appearances of various books, an analysis of their contents, and a statement of historical notices that may be connected with them. Extracts are also given as specimens of the books or of the English of the period. The work is written in an easy fluent style, and can be read with pleasure. The Public Schools Calendar, 1866. Edited by a This volume deserves hearty support from all who are connected with the classical schools of England, and it will furnish exceedingly useful information to those who are not. The present volume differs from its predecessor in the following respects: "1. As to the Nine Schools. The recommendations of the Royal Commissioners having once been given, it has been thought sufficient (and more in character with an annual publication) henceforward to describe the present state of the schools, and to avoid all speculation as to the future. The recommendations have therefore been omitted, except where by acceptance and adoption they have become embodied in the system of any school. The Arms of the nine schools are given in this volume. "2. Advantage has been taken of the space gained by these omissions, and by a considerable condensation of the accounts of the other schools already described, to include a large number of old Endowed Grammar Schools, as well as the most important Schools of Modern Foundation. About fifty have thus been added to the number comprised in the first volume." The volume is divided into three parts. The first is devoted to the Nine Public Schools, and is by far the fullest in information. It not merely gives the names of the governors and masters, but explains the system and other such matters, and concludes in each case with a list of pupils. Naval School, City of London, Liverpool College, Cheltenham, Marlborough, Leamington, Rossall, Brighton, Radley, St Nicholas College (1. Lancing ; 2. Hurstpierpoint; 3. Shoreham), Bradfield, Jersey, Wellington, Bath (Proprietary College), Bath (Somersetshire College), Clifton, Haileybury, Malvern ; and the information given is of the same nature as that contained in Part II. As specimens of the kind of information given, which will be interesting to all educationists, we extract the following: The Upper School in Eton.-"The arrangement of six Forms and a Remove, which still prevails at Eton, is incompatible for school instruction with the present numbers of the school. Of the Forms into which the Upper School is divided, one only, the Sixth, represents a class; the Fifth, Remove, and Fourth, containing upwards of 700 boys. "The Forms composing the Upper School are subdivided as follows: "There are thus eleven Forms or subdivisions in the Upper School; but as the Removes no less than the Forms have grown too large for single masters, the whole mass has been redistributed into manageable groups called Divisions, which may be multiplied or reduced without affecting the Removes. Thus, boys in different divisions may be in the same Remove; and a boy may be promoted into a higher Remove without changing his class-master. Sometimes a boy passes over a division without entering it. "An examination precedes admission, consisting of easy translation from English into Latin, prose and verse, and from Greek and Latin into English. There is no inferior limit of age; but no boy is ad The second part is devoted to the old endowed grammar schools, namely, Derby, Oxford (Magdalen College), Lancaster, Loughborough, Manchester, King's Lynn, Grantham, Durham, Canterbury, Rochester, Norwich, Bruton, Bury St Edmunds, Sher-mitted, except on special grounds, after fourteen; and borne, Louth, Bedford, Birmingham, Christ's Hospital, Leeds, Bromsgrove, Tonbridge, Oundle, Repton, Brentwood, York, Guernsey, Felsted, Highgate, Ipswich, Richmond, Yorkshire, Hereford, Lincoln, Colchester, Oakham, Uppingham, Preston, Beaumaris, Dulwich, Exeter, Cowbridge. Information is given in regard to the masters of each school, the exhibitions and exhibitioners, the school hours, vacations, expenses, number of boys, and honours gained, none can be placed higher than the lower part of the Remove, or seven steps from the top of the school. The average time of remaining at school is four or five years. "Removes, as the system of promotion is called, take place in June and December. At each Remove, each subdivision of every Form, except the Sixth and Upper Fifth, is promoted in a body, and takes rank 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. II. k k may be interrupted by his failing to pass the examinations required at certain stages, or accelerated by his taking a double Remove; otherwise, as a rule, a boy remains during his stay at Eton in the remove in which he is placed when he first goes there. Within each Form, the removes take place without examination; to pass from Form to Form, 'Trials' are held to test the fitness of the boys to pass. A clever boy is sometimes allowed to offer himself for a double Remove. Thus, when the Upper Fourth are going into Trials for the Remove, a boy in the Middle Fourth may obtain permission to offer himself for the same Trials; and if he excels two-thirds of those of the Upper Fourth, he is promoted into the Remove, and passes the Remove above his own. "The average age for reaching the highest Division appears to be 16 years 4 months; the average time taken to reach it, 4 years 3 months; the average number of Divisions passed, 9." System of Promotion at Winchester." The system of promotion at Winchester is nearly the reverse of that at Eton, where a boy rises chiefly by seniority. At Winchester, his progress is the result of an inces sant competition, which only terminates when he 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 Remove. Fourth. Third. (Second.) (First.) "In the parallel divisions the same work is done, and boys are promoted, not from one to the other, but from both into the Form above. The first institution of parallel classes took place in the Head Mastership of Dr Tait. They were discontinued for a time, and revived by the present Head Master. The system exists at Rugby alone of the nine public schools comprised in the inquiry of the Commission of 1861, 'but more than one school of reputation lying outside of this circle has adopted it.' "The 499 boys, all of whom necessarily learn classics, are taught by fifteen masters, one of whom however, gives a substantial portion of his time to modern languages. Each master instructs 33 boys on an average; the lower classes, however, commonly falling below this number." Table (combined). We have had the pleasure of inspecting this remarkable invention, which is likely to be of great service in schools. 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 marks also of the German, French, and Mathematical classes, for maps and for composition, are entered in the same way at the end of each week, the three first according to a maximum supposed to represent the value of each of those studies compared with classics; i.e. one-eighth of the grand total for best work in French and German, one-fourth in mathematics. The marks are further added up at the end of each month. A boy's promotion at the end of a half-year or term depends on the number of his marks on the Classicus paper. 'There is thus an unceasing stimulus applied to those capable of rising, and the disadvantage, such as it is, which a steady but slow and backward boy suffers from the disheartening effect of being constantly outstripped and left behind.' From this cause, and the fact that boys are admitted at almost any age, the number of great boys in the lower classes doing elementary work is very large." It consists of a comfortable backed seat, which can at once be changed into a desk or table, without entailing any confusion or loss of time. The special feature, however, of it, is, that the back of the seat, or the desk, or the table, as the case may be, can be transferred in a moment from one side of the seat to the other, so that the invention comprises, as it were, a double seat, desk or table. It is particularly well adapted for purposes of examination, as the pupils can be placed face to face, or back to back, at a moment's notice. Underneath the seat a shelf is fixed for books or slates, and provision is also made for the ink-wells. It will be seen from the description, that Mr Laurie's invention is admirably adapted for every school purpose; and, further, that it will be difficult-if not impossible-to supersede it, as it fulfils every requirement. It may be mentioned, that when changed into a desk or table, it obviates the necessity of the pupils' stepping over the forms-a provision which, in the case of girls or young ladies, is of manifest importance. Moreover, the arrangements are so simply, yet so strongly constructed, that a boy can convert the seat into a desk or table in a couple of seconds. The price of the desk brings it within reach of the most elementary schools. 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 particle varies as its distance from the centre. Solution by H. c.— == Let ABCEFG be a half cylinder whose height: the distance of the point from the centre D. Therefore the point ind Moment ABC when weight of each of its particles varies as its dis-mot) darget Tem!T tance from the centre moment remaining solid moment half cylinder - moment half cone; C == distance that is, distance centre gravity ABC 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 centre gravity ABC × weight half cylinder distance centre gravity half cone X weight half cone; or Distance centre gravity ABC when weight of each particle varies as its distance from centre and, distance centre gravity ABC when weight of each of its particles varies as its distance from the centre G The four values of a are therefore 1, 16, § (1 + 3 √ — 7), and § (1 − 3 √√ — 7). (Solved also by Tyro, A, H. C., Beta, A. F. B., and Ricardo.) [Note. Whence x = 2 or 1. 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 H. C.-Let the side of the cubical box be (x) inches, then number of inch cubes it takes to fill the box. Adding, we get, = (Solved also by ▲, and A. F. B.) a Taking the Naperian logarithm of both sides, log., u=nTM. log., (1 — 2 (sin. 2)") 2n (3. (sin. ;)*+ 2.(sin. 2)*+ 2 * . (sin. 2)*+ &c.) 2n 2n 3 When n approaches infinity, the terms of this fraction vanish, and the limit may be found by repeated differentiation. 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 from the focus are respectively T1, T2, T3, T4: Shew that sides 1 1 1 + + + T1 4 26. Given the base and perpendicular of a triangle: to construct it so that the ratio of the two may be a maximum. |