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rhòs College; Crewe, The Academy; Dawlish, West Cliff House School; Deal,
The College; Dedham, Grammar School; Derby, Spondon House School;
Devonport, H.M.S. Lion; Dublin: Blackrock College, and Alexandra College;
Dunfermline, High School; Easingwold, Grammar School; Eastbourne, Southdown
College; Eccles, Modern School; Edinburgh: The Academy, and Cargilfield
School; Elgin, The Academy; Elmham, Norfolk County School; Ely, King's
School; Epsom, The College; Falkirk, High School; Fochabers, Milne's Institu-
tion; Forfar, The Academy; Framlingham, The College; Gateshead, Gateshead
School; Glasgow: Technical College, Allen Glen's School, Newton Terrace School,
Girls' Grammar School, and The Academy; Glenalmond, Trinity College; Gos-
port, Collegiate School; Grange-over-Sands, Preparatory School; Gravesend,
Proprietary School, Greenock, Kilblain Academy; Grimsby, St. James's College;
Hastings: University School, and Hurst Court; Helensburgh, Larchfield Academy;
Hereford, Cathedral School; Heversham, Grammar School; Horsham, Grammar
School; Huddersfield, Technical School; Hurstpierpoint, St. John's College;
Ilminster, Grammar School; Ipswich, Middle School for Boys; Kenley, Beaumont
School; Kidderminster, Grammar School; Kingston: Elmhurst School, and
Tiffin's Boys' School; Lancaster, Grammar School; Leeds: Central Higher Grade
School, and Woodhouse Grove School; Leicester, Wyggeston Boys' School; Lin-
coln, Northgate School; Liverpool: Waterloo High School, Warbreck College,
Parkfield School, and Sandholm, Waterloo; Londonderry, Foyle College; Lurgan,
The College; London: City Central Foundation School, E. C., London Institution,
E.C., School for Sons of Missionaries, Blackheath, St. Dunstan's College, Catford,
Aske's School, Hatcham, Wilson's Grammar School, Camberwell, Roan Girls'
School, Greenwich, Alleyne's School, Dulwich, United Westminster School,
Victoria Street, S. W., Tooting College, S. W., Haberdashers' School, Hoxton, N.,
High School, Willesden, N.W., Technical School, Peckam, S. E., Penywern
House College, Earl's Court, S. W., Polytechnic Middle School, Regent Street, W.,
and Polytechnic Institution, Regent Street, W.; Malvern (Great), Greville House
School; Marlborough, Grammar School; Monmouth, Grammar School; Mon-
trose, Technical College; Newcastle-on-Tyne, Rutherford College; Newcastle
(Staff.), High School; Nottingham, Baptist College; Oxford: High School, St.
Kenelm's College, and School House, Crick Road; Perth: The Academy, and
Sharp's Institution; Plymouth, Mannamead School; Probus, Grammar School;
Portsmouth, Buckingham Place Academy; Ramsgate, St. Augustine's College;
Red Hill, Royal St. Anne's School; Retford (East), Grammar School; Rotting-
dean, The School; Ruabon, Grammar School; Saltburn, Collegiate School;
Sedbergh, Grammar School; Sheffield, Central Higher Grade School; Shildon,
Friend's British School; Silcoates, Northern Congregational School; St. Andrews,
St. Leonard's School; St. Asaph, Grammar School; St. Bees, Grammar School;
St. Kitt's, B.W.I., Grammar School; St. Leonards: Maze Hill School, and Win-
chester House School; Sandwich, Grammar School; Storrington, The Forge
School; Sunderland, The Hall School; Swansea, St. Andrew's College; Taunton,
The Huish School; Tipperary, Christian School; Torquay, Torbay College;
Twickenham, King's College; Warwick, King's School; Waterford, Ursuline
Convent School; Watford, London Orphan Asylum; Weybridge, St. George's
College; Windsor, St. Mark's School; Winchester, Wellington House School;
Woodford, Bancroft School; Yarm-on-Tees, Grammar School; Yarmouth,
Grammar School.

Now Ready. Globe 8vo. Price, with Answers, Green Cloth, 4s. 6d. Without Answers, Maroon Cloth, 4s. 6d. [Examples separately, 3s. Answers, 6d.]

AN ARITHMETIC

FOR SCHOOLS

BY

S. L. LONEY, M.A.

SOMETIME FELLOW OF SIDNEY SUSSEX COLLEGE, CAMBRIDGE

London

MACMILLAN AND CO., LIMITED

NEW YORK: THE MACMILLAN COMPANY

All rights reserved

XXIII. Square Root; Miscellaneous Examples on Square Root.
XXIV. Cube Root; Miscellaneous Examples on Cube Root.
XXV. Some Miscellaneous Problems and Methods-Averages ;
Mixtures and Alloys; Work Problems; Clock Problems;
Velocity Problems; Stream and Race Problems; Thermo-
meters; Areas of Circles, etc.; Duodecimals.

XXVI. The Metric System; Decimal Coinage.
XXVII. Foreign Moneys; Foreign Exchanges.

Appendix-Note A. The Roman System of Numeration; B. On Money; C. On Time and the Calendar; D. On Measures of Length; E. On Measures of Weight; F. On Measures of Capacity; G. On Casting out the Nines; H. On Recurring Decimals; K. On the Third, Tenth and Tenth Rule; L. On Bills of Exchange; M. On Paper Currency.

Answers to the Examples.

PRESS OPINIONS

Guardian." Mr. Loney is so well known now as a most successful writer that it is almost sufficient notice to say that he has brought out an Arithmetic for use in public schools, and that his last production is quite as good as the others. . Its cheapness, good binding, and excellent typography make one inclined to say that Mr. Loney has said the last word on the subject-at any rate for many years to come.

Nature.-"A comprehensive text-book, clearly written and well arranged. The examples are numerous, sensibly chosen, and carefully graduated. . . Deserves to rank with the best of its class.'

"

English Mechanic.—“An excellent text-book."

Scotsman.-"An admirable book of its kind."

Educational Times.-"A clear and well-illustrated account of abstract and concrete arithmetic in its higher applications."

Teachers' Aid.-"In this book everything generally given under the head of arithmetic is included, and in some of the chapters, such as stocks and foreign exchanges, some trouble has been taken by the author to furnish the student with an elementary knowledge of those subjects. Many of the more typical and difficult questions are worked out, and appended to most of the more im

portant chapters there is a set of miscellaneous examples; which will be found of great value to students. The answers are placed at the end of the book, which appears to have been compiled with great care, and is well adapted for the purpose the author had in view."

School Guardian.-"Many excellent text-books of arithmetic have been published of late years, and not a few of really high merit, altogether surpassing and (we trust) supplanting their indifferent predecessors of thirty or forty years ago. Yet we think that Mr. Loney's volume altogether justifies its existence by the various points in which it either equals or excels its rivals. Whether this be so or not, it seems to us an admirable and praiseworthy compilation that may be safely commended to the notice of teachers who are on the look-out for a new text-book for the use of their pupils. The exercises are abundant and well graduated, what may be called the more important classes of problems are dealt with in separate chapters, and there are some capital Appendices on such subjects as Roman Numeration, Money, the Calendar, and others akin to these."

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The examples The book is a thoroughly good

Practical Teacher." An excellent book for school use. given are well graded and well arranged. one which we can heartily recommend."

Schoolmistress.-"The author has endeavoured to state very clearly the principles and methods of arithmetical calculations, and has succeeded in his endeavour. There is much useful matter towards the end of the book that will prove valuable to those attending higher class schools. We have verified a goodly number of the exercises, and have found the answers given correct. This is a carefully-compiled, complete, and up-to-date school arithmetic."

School Board Chronicle.-"The book before us justifies its title, and will prove as useful to the teacher as to the scholar. Not only are the mental processes for each operation set out for the scholar to follow, but the proofs of rules are simple enough to be readily intelligible to the mind of the ordinary schoolboy, and consequently are such as might be adopted by any teacher, and will certainly be of use to those preparing for teachers' examinations, where such simple explanations are required. The four fundamental rules are thoroughly considered-thirty-two pages being devoted to them. The book contains everything usually given under the head of arithmetic. Every portion receives adequate treatment, and this of such a character as makes it possible to read and follow it with a minimum of effort. In some chapters, as those on Stocks and Foreign Exchanges, the author has been at some pains to impart an elementary knowledge of those subjects, such as is necessary if a scholar is to intelligently tackle the problems set for his solution. That is an excellent way of presenting calculations of this nature. In a severely abstract form they are often repugnant to the same lad who will pursue them with intelligence and pleasure when he perceives them in their practical application, to those actual transactions of business life of which he is usually more or less vaguely aware. The examples set at the end of each chapter are very numerous and comprehensive, embracing every form of problem usually met with in schools. In an Appendix at the end of the book will be found some useful information, especi ally concerning Money, Roman Numeration, the Calendar, Weights and Measures, and Recurring Decimals. It would be difficult to suggest what could usefully have been embodied in an Arithmetic for Schools more than is provided within these 450 pages."

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