book is warmly to be recommended, and should find a place on the shelves of

every one interested in mathematics and on those of every public library. — The Manckesler Guardian.
A work which will interest all who delight in mathematics and mental exercises generally. The student will often take it up. as it contains many problems which puzzle even clever people. — The English Mechanic and World of Science.
This is a book which the general reader should find as interesting as the mathematician. At all events, an intelligent enjoyment of its contents pre- supposes no more knowledge of mathematics than is now-a-days possessed by almost everybody. — The Athenceum.
An exceedingly interesting work which, while appealing more directly to those who are somewhat mathematically inclined, it is at the same time cal- culated to interest the general reader. . . . Mr. Ball writes in a highly interesting manner on a fascinating subject, the result being a work which is in every respect excellent. — The Mechanical World.
E um livro muito interessante, consagrado a recreios mathematicos, alguns dos quaes sao muito bellos, e a problemas interessantes da mesma scieucia, que nao exige para ser lido grandes conheciraentos mathematicos e que tem em grao elevado a qualidade de instruir, deleitando ao mesmo tempo. — Jour- nal de sciencias mathematicas, Coimhra.
The work is a very judicious and suggestive compilation, not meant mainly for mathematicians, yet made doubly valuable to them by copious references. The style in the main is so compact and clear that what is central in a long argument or process is admirably presented in a few words. One great merit of this, or any other really good book on such a subject, is its suggestiveness ; and in running through its pages, one is pretty sure to think of additional problems on the same general lines. — Bulletin of the New York Matheinatical Society.
A book which deserves to be widely known by those who are fond of solving puzzles . . . and will be found to contain an admirable classified collection of ingenious questions capable of mathematical analysis. As the author is him- self a skilful mathematician, and is careful to add an analysis of most of the propositions, it may easily be believed that there is food for study as well as amusement in his pages. ... Is in every way worthy of praise. — The School Guardian.
Once more the author of a Short History of Mathematics and a History oj the Study of Mathevuitics at Cambridge gives evidence of the width of his reading and of his skill in compilation. From the elementary arithmetical puzzles which were known in the sixteenth and seventeenth centuries to those modern ones the mathematical discussion of which has taxed the energies of the ablest investigator, very few questions have been left unrepresented. The sources of the author's information are indicated with great fulness. . . , The book is a welcome addition to English mathematical literature. — Tiie Oxford Magazine.
500
A HISTORY OF THE STUDY OF
MATHEMATICS AT CAMBEIDGE
By W. W. house BALL. [Pp. xvi. + 264. Plaice Qs.]
THE UNIVERSITY PRESS, CAMBRIDGE.
This work contains an account of the development of the study of mathematics in the university of Cambridge from the twelfth century to the middle of the nineteenth century, and a description of the means by which proficiency in that study was tested at various times.
The first part of the book is devoted to a brief account of the more eminent of the Cambridge mathematicians, the subject matter of their works, and their methods of exposition. The second part treats of the manner in which mathematics was taught, and of the exercises and examinations required of students in past times. A sketch is given of the origin and history of the Mathematical Tripos; this includes the substance of the earlier parts of the author's work on that subject, Cambridge, 1880. To explain the relation of mathematics to other departments of study an outline of the general history of the university and the organization of education therein is added.
The present volume is very pleasant reading, and though much of it neces- sarily appeals only to mathematicians, there are parts — e.g. the chapters on Newton, on the growth of the tripos, and on the history of the university — which are full of interest for a general reader. . . . The book is well written, the style is crisp and clear, and there is a humorous appreciation of some of the curious old regulations which have been superseded by time and change of custom. Though it seems light, it must represent an extensive study and investigation on the part of the author, the essential results of Avhich are skilfully given. We can most thoroughly commend Mr. Ball's volume to all readers who are interested in mathematics or in the growth and the position of the Cambridge school of mathematicians. — The Manchester Guardian.
501
Voici un livre dont la lecture inspire tout d'ahord le regret que dcs travaux analogues n'aient pas et^ faits pour toutes les Ecoles cdl^bres, et avec autant de soin et de clarte. . . . Toutes les parties du livre nous ont viveniont interesse. — Bulletin dcs sciences matMmatiqxies.
A book of pleasant and useful reading for both historians and mathemati- cians. Mr. Ball's previous researches into this kind of history have already established his reputation, and the book is worthy of the reputation of its author. It is more than a detailed account of the rise and progress of mathe- matics, for it involves a very exact history of the University of Cambridge from its foundation. — The Educational Times.
Mr. Ball is far from confining his narrative to the particular science of which he is himself an acknowledged master, and his account of the study of mathematics becomes a series of biographical portraits of eminent professors and a record not only of the intellectual life of the elite but of the manners, habits, and discussions of the great body of Cambridge men from the six- teenth century to our own. . . . He has shown how the University has justified its liberal reputation, and how amply prepared it was for the larger freedom which it now enjoys. — The Daily News.
Mr. Ball has not only given us a detailed account of the rise and progress of the science with which the name of Cambridge is generally associated hut has also written a brief but reliable and interesting history of the university itself from its foundation down to recent times. . . . The book is pleasant reading alike for the mathematician and the student of history. — St. James's Gazette.
A very handy and valuable book containing, as it does, a vast deal of interesting information which could not without inconceivable trouble bo found elsewhere. ... It is very far from forming merely a mathematical bio- graphical dictionary, the growth of mathematical science being skilfully traced in connection with the successive names. There are probably very few people who will be able thoroufrhly to appreciate the author's laboriouo researches in all sorts of memoirs and transactions of learned societies in order to unearth the material which he has so agreeably condensed. . . . Along with this there is much new matter which, while of great interest to mathemati- cians, and more especially to men brought up at Cambridge, will be found to throw a good deal of new and important light on the history of education in general. — The Glasr/ow Herald.
Exceedingly interesting to all who care for mathematics. . . . After giving an account of the chief Cambridge Mathematicians and their works in chrono- logical order, Mr. Rouse Ball goes on to deal with the history of tuition and examinations in the University . . . and recounts the steps by which the word "tripos" changed its meaning "from a thing of wood to a man, from a man to a speech, from a speech to two sets of verse.'^, from ver.ses to a sheet of coarse foolscap paper, from a paper to a list of names, and from a list of names to a system of examination. — Never did word undergo so many alterations. — The Literary World.
In giving an account of the development of the study of mathematics in the University of Cambridge, and the means by which mathematical proficiency was tested in successive generations, Mr. Ball has taken the novel plan of de- voting the first half of his book to . . . the more eminent Cambridge mathe- maticians, and of reserving to the second part an account of how at various times the subject wa.s taught, and how the result of its study was tested. . . . Very interesting information is given about the work of the students during the different periods, with specimens of problem-papers as far back as l>s()2. The book is very enjoyable, and gives a capital and accurate digest of many excellent authorities which are not within the reach of the ordinary reader. — TJie Hoots Observer,
502
AN ESSAY ON THE GENESIS, CONTENTS, AND HISTORY OF
KEWTON'S "PRINCIPIA"
By W. W. EOUSE BALL. [Pp. X. + 175. Price 6s. net]
MACMILLAN AND CO. Ltd., LONDON AND NEW YORK.
This work contains an account of the successive discoveries of Newton on gravitation, the methods he used, and the history of his researches.
It commences with a review of the extant authorities dealing with the subject. In the next two chapters the investigations made in 1666 and 1679 are discussed, some of the documents deal- ing therewith being here printed for the first time. The fourth