EDUCATIONAL AND LITERARY SUMMARY OF THE MONTH. THE Senate of the University of London has announced that the next examination for the degrees of Bachelor of Arts and Bachelor of Science will take place on Monday, the 27th of October, and following days. The candidates wil! be examined in Greek, Latin, Animal Physiology, Mechanical and Natural Philosophy, Logic and Moral Philosophy, Chemistry, &c., by the Rev. J. W. Blakesley, B.1)., Vicar of Ware, late Fellow of Trinity College, Cambridge, Dr. Wm. Smith, LL.D., Mr. W. H. Besant, M.A., of St. John's College, Cambridge, Mr. Edwin Routh, M.A., of St. Peter's College, Cambridge, the Rev. Dr. Joseph Angus, President of Stepney Baptist College, Mr. J. Girling Fitch, M.A., Principal of the Borough-road Schools, Mr. T. Spencer Baynes, LL.B., and Professor Ferrier, LL.D. The examination for the degree of Bachelor of Science will take place on the same day, the examiners heing-Professor William Allen Miller, M.D., F.R.S., Professor Williamson, F.R.S., Professor John Morris, F.G. S., Professor Andrew C. Ramsey, F.R.S., Mr. George Busk, F.R.S., and Professor T. H. Huxley, F.R.S. The examination for the degree of Bachelor of Medicine will commence on Monday, the 3rd of November, and that for Doctor of Medicine on Monday, Nov. 24. There will be no further matriculation examination until the 12th of January next.

1863.

Rugby, and he now succeeds the Rev. E. H.
Gifford, D.D., at Birmingham.

The Rev. J. Percival, M.A., Fellow of Queen's
College, and one of the assistant masters of Rugby,
has been appointed to the head mastership of
Clifton College, in the place of the Rev. Charles
Evans, the newly appointed head master of King
Edward's School, Birmingham.

Mr. Charles James Wood, M.A., of Brasenose
College, and formerly Fellow, Tutor, and Latin
Lecturer, has just been elected (out of upwards of
twenty candidates) Principal of Elizabeth College,
Guernsey (founded by Queen Elizabeth in 1563).
Mr. Wood, in Michaelmas Term, 1853, obtained
a first-class in Classics, and a second-class in Law
and Modern History.

The Rev. Henry Arlett, M.A., Senior Fellow of Pembroke College, has been made Vice-President of the Albert Middle-Class School and College, Ipswich.

As the period of Lord Elgin's Rectorship of the University of Glasgow expires this year, and there is no likelihood of his re-election, the members of the University are again on the qui vive as regards his successor. Among the Conservative party the names of Disraeli, Stirling of Keir, and Lord Glencorse are spoken of favourably. For Disraeli there has been for many years a very strong party; but to many the claims of Lord Glencorse, in connection with the late Universities Act, appeal more strongly; thus there will likely be a division in the camp at next election. The Liberals regard with favour Sir G. Cornewall Lewis, the present Lord Advocate, and Mr. Layard, M.P., of Nineveh fame. The names of the first two will likely be submitted to the Association that a section of the Liberal Club have written to when it meets in November. It is also reported Lord Palmerston, requesting permission to nominate him, but that his assent has been withheld.

The next examination of candidates for admis. sion to the Royal Military College, Sandhurst, will take place before the vice-president and members of the Council of Military Education on the 17th of December; the examination of candidates for the Royal Artillery and Royal Engineers for admission to the Royal Academy, Woolwich, will be held on the 5th of January; and the examination for direct commissions on the 26th of January, visit the Reformatory Schools of Great Britain, Mr. Sydney Turner, the Inspector appointed to has presented his annual report. He states that The results of the Quarterly Examinations held the number of young offenders in the 62 certiat Portsmouth, of the competitors for appointments fied reformatories increased in the course of the as Naval Cadets and Master's Assistants in the year 1861 from 3803 to 4337, including 186 placed Royal Navy, have been announced. There were out on license and not yet finally discharged. In no Marine Cadets for examination this quarter. estimating the value and results of the reformatory Ninety-one young gentlemen came up for the system, we look naturally to the number of young Naval examination, one being disqualified by the offenders committed to prison year by year. surgeon. The examinations commenced on Wed- Now, the commitments of persons under 16 will nesday, September 2nd, and terminated on the be found to have decreased since 1856 about 43 Saturday following. On the first day one lad was per cent. in England, allowing for increase of disqualified in Euclid, and, on the next day, two population. The number steadily diminished from in geography, English, and Scripture history. As 1856 to 1860, but in 1861 increased above 9 per one-third (59) out of the number passed the ex- cent, over the previous year; and the number of amination, it must be looked upon as, on the whole, adult commitments increased still more. Various an average one. circumstances may have contributed to this increase. There is scarcity of employment, which affects especially the class of discharged criminals -a class which is every year augmenting, and the increase tells very seriously on the amount of juvenile delinquency. The returns of reconvictions show how large a proportion of this class defy the efforts made for their reformation in our convict as well as our ordinary prisons, and Mr. Turner again expresses his hope that some means will be found for the more effectual surveillance of at least the habitual criminal offenders, the men who have lived for years on the produce of their criminal or vicious habits, and have made violence or theft their profession; it is perhaps to be regretted that their sentences are often so short. Another cause of the increase in the number of juvenile commitments in 1861 is probably the over-use of reformatories. Of the whole number sentenced to reformatories in the year, more than five-eighths were sent on a first commitment, nearly a fourth were under 12 years of age, and the commitments in a large number of cases were for very petty offences, the sentence being apparently passed rather in reference to what the child was likely to become from the bad example or neglect of its late Fellow of Trinity College. parents, or from its destitute circumstances, than Mr. Evans graduated in 1847, when he was to its actual criminality or viciousness. Refora Senior Optime, bracketed Senior Classic, and matories are for those who are not curable by a was also first Chancellor's Classical Medallist. less extensive and less protracted system of treatMr. Evans is at present an Assistant Master at ment. Until the parent is made to contribute to

The election vacation at Eton College, which commenced on Friday, August 1, terminated on the 17th of September, when the lower boys returned. The extra week's holiday, on account of the appointment of the new head-master, the Rev. Edward Balston, will be given on separate days. During the recess, the Rev. W. L. Elliott has removed to his residence, as Fellow, in the Cloisters; the Rev. H. Snow is to occupy the late residence of the Rev. W. L. Elliott. Oscar Browning, Esq., M.A., removes to Mr. Snow's house, and the Rev. Austin Leigh is to occupy that of Mr. Browning. St. Matthew's-day falling this year on a Sunday, the annual orations at Christ's Hospital were postponed until Monday the 22nd ult., when the Lord Mayor, Sheriffs, Aldermen, and Common Council attended in state. Divine service was performed in Christ Church, Newgate-street; the sermon was preached by the Rev. T. W. H. Gurney, M.A., of Trinity College, Cambridge, lately one of the masters of the school, now vicar of Clavering, Essex.

The Head Mastership of King Edward the Sixth's School, Birmingham, worth about 17007. year, has been conferred on the Rev. Charles Evans, M.A.,

the child's maintenance in every possible case, Mr. Turner holds it desirable to refuse admission to children (not being orphans or really destitute) on a first commitment. Of the results of reformatories in the diminution and prevention of crime, he has to report that, after making allowance for unknown and doubtful cases, it may be taken as well ascertained that the treatment is successful in reforming at least 70 per cent.; and, considering that the system has had to deal at first with the more hardened offenders, the proportion may be expected to increase. It is rare to find in these institutions the dogged downcast look or manner, which shows that the masters are more anxious to be obeyed than to be liked or trusted; there is generally a kindliness and consideration for the children which indicate right views of the work undertaken. It would be difficult to find a movement so widely spread, and embracing persons so various in their religious views and their social position, which has been carried on with so few failures and so little rivalry or dissension. Of the whole 1031 discharges in the year, only 18 boys or girls were sent away as hopelessly incorrigible, 90 went to sea, 22 enlisted, 110 emigrated, 660 went to service or employment or to the care of friends, 27 died, 15 were discharged on the ground of health, 89 absconded and were not recovered. The expenditure was 98,6381.; the Treasury payments for maintenance amounted to 66,3741.; the parents' payments were only 2,4391. ; contributions from the rates produced 4,750/.; contributions from voluntary associations and payments for voluntary inmates, 9757.; subscriptions and legacies, 14,1367

MONTHLY RECORD OF SCIENCE
AND ART.

The thirty-second annual meeting of the British
Association for the Advancement of Science is to
The president is the Rev. Professor Willis, M.A.,
be held at Cambridge on Wednesday, October 1st.
and the vice-presidents are the Dean of Ely, the
Master of Trinity, Prof. Sedgwick, G. B. Airy,
Esq., M.A., F.R.S., the Astronomer Royal, Prof.
Stokes, M.A., and Prof. Adams, M.A.; the
secretaries, Mr. Hopkins, F.R.S., and Prof. Phillips,
of Oxford. The local secretaries are Professors
Babbington and Liveing, and Mr. Ferrers, of
Caius College. The objects of the association are
well known, being to encourage and help forward
everything that tends to the progress of sound phi-
losophy, and to cultivate the intercourse of British
philosophers with each other and with those of
foreign lands. The reception-room will be at the
Town-hall, where tickets, information as to the
meetings, &c., can be obtained. The first meeting
of the general committee will take place in the
Town-hall, on Wednesday, October 1, at one p.m.,
for the election of sectional officers, &c., and at
three p.m. on the following Monday the same
committee will meet in the same room for the pur-
pose of fixing on the place of meeting for 1863.
The first general meeting is fixed to be held in the
Town-hall, on Wednesday, October 1, at eight
p.m., when Dr. Fairbairn will resign the chair to
Professor Willis, who will deliver an address. The
sectional meetings will be held in the rooms ap-
pointed for them, on Thursday, October 2, and
following days (except Sunday), until Tuesday,
October 7; the various sections being, mathe-
matical and physical science (president, Professor
Stokes); chemical science (Professor Miller);
geology (J. B. Jukes, Esq., Director of the Geo-
logical Survey of Ireland); zoology and botany,
including physiology (Thomas Huxley, Esq.,
secretary of the Geological Society); geography
and ethnology; economic science and statistics
(Edwin Chadwick, Esq.); mechanical science (Dr.
Fairbairn). The general and evening meetings
are announced as follows:-On Thursday evening,
October 2, eight p.m., in the Town-hall-soirée ;
on Friday evening, Professor Willis's discourse;
on Monday evening, Dr. Odling's discourse; on
Tuesday evening, soirée. We expect that Cam-
bridge will be full of strangers during the session
of the association, and it is to be hoped that all
proper preparations will be made for their recep-

tion; and that circumstances will prove favour of two boats' crews of Sir John Franklin's expe-
able for a prosperous meeting. Happily there will dition who perished in endeavouring to return.
be no particular attraction in the metropolis during Mr. Hall learned the fate of five men captured
that time; the great display of the Royal Horti- from Frobisher on his first voyage, and identified
cultural Society-the last and, perhaps, the most the exact places of their landing. Mr. Hall ex-
attractive of the season-will be held on Wed-plored over 1000 miles of the coast, including the
nesday, October 8, when the work of the Asso-so-called Frobisher Straits, which proved to be a
ciation will have been done. Some of the details deep bay, terminating in latitude 63-48, longitude
are incomplete, and the nature of the town will 79 W. Mr. Hall also discovered a great glacier
not permit of soirées and excursions on the scale and mountain of fossils between Hudson Straits
of those arranged last year at Manchester. But and Frobisher Bay. The George Henry was about
Cambridge has within its own limits treasures to start for the States in October, 1861, but was
enough to excite and reward curiosity for many a prevented doing so by the ice until the 9th ult.
day; and these, we doubt not, will attract the The ship's company subsisted through last winter
attention of many visitors.
by the hospitality of the Esquimaux."

The inaugural Congress of the International Association for the Promotion of Social Science, was held in Brussels on the 22nd Sept., and from the number of distinguished men in all parts of the Continent as well as in this country who attended, there is every reason to believe that the meeting will prove of a highly interesting and important

nature.

The Royal Society of Edinburgh has awarded the Keith biennial Prize to Mr. John Allan Broun, Director of the Trevandrum Observatory, for his papers "On the Horizontal Force of the Earth's Magnetism, ," "On the Corrections of the Bifilar Magnetometer," and "On Terrestrial Magnetism generally."

The report of the select committee of the House of Commons appointed to consider the practicability of adopting a simple and uniform system of weights and measures, referred to in our August number, has since been published in extenso. The following recommendations were laid before the House, together with a great mass of evidence and tabular appendices:

1. That the use of the metric system be rendered legal. No compulsory measures should be resorted to until they are sanctioned by the general conviction of the public.

The Rev. B. H. Kennedy, D.D., was re-elected President of the Council for the current year. The Rev. J. D. Collis, D.D., the Rev. J. S. Howson, D.D., and Mr. J. Paine, F.C.P., were elected Vice-presidents of the Council. Dr. E. T. Wilson, F.C.P., was re-elected Treasurer. The various standing Committees were appointed.

The Diploma of Associate was conferred upon Miss Brake, of Pimlico, the Rev. W. J. Pickard, Vice-Principal of Culham College, Mr. A. R. Rutter, of Roxwell Academy, and Mr. G. Welch, of Birmingham.

The following ladies and gentlemen were elected Members of the College :

Mr. W. N. Barker, B.A., the Palace School, Enfield.

Mr. A. J. Christie, Trinity Schools, Marylebone. Rev. G. R. Green, M.A., Upper Clapton. Miss K. Smithers, Collegiate Ladies' School, Brighton.

Miss S. Smithers, Collegiate Ladies' School, Brighton.

Rev. W. D. L. West, M.A., Grammar School, Brentwood.

The Secretary laid before the Council a Memo2. That a Department of Weights and Measures rial from the Farnham Association for supporting be established in connection with the Board of the movement for a Scholastic Registration Act, in Trade. It would thus become subordinate to the which the memorialists expressed their approval Government, and responsible to Parliament. To it of the plan suggested in the Circular issued by should be entrusted the conservation and verifica- the Council, and their willingness to co-operate tion of the standards, the superintendence of in- with the College in the measures necessary to obtain spectors, and the general duties incident to such a such a legislative measure. The Secretary was department. It should also take such measures as directed to convey to the Memorialists the satis may from time to time promote the use and extend faction with which the Council received their the knowledge of the metric system in the depart-assurances of support and co-operation. ments of Government and among the people.

3. The Government should sanction the use of the metric system (together with our present one) in the levying of the customs duties; thus familiarising it among our merchants and manufacturers, and giving facilities to foreign traders in their dealings with this country. Its use, combined with that of our own system in Government contracts, has also been suggested.

4. The metric system should form one of the subjects of examination in the competitive examinations of the civil service.

5. The gramme should be used as a weight for foreign letters and books at the post-office.

6. The Committee of Council on Education should require the metric system to be taught (as might easily be done by means of tables and diagrams) in all schools receiving grants of public money.

MATHEMATICAL QUESTIONS AND

SOLUTIONS.

1230 (Proposed by Mr. S. Watson, Haydonbridge.)-Within a given triangle another is inscribed at random; what is the chance that the area of the latter does not exceed half that of the former ?

SOLUTION BY W. J. MILLER, B.A., MATHEMA.

TICAL MASTER, HUDDERSFIELD COLLEGE. Let λa, b, c be the distances of the angu lar points of the inscribed triangle (A') from the middles of the sides of the given triangle (4), these distances being estimated in the same direction around the given triangle; then, when A'=eA, we shall have the condition λμ+με+»λ=4-1 ........ . (a) ; and when ▲'=▲, or e=1, (a) gives, as the condition that the inscribed triangle should be just half the given triangle,

The Report of the Director-General of the Government School of Mines has been published. The Report states that the number of students has largely increased during the past year. A considerable diminution was experienced in the previous twelve months, owing to a cause now removed. The success of the evening lectures, which were commenced in the past session, and to which the public were admitted (to ten lectures, on the payment of 5s.), was deemed sufficient to induce the lecturers to repeat the course during this session. The lectures to working men continue to be as attractive as ever, the whole of the cards of admission (600) being generally applied for and issued in two hours. The additions to the contents of the Mining Record Office have been considerable. By these Mr. R. Hunt hopes to be able to illustrate on the six-inch Ordnance maps the plans of all collieries that have been abandoned during the last thirty years, showing their proximity to works now in activity. This gentleman has ascertained that the total consumption of coal has reached eighty-four millions of tons, being an increase of ten millions of tons in the last year, and of twenty millions of tons as compared with the return of 1855. Dr. Percy reports very favourably of the condition of the Metallurgic La- 7. In the public statistics of the country, quanboratory, a branch of the above institution, and tities should be expressed in terms of the metric regrets that its small size does not afford accom- system in juxtaposition with those of our own; as modation for more than eight students; many suggested by the International Statistical Conmen trained therein are found in every region of gress. the globe, and their services are eagerly sought 8. In private bills before Parliament the use of after. The Directors of the Geological Survey the metric system should be allowed. have supplied a government agent of the King of ƒ (λ, μ, v)=λμ +μv+vλ=1 .......................... (8). 9. The only weights and measures in use should Italy with all necessary information towards the be the metric and imperial, until the metric has These equations correspond to (a), (E),' in the commencement of such a survey in the new been generally adopted. Cor. to my Solution of Quest. 1298. From (8) kingdom. 10. The proviso in the 5 and 6 Wm. IV., chap. we see that for every value of A from -1 to 0, Admiral Fitzroy, of the Meteorological Depart-63, clause 6, allowing the use of "local and cus- and for every corresponding value of μ from -1 ment of the Board of Trade, has in preparation a tomary measures" in cases where the vessel em- to ', where ƒ (A, ',-1)=1, there will be a value "Weather Book; or, Manual of Practical Me- ployed "is not represented as containing any of such that, for every value of from -1 to, teorology," intended for popular use. Considering amount of imperial measure, or of any fixed local the triangle A' will be greater than ▲; and this the interest everybody whose lot is cast on these or customary measure heretofore in use," should will also be the case when A, p, are between the stormy British Isles has in the weather, Admiral be repealed, as giving facilities to evade the respective limits (0, 1), (μ", 1), (›”, 1), where Fitzroy has only to make his handbook plain and statute. ƒ (^, μ, v')=1=ƒ (^, μ”, 1). easy to reap a little fortune out of its copyright. 11. The department which it is proposed to ap- Now, λ, μ, may, with equal probability, take In the American papers we have the follow-point should make an annual report to Parliament. any value from 1 to +1; hence the probability. ing news of the last effort in the polar seas that they will be simultaneously between in search of the lost Expedition of Sir John Franklin :-"The barque George Henry, of New (a, a + dλ), (μ, μ + dμ), (v, › + d») is dλ. dụ. d London, Captain Buddington, from Frobisher Let P, Q denote the respective probabilities Bay, has arrived here short of provisions, and AT a Meeting of the Council held on the 6th of that ▲'<▲, and A'> ▲, so that P+Q = 1; with Mr. Hall, of the new Sir John Franklin September, Present, Mr. A. Hill in the chair, then we shall have 8Q-Q1 + Q2, where Expedition, on board. The Expedition lost one Dr. Adams, Dr. Aldom, Mr. Bidlake, Mr. Clenman the first winter out. He was frozen to nell, Mr. Herbert, Mr. Isbister, Rev. W. T. Jones, death. Mr. Hall reports that, in consequence Mr. Kimber, Mr. Knightley, Mr. Long, Dr. of the loss of some of his craft, he was unable to Pearce, Dr. Pinches, Mr. J. Reynolds, Mr. W. J. prosecute his mission to the extent of its purpose. Reynolds, Dr. Schaible, Dr. Skerry, and Dr. The Expedition had probably determined the fate White.

COLLEGE OF PRECEPTORS.

=

-1 -1 -1

· dμ=I2 =2x+ (1 + x2) loge (1 +λ)2

f1,. '

NS AT

f1,. dv=f (1 + x)2 + † (3λ + x3) log。 (1+x2)

-(4+2x+x3) log (1+λ) + tan- A;

1

·· Q2 = ƒ 12 • dv=¿ (x + 6) — 4 log 2.

In like manner we should find

+(v−x)

be

(b-u) dz =

a

bc

a2

(x2 — ax + ya2) log

e

=

contain given areas A1, A2, A3, A4, or e, ▲,
e A, e, A, e,▲, where ▲, + A+ A+ A 1
A, ore, +e2 + e + e1 = 1.

1

Suppose H, K, L to be the points of bisection of the sides BC, CA, AB, and put

so that a, b, c are the distances of the angular points of the inscribed triangle from the middles of the sides of the given triangle, these distances being estimated in the same direction around the triangle;

Proceeding thus, we obtain the equations

1298 (Proposed by Mr. S. Watson.) — In how many ways can a triangle PQR be inscribed = v(suppose). in a triangle ABC, so that the lines PQ, QR, Now when cx >az, in order that y may be less RP, shall divide it into four equal parts? c (x− a) than b, z must be < =λ(suppose); and SOLUTION BY W. J. Miller, B.A., MATHEMATICAL MASTER, HUDDERSFIELD COLLEGE. therefore the limits of x are a and a. Also when To take the Question more generally, under az > cz, in order that y may exceed 0, z must another form, let it be required to inscribe a triλ' (suppose), and a must lie be-angle PQR in a given triangle ABC (A), so that the triangles QAR, RBP, PCQ, PQR, may

parts.

Let a, b, c denote the sides of ABC; and put AR=x, AQ=y, and BP=z.

Now we have area ARQ=xy sin A=1 ABC= bc sin A, or

4xy=bc

Similarly,

4z (c-x)= ac

and

....

(1)

(2),

(3)

ac

4 (a−z) (b−y)=ab bc From (1), y=x' and from(2), x=4(c-x) Substituting these results in (3), and reducing, we

From what precedes it is obvious that a
(2), be written for 2; and then, putting y=zx
shall have to find
.(3).

Now by proceeding as directed in Euler's AlgeNow (9) may be put under the form bra, Part ii. Chap. ix. Art. 144, we find n = (2r2-r+10)2-40r (2r2-9r+10) = □ ; or -16. But these values of n, and others that may which is evidently the case when 2r-9r+10=0. be got from them, give z=0,which is inadmissible;

The solution of this quadratic gives r = 2, or 24. we must therefore seek for another value of n. Taking the value r=2, we find v = 3 and z = = 3;| In (4) and (5), 80-32+1 (7) and 105-42+1 also r=24 gives z = 3; hence we shall have y

ODCEAB give the harmonic ranges [CDBP], [CEAQ AFBR]; therefore [ACDBP], [B. CEAQ], [C. AFBR] are harmonic pencils; hence AP is the fourth harmonic to AC, AD, AB; BQ to BC, BE, BA; and CR to CA, CF, CB.

Suppose QP to meet AB in R'; then [P. QAEC], [P. R'BFA], [P. RBFA] are harmonic pencils, therefore R coincides with R', and QPR is a straight line.

The triangle DEF is an inscribed co-polar to ABC; and these triangles are therefore co-axial; O is their pole, and QPR their polar-axis. The point O and the line QPR are called by Ferrers ("Trilinear Coordinates," p. 30) "harmonics of one another with respect to the triangle ABC."

When AD, BE, CF are perpendicular to BC, CA, AB, the 4s BFC, BEC are rights, and the quadrilateral BFEC is inscriptible in a circle; therefore CP. PB= EP. PF, and P is a point on the radical axis of the circles described about the triangles ABC, DEF. The same may be proved of Q and R; hence QPR is the radical axis (or "common chord") of the circles ABC and DEF. The same results may be readily obtained by trilinear coordinates: for if μB-vy=0, vya =0, λa-μB=0, be the equations of AD, BE, CF, the equations of AP, BQ, CR will be μB+y=0, +λα=0, λα+ μβ=0; and the intersections of these lines with the opposite sides of the triangle will obviously lie on the straight line Aa + B+ y=0. When AD, BE, CF are perpendicular to BC, CA, AB, then λ=cos A, μ=cos B, cos C, and the equation of QPR is a cos A + B cos B + y cos C = 0, which, by what is proved in the solution of Question 1290 (“ Educational Times" for August) is that of the radical axis of the circles

ABC, DEF.

Note. The circle DEF is the Nine-point-circle referred to in the note on the solution of Question 1290. If S be the centre of the circle ABC, H, K, L the middles of the sides BC, CA, AB, and M. M,, M2, M, the middles of the lines OS, OA, OB, OC, the circle DEF will pass through the nine points D, E, F, H, K, L, M,, M2, M3, its centre will be at M, and its radius half that of the circle ABC.

[In line 20 of the note to 1290, for “inscrit" read "circonscrit."]

NEW QUESTIONS. 1312 (Proposed by Dr. Rutherford, F.R.A.S., Royal Military Academy, Woolwich.)--A uniform beam rests with its ends against the opposite sides of an oblique shaft inclined to the vertical at an angle a; find the least coefficient of friction consistent with equilibrium, when the beam is of such a length as to be inclined to the vertical at an angle B.

1313 (Proposed by Dr. Rutherford, F.R.A.S., Royal Military Academy, Woolwich.)-A heavy rectangular beam, whose weight is W and length 2a feet, rests with one side of its square end, which is 26 feet, on a rough horizontal floor, and the corresponding side of the other square end against a rough vertical wall; find its position when it is on the point of slipping along the floor, and its pressure against the wall, being the coefficient of friction on the floor, and ' that on the wall.

1314 (Proposed by W. J. Miller, B.A., Mathematical Master, Huddersfield College.) Find the relation between the radii of three circles, and the distances of their centres, in order that it may be possible to draw a common tangent to the three circles..

32mo, 2s.

Thurlow's Land Surveyor's Ready Reckoner, new edition,
Unwin's Training-School Reader, First Book, f'cap. 8vo,
Zotti, Grammaire Italienne et Française, nouvelle edit.

1s. 6d., cloth.

12mo, 6s.

WOOLWICH ACADEMY.

A, B, C, D pass through one point P, every 3 of
them form a circular triangle. Let D' be the point
of intersection of 3 circles passing through P, and
through the corners of the circular triangle formed
by ABC, cutting the opposite sides orthogonally;
and let C', B', A' be the analogous points for the
other 3 circular triangles, formed without C. B, A
respectively. Prove that the 5 points A', B', C',
D', P lie upon one circle (Q). Moreover if (AB) THE following is the official return of the
denote the other point (not P) of intersection of seventeen candidates next on the list for ad-
the circles A, B, and if P, be the harmonic con- mission to the Royal Military Academy, Wool-
jugate point of P on the circle passing through the wich, as determined by the competitive exa-
points P, (AB), (CD), P, the analogous point on mination of July last, who have been elected
the circle through P, (AC), (BD), and P ̧ the to fill additional vacancies :-
analogous point on the circle through P, (AD),
(BC); then prove also that the 4 points P, P.,
P2, P, lie all upon the circumference of another 33 Mallock, R., age 18, places of education,
Harrow; and Rev. W. H. Pritchett, Old
circle (R), which cuts (Q) orthogonally.
Charlton
1317 (Proposed by Mr. S. Watson.)-Show 34 Le Mesurier, H. S., 17, Dr. Bridgman,
Woolwich; and Rev. F. W. Waldron,
that any parallelogram is to its greatest inscribed
Woolwich
ellipse as 4: T.
Congdon, J. J., 17, Royal Naval School,
New-cross; Mr. Taylor's, Woolwich
Denny, W. T. G., 18, Royal School, Ennis-
killen; Mr. De Burgh's, Dublin

3

2

1318 (Proposed by Alpha.) — ABCD is a rectangle in the side AB a point P is taken at random, and a point Q is taken at random upon the area ABCD: find the probability that the triangle APQ will be acute-angled.

Ord.

35

86

37

Names.

Marks.

3794

.3776

3744

3728

Dalrymple, H. L., 18, Wimbledon School 38 Grattan, J. A., 18, Mr. Taylor's, Woolwich Common

3667

3653

1319 (Proposed by N'Importe.)-It is an- 39 Dunnage, A. J., 17, Mr. Jackson's, 72, Lansdowne-place, Brighton nounced at p. 205, vol. ii. 12th edition, Davies's Hutton, that "if a tetrahedron be drawn, formed 40 Woodthorpe, R. G., 17, Mr. Taylor's, Woolof four tangent planes to a paraboloid, the sphere Nugent, F. F. F., 17, Cheltenham; Rev. G, described about it will pass through the focus of Frost's, 28, Kensington-square the paraboloid." Prove or disprove this. Walker, G. R., 18, Waterford School; and Trinity College, Dublin

1320 (Proposed by the Rev. W. Mason,
Quid faciam, docti, carum visurus amicum,
Normanton, Yorkshire.)-

Quem late extensâ degere valle juvat?
Hujus ab æde domus tredecim mea millia distat,
Quadrigis rapidis attamen ire queam
Cauponam versus distantem millia bis sex;
Millia cauponâ quinque et amicus abest.
Quadrigis horâ sex millia curritur unâ,

Quatuor interea millia vado pedes,
Quam longe utemur quadrigis, dicite tandem,
Tempore quò minimo conticiamus iter?

43 Stewart, H. T., 18, Rugby; Mr. Fleming's, Tonbridge

44 St. George, W. B., 18, Mr. Hopkirk's, Eltham; Mr. Miller's, Woolwich; Mr. Wilson's, Old Charlton.

45 Gillespie, J. C., 16, Mr. Hopkirk's, Eltham; Mr. Fleming's, Tonbridge

46 Annesley, A., 18, Mr. Hopkirk's, Eltham;
Rev. H. Callendar, Hatherop Rectory,
Fairford

47 Woodland, V. R., 17, Sidney College, and
Captain Targett's, Bath; Mr. Fowler's
and Mr. Fleming's, Tonbridge
48 Godson, G. R., 17, Tonbridge School; Rev.
E. A. Claydon, Lee

49 Buckle, D. W., 18, Wimbledon School
13, Great George-street, Sept. 22.

QUEEN'S COLlege, KingstON.-The Trustees and Medical Faculty of Queen's College have appointed Dr. Roderick Kennedy, of Bath, a licentiate of the Edinburgh College of Surgeons, to be Professor of Anatomy. This gentleman, we hear incidentally, is very well qualified for such a position, having passed his examination at Edinburgh with honours in anatomy and surgery. Dr. Octavius Yates, of Kingston, has been appointed to the chair of Institutes of Medicine vacated by Dr. Litchfield. Dr. Michael Sullivan, of Kingston, a graduate of the college, has been appointed Demonstrator of Anatomy. These new arrangements, it is hoped, will contribute to the success of the Kingston Medical School.-Kingston News,

Canada West.

REPORT OF THE DEPARTMENT OF

SCIENCE AND ART FOR 1862. THIS document, which gives an account of the results, both as regards the expenditure and the work done, of the past year, has just been published. From it we learn that the Science and Art Department, South Kensington, and the Schools of the United Kingdom, including general management, absorbed the sum of 68,4017.; the School of Science and Pope's History of the Kings of Ancient Britian, cr. 8vo, Geological Museum, Jermyn Street, 6,3137.; Geological Surveys of the United Kingdom, Place's Catechism of Music, for the Use of Young Chil-9,5887.; Industrial Museum, Scotland, 2,2921.; Reason Why, General Science, new edition, cr. 8vo, 2s. 6d., Rhind's First Class-Book of Physical Geography. 10th

Mercantile Penman, The, new edit., 4to, 5s., cloth. 1315 (Proposed by W. J. Miller, B.A., Morton's Manual of Geography, Maps, 18mo, 1s. 6d. bds. Mathematical Master, Huddersfield College.) Neuman and Baretti's Spanish and English Dictionary, Divide unity into four parts such that, if the by Seoane, 28s. square of one of them be diminished by four times the product of the other three, the remainder may be a rational square.

3s. 6d., cloth.

dren, 1s., sewed.

cloth.

edit. 1s, cloth.

Museum of Irish Industry, 4,8951.; Royal
Dublin Society, 6,000l.; Royal Hibernian
Academy, 300l., making a total of nearly