimously accepted, and

quadrilateral figure, the diagonals, two opposite the thanks of the Council were voted to Mr. Dawes -m-1> 1, another obvious truth ;

sides, and the angle of inclination of these sides for the same.
when produced ; construct it.

The Diploma of Associate was conferred upon hence the proposition is fully established.

1233 (Proposed by Mr. J. W. Mulcaster,

om | Miss Sarah Stanger, who had passed the required Woolwich Common.)– Three rods are connected

examination. at their middle points by strings of equal lengths, /,

The Treasurer presented the Report of the 1224 (Proposed by a Cornishman.)--Given, 203 – 3ry=2y3 and thrown up; what is the probability of their

: Finance Committee respecting the office of Secre. forming a triangle?

tary, which was received and ordered to be taken 3 – xy2-2y3=40-43.

into consideration at an adjourned meeting of the Find x and y.

284 (Proposed by Mr. S. Watson, Haydon Council, on the 19th of October.

bridge.) SOLUTION BY MR. JOHN WALLES MULCASTER,

The Rev. Dr. Lee, Head Master of the Royal

(w + 2 + y + z =a, Woolwich COMMON.

Grammar School, Lancaster, was elected a Member Given 02 + xo + y2 +22=b,

of the Council, in the room of the Rev. H. Christ. In (1) assume x = ty,

w3 + x2 + y3 + 23=C,

mas, resigned.
13_3t = 2,
( w+ 24 + y4 +z=d.

The Very Rev. R. Dawes, M.A., Dean of or t-2ť?+ 1 = + 2t + 1,

Then if 8c = a (66 - a"), the values of w, x, y, z Hereford, was unanimously elected an Honorary .. t-1 = t+1,

can be found by quadratics. It is required to do Member of the College.
this.

1 The following Members of the Council, whose from which t = 2 or-1,

1235 (Proposed by Mr. S. Watson. Haydon / seats had become vacant through non-attendance, . x = 2y or-y.

bridge.)– What is the average area of all the were re-elected : Let x = 2y, then from (2) quadrilaterals that can be inscribed in a given

Rev. Dr. Collis.

Dr. W. B. Hodgson.
5y3 = 40,
circle?

Rev. Mr. Holden,
1. y = 2' and x = 4.
1236 (Proposed by Mr. S. Watson, Haydon-

Mr. C. P. Mason,
Let æ = – y, then from (2)
bridge.)- CD, ČE are focal chords in an ellipse ;

Mr, Ogle.
P the intersection of tangents at D and E. Find

Rev. Mr. Osborne.
y = - 40,
the locus of P.

Mr. Payne.
y = - 275 and x == 245.
1237 (Proposed by W. J. Miller, B.A., Ma-

Rey, Mr. Selwyn.
thematical Master, Huddersfield College.)-If a,

Dr, W, Smith,
The same.

Rev. Dr. Temple.
B,q be the trilinear coordinates of a point, a, b, c
the sides of the triangle of reference, and p, q, r1

Mr. Templeton.
SOLUTION BY R. J. Nelson, M.A.
the perpendiculars from the angles on any straight

Mr. J. Andrews, of Brighton, was eleoted a

+ Member of the Council, in the room of the Rev. Given 33–3.ry2 = 2y3 ...........

line, prove that the trilinear equation of that straight
.....(1)

P. Smith.
line is
23 – xy2-2y3 = 40 - 43 ..........(2).

apa + 69B+ cray = 0.

The following gentlemen were elected Members By transposition of equation (1) and adding ys

of the College:-
1238 (Proposed by W. J. Miller, B.A., Ma-|
23+ y3 = 3y2 (x + y),

Mr. C. W. Hayes, of Brampton, near thematical Master, Huddersfield College.) – A

Rotherham.
1. x - xy + ya = 3y?,

conic passes through the angular points and the Mr. Henry Smith, of Brewood.
centroid of a given triangle; find the area of the

Mr. John Tyrer, of Wolverhampton. i. * -= 5, and x = 2y, or - y. locus of its centre. By substitution of the former value of x in equa.

1239 (Proposed by W. J. Miller, B.A., Ma. An adjourned Meeting of the Council was held tion (2),

thematical Master, Huddersfield College.)-Given on Saturday the 19th of October : Present, the

one side of a right angled triangle; construct it, so Rev. Dr. Kennedy, President of the Council, in the 5y3 = 40,:. y = 2, and a = 4.

that the difference between the other side and the chair; Dr. Adams, Dr. Aldom, Mr. Andrews, Mr. By the latter value of x we find

adjacent segment of the hypothenuse, cut off by a Bidlake, Mr. Clennell, Mr. Freeman, Mr. Herbert, y3 = - 40, and

perpendicular from the right angle, may be a maxi. Mr. Hill, Mr. Jsbister, Rev. Dr. Jacob, Rev. Mr. y = - 295

mum. Prove that the perpendicular divides the Jones, Mr. Kimber, Mr. Knightley, Mr. Long,

hypothenuse in extreme and mean ratio, and that Mr. McLeod, Rev. Dr. Major, Mr. Mason, Mr. x = 27/5.;

the greater segment is equal to the remote side of Ogle, Dr. Palmer, Mr. R. Palmer, Mr. Payne, the triangle,

Dr. Pearce, Dr. Pinches, Mr. J. Reynolds, Mr.

W. J. Reynolds, Dr. Schaible, Dr. Skerry, Dr. 1225 (Proposed by Mr. B. Marks.)-Given

W. Smith, Rev. Mr. Watson, Dr. White, Rev. x + y + 2= 6, 2 + y2 + 22 = 14, and x3 + x3 + x3 =36;

SOLUTIONS RECEIVED: to find x, y, and z by quadratics. R. St. S., Cornwall.- 1223, 1224.

Dr. Wilson, and Dr. E. T. Wilson.

The Report of the Finance Committee, on the
Mr. S. Watson.-1210, 1215, 1217, 1222, 1226.
SOLUTION BY J. R. W.
J. R. W.-1209, 1225.

future arrangements to be made in reference to

the office of Secretary, was taken into consideraTransposing in each equation, we get Rev. J. Nelson, M.A.-1224, 1225.

tion. G. H. S.-1224, 1225.

Various amendments and modifications of y +z = 6 - 0 . ...... (1) | Mr. J. W. Mulcaster.—1222, 1224, 1225, 1226.

the Report were adopted, and its remaining re.
yö + zi=14-x?...
...... (2) Mr. W. Haslam, Hollenwood.-1224, 1225.

commendations were approved.
33 + 93=36-23............
E. R., Sydenham,--1222.

The next evening Meeting of the Members will Multiplying (1) and (2) and subtracting (3), we

be held on Wednesday, the 13th of November,

NOTICES TO CORRESPONDENTS. have

when Mr. Dibdin will read a paper on “The Edu. The Geometrical Solution of 1223 was left out yz (y+z) = (6-x) (14-22)-(36–29).... (4),

u cation of the Eye."

I for want of space last month.
Cubing (1) and subtracting (3), we get
We think it desirable to give some simple Ques-

The Pupils' Examination will commence on 3yz (y+z) = (6-)--(36 — 23)..........(5), |

tions and Solutions for the benefit of the Tiros.

Monday, the 18th of November, at 10 a.m.; nearly :. 3 (6—2) (14 – ~~) -- 36+ x3 = (6— )– 36 +23.

500 candidates have been entered, being an inSimplifying which,

crease of about 150 on the number examined last COLLEGE OF PRECEPTORS,

Christmas.
xi? – 6x2 + 11x-6=0,
.. -6x3 + 11x2-6x = 0,

A Meeting of the Council was held on Satur- Some hitherto unpublished writings of J. J.

day the 12th of October : Present, Mr. A. Hill, Rousseau's are about to be given to the world. It .. 24- 6x3 + 9x2 + 2.22 – 6x = 0,

V.P., in the chair, Dr. Adams, Dr. Aldom, Mr. is well known that Rousseau left numerous manu.. (x2 – 3x)2 + 2 (2o – 3x) +1 = 1, Bidlake, Mr. Freeman, Mr. Isbister, Rev. Mr. scripts in the hands of his friend the Protestant .. ~'-3x+1 = +1. Izard, Rev. Dr. Jacob, Mr. Kimber, Mr. Knight

clergyman, Moulton, whose name occurs more Whence x = 3 or 2 or 1,

ley, Mr. Long, Mr. R. Palmer, Dr. Pearce, Dr. than once in the “ Confessions.” It is from these

Pinches, Mr. J. Reynolds, Dr. Schaible, Dr. manuscripts, now in the possession of the grandy = 2 or 1 or 3, Skerry, Dr. White, and Dr. E. T. Wilson.

son of the gentleman just named, that the selection z = 1 or 3 or 2.

The Secretary reported that the Dean of Here about to be published bas been made. It includes ford, the Rev. Ř. Dawes, M.A., had expressed his a correspondence of Rousseau with M.Moulton and

willingness to offer four prizes for proficiency in the Genevese Council, a Project of a Constitution NEW QUESTIONS.

Economic Science, to be competed for by the for Corsica, Letters on Virtue and Happiness,

Teachers and Pupils examined by the College at a Treatise on the Sphere, a Fragment on Lan. 1231 (Proposed by Cantab.)– To construct Midsummer, 1862. The prizes for Teachers are guages, two novels, a portrait of Rousseau by him. a polygon of n sides, (2n-3) independent data are to be of the value of £3 and £2; and those for selt, and a collection of aphorisms--a sufficiently required. | Pupils, of £2 and £1.

yaried and inviting list of contents, Daily News.

Nov., '61.)
Alphabetical List of the Principal College and ber, the pupils passed by Dr. Wilson, of Brixton claims, or any differences that may arise between

The School Books, and New Editions, published during Hill Collegiate School, in 1861, should have been the parties interested in the debtor's estate. the Month ending October 31.

| entered as four instead of three. In common with Court is not, however, to interfere in any manner,

others on the List, Dr. Wilson has also passed alexcept its aid is invoked by some person baving a Apel (Madame) Essentials of French Grammar, 18mo.

Every deed of comArmstrong's Manual of Etymology for Junior Classes, 12mo., large number of Candidates for the Cambridge Ex-l direct interest in the matter. Bayley (W. II.) Handbook of the Slide Rule, its Appli

position must be registered. It is believed that a cability to Arithmetic, &c., 12mo.

bill will be brought in next session to consolidate Beatson (B. W.) Exercises in Composition of Greek Iambic

the law in one statute. Verse, 8th edit., 12mo.

THE NEW LAW OF BANKRUPTCY. Blackie (Rev. W. G.) Outlines of Bible Geography, Phy-|sical and Political, fcap. Svo.

A PLEA FOR SMALL BIRDS. Bohn's Classical Library. "Demosthenes' Orations against The “ Times” gives the following succinct state. M. Marshal, ex-deputy of La Meurthe, this Agri Timocrates, &c., trans., post 8vo.

ment of the most important changes made in the cultural Society of Toulon, the Acclimatisation Bristow (Hen. Wm.) Glossary of Mineralogy, post 8vo. Bromby (C. H.) Letter to Hon. Robt. Lowe on Revised law of bankruptcy by the bill which received the Society of Nancy, and M. P. Schoeffer, of Robertsat Educational Code, 8vo. royal assent at the close of last session.

(Haut-Rhin), have petitioned the French Corps LeCircle of the Sciences (The), Vol. 8. -- Mathematical Non-traders are to be liable to the bankruptcylgislatif, requesting that steps may be taken for the Sciences, new edit., or. 8vo.

-new edit., Vol. 9.-Me-l laws in respect of future debts. The seizure and I preservation of those birds that destroy insects de. chanical Philosophy, cr. 8vo.

sale of the goods of a debtor under an execution trimental to agriculture. The Times gives the fola Collier (Wm. Francis) History of English Literature, for a debt above £50 will be an act of bankruptcy. I lowing interesting abstract of the Report presentca

sm. cr. 8vo. Cooler (Arnold J.) Dictionary of the English Language, Ladvertised.

and all such sales must be by public auction, duly by these gentlemen :-“It has been concluded that

Per centages are no longer to be by no agency save me Part 1, cr. 8vo.

ntages are no longer to be by no agency save that of little birds can the ravages De Porquet (L. P. R. F.) Le Tresor de l'Ecolier Francais. I taken from bankrupts'estates, and the official as- of insects be kept down. There are some birds

38th edit, 12mo. Rome, Pictorial History of, 3 vols., cr. 8vo, rod (Encyclop. in

signees and messengers are to be greatly reduced which live exclusively upon insects and grubs, Met.)

in number, and paid by fixed salaries. At the first and the quantity which they destroy is enormous. Froembling (F. Otto) Elements of the German Language. meeting under a bankruptcy, the creditors may There are others which live partly on grubs and Part 1, 12mo.

remove the proceedings to any county court, or, I partly on grain, doing some damage, but providing Gamgee (sno.) and Law (Jas.) Anatomy of the Domestic Animals, illustr., roy. 8vo.

if they think fit, determine to wind up the estate an abundant compensation. A third class-the Ganot (A.) Elementary Physics, edit. by E. Atkinson,

under a private arrangement, and also decide birds of prey-are excepted from the category of Part 1, post 8vo,

whether the bankrupt shall have any, and what. I benefactors, and are pronounced-too precipitately, Giles' Kers to the Classics. Homer's Iliad, Vol. 1, Books allowance for support. The official assignee is to we think-to be noxious, inasmuch as they "

1-0, 18mo. Gosse (P. H.) Natural History; Birds, Mammals, Reptiles,

collect the debts not exceeding £10, and the mostly upon the smaller birds. If the arrangefcap. 8vo.

Court is to order in whose custody the books and ments of Nature were left undisturbed, the result Greek Testament (The), with Notes by W. Webster and papers belonging to the estate shall be deposited. I would be a wholesome equilibrium of destruction.

W.F. Wilkinson, Vol. 2, Svo.
Herschel (Sir Jno. F.W.) The Telescope, from the Ency. I shall be realised

The creditors are to determine whether the estate. The birds would kill so many insects, that the inBrit., fcap. 8vo.

y shall be realised by an official assignee or assignees / sects could not kill too many plants. One class is a Holden (Luther) Manual of the Dissection of the Human chosen by themselves, and in the latter case may match for the other. A certain insect was found

Body, 2nd edit.. 8vo
Homer's Iliad, Books 1-8, with Notes, &c., by A. R.

allow them the assistance of a paid manager. Ai to lay 2,000 eggs, but a single tom-tit was found to Fausset, 12mo.

moneys received by the assignees are to be forth-eat 200,000 eggs a year. A swallow devours about Horace, The Art of Poetry, translated into English Verse with paid into the Bank of England to the account | 543 insects a day, eggs and all. A sparrow's nest by H. G. Robinson, fcap. 8vo.

of the Accountant in Bankruptcy, and in country in the city of Paris was found to contain 700 pair Lacroix (M.) Elements of Algebra, translated, 12mo.

districts, where there shall be no branch of the l of the upper wings of cockchafers, though, of Janual (A) of Elementary Instruction for Infant Schools,

&c., Vol 2, fcap. 8vo. (Home and Colo. School Society3] Bank of England, then into such other bank as course, in such a place food of other kinds was proOllendorff (H.G.) French Method, for Schools, &c., 9th the Court shall direct. The creditors' assignee curable in abundance. A third, and wholly artificial, edit. revised and corrected, 12mo.

must every three months submit a statement of class of destroyers has been introduced. Every Owen (Richard) Palæontology; & Summary of Extinct his accounts, with vouchers, to the official assignee l chasseur during the season a Animals, 2nd edit., Svo.

to the official assignee chasseur during the season kills, it is said, from 100 Philips' Atlas of Physical Geography, edit. by William

for examination; and after such accounts have been to 200 birds daily. A single child has been known Hughes, 20 maps, imp. 8vo.

passed, the official assignee is to send a printed to come home at night with 100 birds' eggs, and it Renton (Geo.) Grazier's Ready Reckoner, new edit., 12mo. Robüsor. Crusoe, Pictures from, in packet, cr. 8vo.

copy thereof, or a statement showing the nature has been caleulated and reported that the number of Rhile (C.) Two Hundred and Two Questions on Essentials

and result of the transactions and accounts of the birds' eggs destroyed annually in France is between of German Grammar, 8vo.

assignee, to every creditor who has proved under 80,000,000 and 100,000,000. The result is, that Soutt (Bir W.) Tales for Young. Scottish Scenes and Cha- the bankruptcy. The proof of debts may be made little birds in that country are actually aying oul;

racters, fcap. 8vo. Smith (T. B.) Pupil's Manual of Choice Reading, Popular

by sending to the assignee through the general some species have already disappeared, and others Edition, fcap. 8vo.

post a statement of such debt and of the account. Jare rapidly diminishing. But there is another Smith (Wm.) Smaller History of Greece, 6th thousand, if any, between the creditor and the bankrupt, to-consequence. The French crops have sultered ter.

feap. Svo. Ecule (R., jun.) and Wheeler (W. A.) Manual of English 1 Bether with a declaration signed by the creditor ribly from the superabundance of insect vermin. Pronunciation and Spelling, cr. 8vo.

| that such statement is a full, true, and complete Not only the various kinds of grain, but the vines, Sowerby's Grasses of Great Britain, with Observations, statement of account between them. False de. the olives, and even forest trees, tell the same tale

&c., by C. Johnson, roy. Svo. Syme (James) Observations on Clinical Surgery, Svo.

claration is to be a misdemeanour. All statements of mischief, till at length the alarm has become Tacitus, Germania and Agricola, with Notes by ]

of account are to be compared with the books serious. Birds are now likely to be protected; Percival Frost, fcap. 8vo.

and papers of the bankrupt by tbe assignees. The lindeed, their rise in estimation has been signally Todhunter (J.) Elementary Treatise on the Theory of classification of certificates is abolished, and the rapid. Some philosopher bsa declared, and the

Equations, cr. 8vo.
Trollope (Rev. Wm.) Examination Questions on the Pen-lis to be entitled to an order of discharge

bankrupt, after the passing of his last examination, I report quotes the saying as a profound' one, that tateoch, fcap. 8vo.

Very the bird can live without man, but

bird can live without man, but man cannot Williams (Monier) Study of Sanscrit, in Relation to Mis- stringent penal clauses are provided, and for a live without the bird.' The Commissioners, though

sionary Work, 8vo. Wood (Rev. J. G.) Illustrated Natural History; Birds,

variety of offences the Court may summarily order they distinctly call for prompt and energetic reme. sup-roy. Svo.

| imprisonment for any period not exceeding one dies,' and point to the great detriment which agriWrigley's Collection of Examples, &c., Companion to, by year, or may refuse or suspend the order of dis-culture is receiving, are evidently doubtful as to Platts and Wrigley, Svo.

charge, or attach conditions thereto as to future the course to be pursued. They suggest that perproperty. For offences made misdemeanours under suasion should be tried before coercion, and that

the act, bankrupts may be tried in the court, with schoolmasters and clergy should endeavour to put ANSWERS TO CORRESPONDENTS. or without a Jury, at the option of the bankrupt, the question in its proper light before the people.

and on conviction may be imprisoned for any term There can be no doubt about the evil, or about its All communications intended for insertion must

not exceeding three years, and be liable to any remedy. Little birds have been recklessly destroyed, be authenticated by the name and address of greater punishment attached to the offence by any and the destruction must be stopped. In some few the writer.

existing statute. The Court may direct the cre and exceptional cases we have been driven to a SIGMA,--You can obtain every information relative ditors' assignee, official assignee, or any creditor similar conclusion over here. Farmers now and

to the Oxford Local Examinations, by applying to act as prosecutor, and the costs of such prose. then combine in sparrow clubs,' each member of to any of the Local Secretaries. The nearest / cution will be borne in the same manner as the ex- which is bound to destroy a certain number of centre to you is Cheltenham.

I penses of prosecutions for felonies are now borne: sparrows in a given time; but it was found on A GOVERNESS,-Ladies are examined at the Cold, and other costs incurred by such prosecutor not more than one occasion that when sparrows were lege Rooms during the Christmas and Midsummer

Corso defrayed are to be paid out of the Accountant too severely persecuted, other peculators not less Vacations. There are no Proctorial Examinations

| General's Fund. Most important facilities are mischievous increased in proportion. There is a for Teachers.

| afforded to enable a debtor and his creditors to balance in all these things. Even carnivorous birds d. W.-We cannot admit vindications of works effect private arrangements under trust or compo- do their turn of service by devouring field mice and criticised in other Journals.

sition deeds. A majority of creditors in number, I worse vermin. It was discovered once on a famous including three fourths in value, may, on execution game preserve that the complete destruction of

of a deed of arrangement, and registering it in the hawks and buzzards permitted other animals to [ERRATUM. - In the list of Schools which have Court, bind a minority, and are to have the use of prey upon the young partridges with fatal effect, paised ten or more Candidates at the Oxford Local the Court in all cases in which they shall require and so the kites were allowed to return again, Examinations, given at page 152 of our last Num.lits assistance to decide questions as to disputed! Something of this kind will be done in France.”

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