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Construction.-Take any straight line EF. Made ADS. From A with radius P describe circle GHK; and from D with radius R describe circle GHL. At A make the angle DAM equal given angle. From AM cut of AN Q; and from N with radius P describe a circle cutting circle GHL in C. Draw AB parallel to CN, and cutting circle GHK in B. Join CB and CD.

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Then ABCD shall be the required quadrilateral. Proof. The side ADS (Con.), and the sides AB, CD = P, R, respectively (Def. 15); Also BC: AN (I. 33) = Q (Con.). Therefore, the quadrilateral ABCD has its sides equal to P, Q, R, S, respectively. Because BC is parallel to AN (I. 33) the angle formed by BC, AD =<DAM (I. 29) = given angle. (Con.).-Q. E. F.

General.

1. X. Y.-Consult the nearest bookseller.

2. A CONSTANT READER.-Articles of special interest to Female Teachers will appear in the new volume.

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6. C. C. J., Great Wakering.-We believe that the particulars of the examination are not yet published. Your query shall be attended to immediately the syllabus is issued.

7. STUDY, Great Bromley.-Pupil teachers have to read at the Scholarship Examinations.

8. J. H., Orkney.-Manford's Solution of Geometrical Exercises, 2s. 6d. ; Dickinson's Difficulties of Euclid Simplified, Is. ; Wollman's Key to Euclid (2s. 6d.): being Solutions to Deductions and Riders Set to P. Ts.; Mathew's Deductions from Euclid and How to Work Them, 3s.; &c.

9. G. BACON, Sheffield.-Your solution to query 43 in last issue is quite correct, and very explicit.

10. ALPHA, Dumfries.-Chemistry, Fowne's, 7s. 6d. ; Roscoe's, 4s. 6d.

Agriculture.-Stewart's Agriculture; Gill's Agriculture.

II. SUBSCRIBER, Wandsworth.-We are sorry we are unable to give you the information you desire.

12. A. O. E., Carnarvon.-Your solutions to query 42 in last issue are incorrect. See correct solution in this number.

13. W. HEMINGTON, Cardiff.-A gas holder 150ft. diameter and soft. deep, contains, say, 400,000 cubic feet. What should be the dimensions of a gas holder of the same proportions to hold 300 cubic feet?

(Your question is rather vague, as the first gas holder will hold nearly 900,000 cubic feet, and you do not say whether the 300 cubic feet of the second be the total or proportionate capacity. It

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of 13.6...ft. 4'5...ft. 14. W. GriffitнS, Slaithwaite.-In preference to the book you name study Huxley's Physiography, the Science Primers written by Grove, Geikie, and Lockyer, in Macmillan's Series. To these add Lockyer's Astronomy and Judd's Volcanoes.

Owing to the Christmas Holidays, we are compelled to publish the PRACTICAL TEACHER much earlier than usual. This has necessitated several queries being left unanswered. They will, however, be fully attended to in our next issue.

GEORGE PHILIP & SON'S

EDUCATIONAL LIST

PHILIPS' SERIES OF LARGE SCHOOLROOM MAPS.

NEW EDITIONS, reducED IN PRICE.

Size-5 feet 8 inches by 4 feet 6 inches. Mounted on Rollers and Varnished, price 14s. each.

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PHILIPS' SCHOOLROOM MAPS of the COUNTIES of ENGLAND.

Prepared expressly for use in Schools. Constructed by JOHN BARTHOLOMEW, F.R.G.S.

CHESHIRE

DERBYSHIRE.

75. 6d.

DURHAM
KENT

7s. 6d. 7s. 6d.

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7s. 6d.

LINCOLNSHIRE

16s. od. IOS. 6d.

125. od.

NORTHUMBERLAND
NOTTINGHAMSHIRE

21s. od.
7s. 6d.
7s. 6d.

Other Counties in preparation.

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LONDON: GEORGE PHILIP & SON, 32, FLEET STREET;
Liverpool: Caxton Buildings, South John Street, and 49 and 51, South Castle Street.

E. T. THEOBALD & CO.'S

CHRISTMAS NOVELTIES.

Entertainments for Schools and Private Parties. Moderate Terms. Magic Ventriloquism, Punch and Judy, Dissolving Views, etc. Particulars free, 56 page Illustrated Catalogue of Magical Apparatus, Scientific Chemicals, Useful and Amusing Novelties. Post free, I stamp.

SPECIAL OFFER OF OUR UNRIVALLED

BIJOU MAGIC LANTERN

AND SLIDE SETS.

THE IMMENSE SUCCESS of last year has determined us to still further improve their quality.

THESE SETS consist of Best English Magic Lanterns, black Japanned Rackwork Lamp, Silver-plated Concave Reflector, Brass front, Lenses of the Best Quality; and the following 57 Good Pictures :

12 Views, Illustrating a Tale, Pilgrim's Progress, or Life of Christ. 3 Landscapes and Sea Views. 1 Panorama Slide with View, and Moving Shipping, figures, etc. 3 Mechanical Changing Slides. 36 Good Comical, and 2 Brilliant Chromatropes. The whole Packet in Wood Box, with Instructions for use.

THESE SETS are not EQUALLED by any other House in London. To prevent disappointment we request orders to be sent early. The SETS are in Three Sizes, No. 1, 10s. 6d.; No. 2, 14s. 6d. ; No. 3, 21s. od. P.O.O payable Nelson Street, Greenwich.

VENTRILOQUISM.-Anyone may learn the art of throwing their voice in any direction. See Maccabe's Book of Instructions and Dialogues. 110 pages, post free, Is. 2d.

THE WONDERFUL BOX.-Polished mahogany. A marked coin put in by anyone; box closed, tied up; coin heard rattling inside; placed on table; passes through, and is found underneath. Box is then opened, and is empty and silent. Post free, 1s. 2d.

NEW YEAR'S CARDS -Being wholesale dealers, we can give better value for money than any provincial houses. See our sample packet, 13 beautiful Embossed Cards 7d.; 13 larger size, 13d.; or 17 assorted, 13d., all post free. List of others, post free.

THE MAGIC CIGAR-BOX.-You offer the case full of splendid cigars to a friend, but directly he attempts to take one, they all instantly vanish. Post free, 14 stamps; or in real leather, 2s. 2d. Large size, 35. 3d. THE MAGIC SNUFF-BOX-Best puzzle of the day. Has a wonderful way of opening, so that no one without the secret can possibly open it. Will contain snuff, stamps. pins, fuzees, etc. Post free, 14 stamps. MAGIC LANTERNS AND SLIDES.-Lanterns, 4s. to £20. Over 6,000 Slides to select from, including Zulu War. Illustrated catalogue 3 stamps.

E. T. THEOBALD, Britannia Magical Works (opposite the Station), Greenwich, London, S.E.

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DARLOW'S MAGNETINE.

DARLOW & CO.'S MAGNETINE APPLIANCES are used and recommended for the Cure of Gout and Rheumatism, Spinal, Liver, Kidney, Lung, Throat, and Chest Complaints, General Debility, Indigestion, Hernia, Sciatica, Neuralgia, Bronchitis, and other forms of Nervous and Rheumatic Affections.

From GARTH WILKINSON, Esq., M.D., M.R.C.S.E.

70, Wimpole Street, London, W. F. W. Darlow, Esq. SIR,-I am able to certify that I have used your Magnetine Appliances pretty largely in my practice, and that in personal convenience to my patients they are unexceptionable, and far superior to any invention of the kind which I have employed; and that of their efficacy, their positive powers I have no doubt. I have found them useful in constipation, in abdominal congestion, in neuralgia, and in many cases involving weakness of the spine, and of the great organs of the abdomen. In the public interest I wish you to use my unqualified testimony in favour of your Magnetic Appliances.-I remain, yours faithfully,

DARLOW'S

GARTH WILKINSON, M.D., M.R.C.S.E.

DARLOW'S DARLOW'S

DARLOW'S

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CHEST PROTECTORS.

LUNG PROTECTORS.

SPINE BANDS.

DARLOW'S KNEE CAPS.

DARLOW'S WRISTLETS.

DESCRIPTIVE PAMPHLET POST FREE.

LONDON:

DARLOW & CO., 443, STRAND

SCHOLASTIC

MUSICAL INSTRUMENT CO. US

(ESTABLISHED 1871),

To supply Teachers, School Board Members, and School Managers with ANY kind of Musical Instrument from ANY Maker at bona fide Trade Price for Cash, or by Easy Instalments.

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Every one

should read

our Circular

and Extracts, which are sent

Post free.

Apply to the

MANAGEB,
89 Oseney
Crescent,

Camden Road,

'We have now had plenty of time to try the piano; and I can say to you how very much we are pleased with it, and how greatly I am obliged to you for procuring me so excellent an instrument so cheap.-MATTHEW ARNOLD, Esq., H.M.I.

You are at liberty to make any use of my wife's and my own opinionthat the piano is excellent both for tone and touch, and that it is a very cheap piano.'-Rev. T. W. SHARPE, M.A., H.M.I. for Training College for Schoolmasters.

15,000 similar Testimonials have been received from all parts of the country, from H.M. Inspectors, Assistant Inspectors, Presidents of N.U.E.T., Principals and Masters of Training Colleges, Teachers and School Board Clerks.

THE ONLY ADDRESS IS

39 OSENEY CRESCENT, CAMDEN BOAD, LONDON, N.W.

Just Published. Price is. 6d.

ELEMENTARY PHYSIOGRAPHY.

By A. FINDLATER, LL.D.

Adapted to the Requirements of the Science Department, South Kensington; with Examination Questions and Illustrations.

W. & R. CHAMBERS, London and Edinburgh.

APPROVED SCHOOL BOOKS.

BY DR. CORNWELL, F.R.G.S.

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Now Ready.

Key to Science of Arithmetic. Showing the Method of Solution for every Question. 4s. 6d.

School Arithmetic. 14th Edition. 1s. 6d.

Key to School Arithmetic. 4s. 6d.

Arithmetic for Beginners; combines simplicity and fulness in teaching the First Four Rules and Elementary Fractions. 4th Edition. is. GEOGRAPHIES.

A School Geography. 68th Edition, 3s. 6d. ; or, with 30 Maps on Steel, 5s. 6d.

Geography for Beginners. 48th Edition, 1s.; or, with 48pp. of Questions, Is. 4d.

Questions on the Geography for Beginners. 6d.

POETRY.

Select English Poetry for Schools and Families. 16th Edition. 4s. 6d. Poetry for Beginners. A Collection of Short and Easy Poems for Reading and Recitation. 7th Revised Edition. Is.

MAPS.

A School Atlas; consisting of 30 small Maps, in which is found every place mentioned in the Author's 'School Geography.' 2s. 6d. ; or 4s. coloured.

Map-Book for Beginners; a Companion Atlas to the 'Geography for Beginners,' consisting of twelve pages of Maps (above seventy large and small). Is. 6d. ; 2s. 6d. coloured.

Book of Blank Maps. The above Maps complete in all but the names, to be filled in by the Learner. Is.

Book of Map Projections. The Lines of Latitude and Longitude only to the above Maps. 1s.

GRAMMAR.

A len and Cornwell's School Grammar. 58th Edition. as red leather; or Is. gd. cloth.

Grammar for Beginners. An Introduction to Allen and Cornwell's School Grammar. 72nd Edition. Is. cloth; 9d. sewed.

SPELLING AND COMPOSITION.

The Young Composer; or, Progressive Exercises in English Composition. 42nd Edition. 1s. 6d.

Key to Young Composer. 13th Edition. 35.

Spelling for Beginners. A Method of Teaching Reading and Spelling at the same time. 3rd Edition.

IS.

London: SIMPKIN & CO.; HAMILTON & CO.; W. KENT & CO. Edinburgh: OLIVER & BOYD.

No more Failures in English Composition,

NOW READY, THE

THIRD EDITION OF THE

Analytic English Composition TEST CARDS

on an entirely New Plan with Suggestive Heads for the Guidance of Pupils

BY ROBERT S. WOOD,

All Saints' Schools, Bolton.

The FIRST SERIES in 3 Packets, 24 Cards in each, adapted for Standards 4, 5, 6, 7, and for Pupil Teachers and Middle-Class Schools.

Price, in Ornamental Tin Case, 1s. 3d. each; in Wrapper, Is. The Subjects and Heads, over 300 in number, are entered at Stationers' Hall. FROM A HEAD INSPECTOR OF SCHOOLS:

'Your EXCELLENT Test Cards. I look forward to a WIDE CIRCULATION and to GREAT RESULTS from their use.'

The CLERK to an influential School Board :

'I think them ADMIRABLE, and shall be glad to promote their use in all our BOARD SCHOOLS.'

THE EDUCATIONAL NEWS OF SCOTLAND:

'Mr. Wood has conferred a DECIDED BOON upon Teachers. The Composition Cards have only to become KNOWN to be largely used.' SCHOOL BOARD CHRONICLE:

'They are EXCELLENT and well arranged.'

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'The Westminster Hook.'

FOR SCHOOLS, Etc.

All Wrought-iron, Unbreakable. Price is. 6d. per dozen.

(A liberal discount to Schools, or when ordered in quantities.)

Sample sent on receipt of 2d. in stamps.

Other patterns kept in stock. Illustrations sent on application.

HALF-PENNY TABLE BOOK. New Edition, Revised and Enlarged. Price 4s. 6d. per gross.

In demy 4to. Price 6d.

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'THE EASTERN COUNTIES,' 'THE COLLEGIATE,' 'THE COUNTY,' and other desks

AT GREATLY REDUCED PRICES.

FOR PARTICULARS, APPLY TO THE ABOVE, AT

CHAPEL FIELD or DUKE'S PALACE WORKS,

NORWICH.

LECTURES ON TEACHING,

Delivered in the University of Cambridge in the Lent Term, 1880. By J. G. FITCH, M.A., Her Majesty's Inspector of Schools. Third Edition, Revised. Crown 8vo. cloth, 6s.

OPINIONS OF 'The lectures will be found most interesting, and deserve to be carefully studied, not only by persons directly concerned with instruction, but by parents who wish to be able to exercise an intelligent judgment in the choice of schools and teachers for their children.'-Saturday Review.

'While Mr. Fitch addresses himself specially to secondary school-masters, he does not by any means disregard or ignore the needs of the primary school.'-Scotsman.

'It would be difficult to find a lecturer better qualified to discourse upon the practical aspects of the teacher's work than Mr. Fitch.'-The Schoolmaster.

All who are interested in the management of schools, and all who have made the profession of a teacher the work of their lives, will do well to study with care these results of a large experience and of wide observation.'-The Nonconformist and Independent.

THE PRESS.

Mr. Fitch's book covers sɔ wide a field and touches on so many burning questions that we must be content to recommend it as the best existing vade mecum for the teacher. He is always sensible, always judicious, never wanting in tact. '-Pall Mall Gazette. 'If his (Mr. Fitch's) work receives the attention it deserves, it will tend materially to improve and equalize the methods of teaching in our schools, to whatever class they may belong.'-St. James's Gazette.

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In no other work in the English language, so far as we know, are the principles and methods which most conduce to successful teaching laid down and illustrated with such precision and fulness of detail as they are here.'Leeds Mercury,

The book is replete with practical sagacity, and contains, on almost all points of interest to the teaching profession, suggestive remarks resting evidently on a wide and thoughtful experience of school methods. We recommend it in all confidence to those who are interested in the problems with which the teaching profession has to deal,'—Galignani's Messenger.

London: C. J. Clay, M.A., Cambridge Warehouse, 17, Paternoster Row.

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IT can look, and laugh, and dance, and love, and hate, and sneer. It can woo or wound, succumb or subjugate, retreat or triumph. This speaking, intelligent organ can be abused and ruined. Dr. Crichett, the celebrated ophthalmist, said at the Wellington College, Manchester, the other day, "that we were fast becoming a race of short-sighted people; children are now compelled to wear

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spectacles, while their grandfathers enjoy perfect sight." RICHARD TISSINGTON'S POPULAR WORKS.

And yet all this mischief can be prevented by wearing the IMPROVED AMERICAN EYE PROTECTOR. Cheap, and the weight of a shilling coin only. Black, green, or flesh colour. A perfect shield, and small enough, when closed, to carry in the vest pocket.

To be had of all Chemists, Opticians, Booksellers, &c., and sent post-free as under :

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IRKBECK BANK.-Southampton Buildings, ChanCurrent Accounts opened according to the usual practice of other Bankers, and Interest allowed on the minimum monthly balances when not drawn below £25. No commission charged for keeping Accounts.

The Bank also receives money on Deposit at Three per cent. Interest, repayable on demand.

and Shares.

The Bank undertakes for its Customers, free of charge, the custody of Deeds, Writings, and other Securities and Valuables; the collection of Bills of Exchange, Dividends, and Coupons; and the purchase and sale of Stocks Letters of Credit and Circular Notes issued. A Pamphlet, with full particulars, on application. 31st March, 1880. FRANCIS RAVENSCROFT, Manager. The Birkbeck Building Society's Annual Receipts exceed Four Millions.

OW TO PURCHASE A HOUSE FOR TWO Rent to Pay. Apply at the Office of the BIRKBECK BUILDIng Society.

HOW TO PURCHASE A PLOT OF LAND FOR

FIVE SHILLINGS PER MONTH, with immediate possession, either for Building or Gardening purposes. Apply at the Office of the BIRK. BECK FREEHOLD LAND SOCIETY.

A Pamphlet, with ull particulars, on application.

FRANCIS RAVENSCROFT, Manager. Southampton Buildings, Chancery Lane.

48 SONGS FOR SCHOOL AND HOME. Words

and Music post free for 18 Stamps.

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BOB-O-LINK BALLADS. Post free for 12 Stamps.

Homely and humorous, and would be effective as recitations.'-Daily Chronicle.

'A welcome volume. Many of the pieces contain a good sprinkling of wit and humour, and, in the hands of a careful reader, would be likely to amuse an audience, and add variety to a programme.'-Fermanagh Mail.

BANKS & ASHWELL, 10, Wells Street, Oxford Street, London, W.

NOW READY. PRICE 35. 6d.

A

Grammar of the French Language,

FOR PUPIL TEACHERS & THE MORE ADVANCED
CLASSES IN SCHOOLS.

By the Author of

"MADEMOISELLE MORI."

This Grammar contains copious Exercises and an English and a
French Vocabulary.

NATIONAL SOCIETY'S DEPOSITORY,
Westminster, S.W.

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