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appearances of various books, an analysis of their Naval School, City of London, Liverpool College, contents, and a statement of historical notices that Cheltenham, Marlborough, Leamington, Rossall, may be connected with them. Extracts are also Brighton, Radley, St Nicholas College (l. Lancing ; given as specimens of the books or of the English 2. Hurstpierpoint; 3. Shoreham), Bradfield, Jersey, of the period. The work is written in an easy fluent Wellington, Bath (Proprietary College), Bath (So. style, and can be read with pleasure.

mersetshire College), Clifton, Haileybury, Malvern ; and the information given is of the same nature as

that contained in Part II. The Public Schools Calendar, 1866. Edited by a As specimens of the kind of information given,

Graduate of the University of Oxford. London: which will be interesting to all educationists, we exRivingtons, 1866.

tract the following

The Upper School in Eton.--"The arrangement of This volume deserves hearty support from all who six Forms and a Remove, which still prevails at are connected with the classical schools of England, Eton, is incompatible for school instruction with the and it will furnish exceedingly useful information to

present numbers of the school. Of the Forms into those who are not. The present volume differs from which the Upper School is divided, one only, the its predecessor in the following respects :

Sixth, represents a class; the Fifth, Remove, and “1. As to the Nine Schools. The recommenda- Fourth, containing upwards of 700 boys. tions of the Royal Commissioners having once been

“ The Forms composing the Upper School are subgiven, it has been thought sufficient (and more in divided as follows: character with an annual publication) henceforward

Sixth. to describe the present state of the schools, and to

Upper Division avoid all speculation as to the future. The recom

Middle Division { Lower Remove.

Upper mendations have therefore been omitted, except Fifth where by acceptance and adoption they have become

Lower Division

Upper Remove. embodied in the system of any school. The Arms of

Lower Remove. the nine schools are given in this volume.

Remove “2. Advantage has been taken of the space gained

Lower Remove. by these omissions, and by a considerable condensa

Upper Remove. tion of the accounts of the other schools already de. Fourth Middle Remove.

Lower Remove. scribed, to include a large number of old Endowed Grammar Schools, as well as the most important “There are thus eleven Forns or subdivisions in Schools of Modern Foundation. About fifty have the Upper School ; but as the Removes no less than thus been added to the number comprised in the first the Forms have grown too large for single masters, volume.”

the wbole mass has been redistributed into manageThe volume is divided into three parts. The first able groups called Divisions, which may be multiplicd is devoted to the Nine Public Schools, and is by far or reduced without affecting the Removes. Thus, the fullest in information. It not merely gives the boys in different divisions may be in the same Renames of the governors and masters, but explains the move; and a boy may be promoted into a higher system and other such matters, and concludes in each Remove without changing his class-master. Somecase with a list of pupils.

times a boy passes over a division without entering it. The second part is devoted to the old endowed An examination precedes admission, consisting of grammar schools, namely, Derby, Oxford (Magdalen easy translation from English into Latin, prose and College), Lancaster, Loughborough, Manchester, verse, and from Greek and Latin into English. King's Lynn, Grantham, Durham, Canterbury, Ro- There is no inferior limit of age; but no boy is adchester, Norwich, Bruton, Bury St Edmunds, Sher-mitted, except on special grounds, after fourteen; and borne, Louth, Bedford, Birmingham, Christ's Hos- none can be placed higher than the lower part of thio pital, Leeds, Bromsgrove, Tonbridge, Oundle, Repton, Remove, or seven steps from the top of the school. Brentwood, York, Guernsey, Felsted, Highgate, Ip- The average time of remaining at school is four or swich, Richmond, Yorkshire, Hereford, Lincoln, Col. five years. chester, Oakham, Uppingham, Preston, Beaumaris, “Removes, as the system of promotion is called, Dulwich, Exeter, Cowbridge. Information is given take place in June and December. At each Remove, in regard to the masters of each school, the exhibitions each subdivision of every Form, except the Sixth and and exhibitioners, the school hours, vacations, ex- Upper Fifth, is promoted in a body, and takes rank penses, number of boys, and honours gained.

as the subdivision next above it. This ceases with The third Part is occupied with schools of modern the upper division of the Fifth, the numbers of the foundation, including Liverpool (Royal Institution Sixth Form being limited, and its vacancies supplied School), Islington, King's College, London, Kensing by the promotion in seniority of boys from the upper ton, University College, London, Isle of Man, Royal | division of the Fifth. The regular progress of a boy

VOL. n.

к k

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may be interrupted by his failing to pass the examina

Middle School tions required at certain stages, or accelerated by his

Upper Middle 1.

Upper Middle 1. taking a double Remove; otherwise, as a rule, a boy

Upper Middle 2.

Upper Middle 2. remains during his stay at Eton in the remove in Lower Middle 1.

Lower Middle 1. which he is placed when he first goes there. Within Lower Middle 2.

Lower Middle 2. each Form, the removes take place without examination; to pass from Form to Form, Trials' are held

Lower School. to test the fitness of the boys to pass. A clever boy

Remove. Fourth. Third. (Second.) (First.) is sometimes allowed to offer himself for a double

“ In the parallel divisions the same work is done, Remove. Thus, when the Upper Fourth are going and boys are promoted, not from one to the other, but into Trials for the Remove, a boy in the Middle from both into the Form above. The first institution Fourth may obtain permission to offer himself for the of parallel classes took place in the Head Mastership same Trials; and if he excels two-thirds of those of of Dr Tait. They were discontinued for a time, and the Upper Fourth, he is promoted into the Remove, revived by the present Head Master. The system and passes the Remove above his own.

exists at Rugby alone of the nine public schools com“The average age for reaching the highest Division prised in the inquiry of the Commission of 1861, appears to be 16 years 4 months; the average time

'but more than one school of reputation lying outside taken to reach it, 4 years 3 months; the average of this circle has adopted it.' number of Divisions passed, 9.”

" The 499 boys, all of whom necessarily learn System of Promotion at Winchester.-" The system classics, are taught by fifteen masters, one of whom of promotion at Winchester is nearly the reverse of however, gives a substantial portion of his time to that at Eton, where a boy rises chiefly by seniority. modern languages. Each mastar instructs 33 bors At Winchester, his progress is the result of an inces on an average ; the lower classes, however, commonly sant competition, which only terminates when he falling below this number.” reaches the sixth. Places are taken in all other divisions, and each boy receives for each lesson a number of marks answering to his place at the end of the lesson. Thus, if he is twentieth from the bottom, he Thomas Laurie's British Patent School Desk, Seat and gets twenty marks on the Classicus paper. The

Table (combined). marks also of the German, French, and Mathematical classes, for maps and for composition, are entered in We have had the pleasure of inspecting this rethe same way at the end of each week, the three first markable invention, which is likely to be of great according to a maximum supposed to represent the service in schools. value of each of those studies compared with classics ; It consists of a comfortable backed seat, which can i.e, one-eighth of the grand total for best work in at once be changed into a desk or table, withont enFrench and German, one-fourth in mathematics. The tailing any confusion or loss of time. The special marks are further added up at the end of each month feature, however, of it, is, that the back of the seat, A boy's promotion at the end of a half-year or term or the desk, or the table, as the case may be, can be depends on the number of his marks on the Classicus transferred in a moment from one side of the seat to paper. “There is thus an unceasing stimulus applied the other, so that the invention comprises, as it were, to those capable of rising, and the disadvantage, such a double seat, desk or table. It is particularly well as it is, which a steady but slow and backward boy adapted for purposes of examination, as the pupils suffers from the disheartening effect of being con- can be placed face to face, or back to back, at a mo. stantly outstripped and left behind.' From this cause, ment's notice. Underneath the seat a shelf is fixed and the fact that boys are admitted at almost any age, for books or slates, and provision is also made for the number of great boys in the lower classes doing the ink-wells. It will be seen from the description, elementary work is very large.”

that Mr Laurie's invention is admirably adapted for The Classical School in Rugby.-" Each of the every school purpose ; and, further, that it will be three Sub-Schools is divided into Forms, and these difficult-if not impossible—to supersede it, as it fulagain are distributed into divisions, which, except fils every requirement. It may be mentioned, that in the Lower School, form a corresponding number when changed into a desk or table, it obviates the of classes. Each division has its own master, though necessity of the pupils' stepping over the forms-a two divisions may be parallel for both work and pro- provision which, in the case of girls or young ladies, motion.

is of manifest importance. Moreover, the arrangeUpper School.

ments are so simply, yet so strongly constructed, The Sixth Form.

that a boy can convert the seat into a desk or tablo The Twenty.

in a couple of seconds. The Fifth Form.

The price of the desk brings it within reach of the Fifth, Division 2. Fifth, Division 2.

most elementary schools.

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Notes and Queries. .

II. MATHEMATICAL.

[The Editor would feel obliged by the Mathematical communications being forwarded either to London

or Edinburgh before the 15th of the Month.]

NOTES,

20. Find the centre of gravity of a semicircle, in which the weight of each partiele varies as its distance from the centre.

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B

Solution by H. C.-
Let ABCEFG be a half cylinder whose height =p=

AD, half
the diameter AC. Let the semicircle EFG be the base of a half.cone
having its apex in D. From the half cylinder take away the half E
cone, then the weight on each point of the semicircle ABO varies as
the distance of the point from the centre D. Therefore the point in
which the perpendicular from the centre of gravity of the remaining

G solid meets DB, is the centre of gravity of the semicircle ABC, when the weight of each of its particles varies as its distance from the centre. Taking moments round D, we have Moment ABC when weight of each of its particles varies as its dis- und +67-3}?!!! tance from the centre = moment remaining solid

= moment half cylinder — moment half cone; that is, distance centre gravity A BC when weight of each particle varies as its distance from centre x weight of ABC when weight of each of its particles varies as its distance from the centre = distance centre gravity ABC X weight balf cylinder distance contre gravity half cone x weight half cone; or Distance centre gravity A BC when weight of each particle varies as its distance from centre

rri 23

TPB

Tp3
Х
2 6

35 2

4r

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and, distance centre gravity ABC when weight of each of its particles varies as its distance from the centre

37 2

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From (A)

16 = 0;
Or, (24) (x + 32+ + 4) = 0
— .

4
16, and x + 3x +4 -0.... (B)
a 32

= Completing square, and taking square root of (B),

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1
whence 2 = (1+8 v=7).

2

(3 v The four values of x are therefore 1, 16, 3 (1 +3 1 - 7), and ) (1.– 3 V – 7). (Solved also by Tyro, 4, H. C., Beta, A. F. B., and Ricardo.)

(2.) * + y = 1 + 2xy + 3.r$y2

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Solution by Tyro

x + y =1+ 2xy + 3x'ya
** — 2xy2 + y 1 + 2xy + x?y?,
Extract root, za y2 =1+ xy,
add 2y2 to both sides and tranpose ay,

(a) 602 — xy + y2 = 2y2 + 1;
and 28 + 38 = 2yox + 2y2 + 2+1,

= 2y" (c + 1) + (x + 1);
Resolving, we have (x + y) (22 – æy + 3) = (2y + 1) ( + 1).

Substituting the value of (2y + 1) from equation (a)
(1 + y) (2 - xy + y) = (x - xy + y^)(x + 1)

1+y=3 +1

y=1.

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Substituting this value in (a),
TC+1=2+1, and x - =2,

Whence x = 2 or 1.

[Note. The other roots are imaginary.-ED.] (Solved also by J. A. J., A, H. C., Beta, A. F. B., and Ricardo.)

22. It requires just 100 inch cubes to fill exactly a cubical box, cover the top of it twice, and form one line on the top of that again : What is its capacity.? Solution by A. C.-Let the side of the cubical box be (2) inches, then

god = number of inch cubes it takes to fill the box. 223

to cover lid twice.

to form line on top. Then 28 + 2x + x = 100,

20 +232 + 100 = 0;

- 6x2 + 6x* — 24x + 24x = 0. Adding, we get, 23 - 4x + 6x2 24x + 25x 100 = 0,

(6-4) + 6x (a - 4) + 25 (x - 4) = 0,

(-4)(** + 6x + 25) = 0. .: 2 - 4= 0 (other equation inadmissible),

and x = 4 inches,

.. capacity of box 64 cubic inches. (Solved also by a, and A. F. B.)

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n

23.

Find the limit of

COS.

n

Solution by A.

Let u =

2 .

2n

.)*" whon n approaches to infinity.

(cos

. 9.)"
-(1-32

2 (sin. 2.)")**
Taking the Naperian logarithm of both sides, log. u=", log. (1 – 2 (sin

. mm)') (*: (sin..A)*+ * . (sin.m)* + 3". (sin. * + 84.) (*)-+ (a)"

.-

2

a

6

n

22
2

.

2n

&c

2n

3

2n

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When n approaches infinity, the terms of this fraction vanish, and the limit may be found by repeated differentiation.

(Solved also by H. C.)

QUERIES. Proposed by A.

24. A triangle is inscribed in an equilateral hyperbola : Shew that the intersection of the perpendiculars lies on the curve. 25. A circle passes through the focus of a conic section, and cuts it in four points, whose distances

I

4 from the focus are respectively ru, reg ren : Shew that th +

latus-rectum 26. Given the base and perpendicular of a triangle : to construct it so that the ratio of the two

be a maximum.

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