chapter is devoted to the investigations made in 1684 : these are

illustrated by Newton's professorial lectures (of which the original manuscript is extant) of that autumn, and are summed up in the almost unknown memoir of February, 1685, which is here repro- duced from Newton's holograph copy. In the two following chap- ters the details of the preparation from 1685 to 1687 of the Prindpia are described, and an analysis of the work is given. The seventh chapter comprises an account of the researches of Newton on gravitation subsequent to the publication of the first edition of the Prindpia^ and a sketch of the history of that work.
In the last chapter, the extant letters of 1678-1679 between Hooke and Newton, and of those of 1686-1687 between Halley and Newton, are reprinted, and there are also notes on the extant correspondence concerning the production of the second and third editions of the Prindpia.
503
For the essay which we have before us, Mr. Ball should receive the thanks of all those to whom the name of Newton recalls the memory of a great man. The Frincipia, besides being a lusting monument of Newton's life, is also to-day the classic of our mathematical writings, and will be so for some time to come. . . . The value of the present work is also enhanced by the fact that, besides containing a few as yet unpublished letters, there are collected in its p:\ge3 quotations from all documents, thus forming a complete summary of every- thing that is known on the subject. . . . The author is so well known a writer on anything connected with the history of mathematics, that we need make no mention of the thoroughness of the essay, while it would be superfluous for us to add that from beginning to end it is pleasantly written and delightful to read. Those well acquainted with the Principia, will find much that will interest them, while those not so fully enlightened will learn much by reading through the account of the origin and history of Newton's greatest work. — Nature.
An Easay on Neivton's Principia will suggest to many something solely mathematical, and therefore wholly uninteresting. No inference could be more erroneous. The book certainly deals largely in scientific technicalities which will interest experts only ; but it also contains much historical infor- mation which might attract many who, from laziness or inability, would be very willing to take all its mathematics for granted. Mr. Ball carefully examines the evidence bearing on the development of Newton's great dis- covery, and supplies the reader with abundant quotations from contemporary authorities. Not the least interesting portion of the book is the appendix, or rather appendices, containing copies of the original documents (mostly letters) to which Mr. Ball refers in his historical criticisms. Several of these bear upon the irritating and unfounded claims of Hooke. — The Athenceum.
La savante monographie de M. Ball est r^digee avec beaucoup de soin, et ^ plusieurs egards elle pent servir de modele pour des ecrits de la meme nature. — Bibliotheca Mathematica.
Newton's Principia has world-wide fame as a classic of mathematical science. But those who know thoroughly the contents and the history of the book are a select company. It was at one time the purpose of Mr. Ball to prepare a new critical edition of the work, accompanied by a prefatory histoiy and notes, and by an analytical commentary. Mathematicians will regret to hear that there is no prospect in the immediate future of seeing this important book carried to completion by so competent a hand. They will at the same time welcome Mr. Ball's Essay on the Principia for the elucida- tions which it gives of the process by which Newton's great work originated and took form, and also as an earnest of the completed plan. — The Scotsman.
In this essay IMr. Ball presents us with an account highly interesting to mathematicians and natural philosophers of the origin and history of that remarkable product of a great genius Pltilosophiae Natnralis Principia Mathematica, 'The Mathematical Principles of Natural Philosophy,' better known by the short term Principia. . . . Mr. Ball's essay is one of extreme interest to students of physical science, and it is sure to be widely read and greatly appreciated. — T/ie Glasgow Herald.
To his well-known and scholarly treatises on the History of Mathematics Mr. W. W. Rouse BhII has added An Essay on Ncicton\t Principia. Newton's Principia, as Mr. Ball justly observes, is the classic of English mathematical writings ; and this sound, luminous, and laborious essay ought
1
504
to be the classical account of the Principia. The essay is the outcome of a critical edition of Newton's great work, which IMr. Ball tells us that he once contemplated. It is much to be hoped that he will carry out his intention, for no English mathematician is likely to do the work better or in a more reverent spirit. ... It is unnecessary to say that Mr. Ball has a complete knowleds;e of his subject. He writes with an ease and clearness that are rare. — The Scottish Leader.
Le volume de M. Rouse Ball renferme tout ce que I'on pent desirer savoir Bur riiistoire des Principes ; c'est d'ailleurs I'ceuvre d'un esprit clair, judi- cieux, et methodique. — Bulletin des Sciences Math6matique&.
Mr. Ball has put into small space a very great deal of interesting matter, and his book ought to meet with a wide circulation among lovers of Newton and the Principia. — The Academy,
Admirers of Mr. W. W. Rouse Ball's Short Account of the History of Mathematics will be glad to receive a detailed study of the history of the Principia from the same hand. This book, like its predecessors, gives a very lucid account of its subject. We find in it an account of Newton's investiga- tions in his earlier years, which are to some extent collected in the tract de Motu (the germ of the Principia) the text of which Mr. Rouse Ball gives U3 in full. In a later chapter there is a full analysis of the Principia itself, and after that an account of the preparation of the second and third editions. Probably the part of the book which will be found most interesting by the general reader is the account of the correspondence of Newton with Hooke, and with Halley, about the contents or the publication of the Principia. This correspondence is given in full, so far as it is recoverable. Hooke does not appear to advantage in it. He accuses Newton of stealing his ideas. His vain and envious disposition made his own merits appear great in hia eyes, and be-dwarfed the work of others, so that he seems to have believed that Newton's great performance was a mere expanding and editing of the ideas of Mr. Hooke — ideas which were meritorious, but after all mere guesses at truth. This, at all events, is the most charitable view we can take of his conduct. Halley, on the contrary, appears as a man to whom we ought to feel most grateful. It almost seems as though Newton's physical insight and extraordinary mathematical powers might have been largely wasted, as was Pascal's rare genius, if it had not been for Halley's single-hearted and self- forgetful efforts to get from his friend's genius all he could for the enlighten- ment of men. It was probably at his suggestion that the writing of the Principia was undertaken. When the work was presented to the Royal Society, they undertook its publication, but, being without the necessary funds, the expense fell upon Halley. When Newton, stung by Hooke's accusations, wished to withdraw a part of the work, Halley's tact was required to avert the catastrophe. All the drudgery, worry, and expense fell to his share, and was accepted with the most generous good nature. It will be seen that both the technical student and the general reader may find much to interest him in Mr. Rouse Ball's book, — The Manchester Guardian.
Une histoire tres bien faite de la gen^se du livre immortel de Newton. . , . Le livre de M. Ball est une monographie precieuse sur un point important de I'bistoire des mathematiques. II contribuera a accroitre, si c'est possible, la gluire de Newton, en revelant a beaucoup de lecteurs, avec quelle merveilleuse rapidite I'illustre geom^tre anglais a eleve a, la science ce monument immortel, les Principia. — Mathcsis.
50
i)
THE HISTORY OF
TEINITY COLLEGE, CA]\I BRIDGE
By W. W. rouse BALL. [Pp. xiv + 183. Price 2s. 6d. net]
MACMILLAN AND CO. Ltd., LONDON AND NEW YORK.
This booklet gives a popular account of the History of Trinity College, Cambridge. It was written mainly for the use of the author's pupils, and contains such information and gossip about the College and life there in past times as he believed would be intere:iting to most undergraduates and members of the House.
This . . . little volume seems to us to do more for its subject than many of the more formal volumes . . . treating of the separate colleges of the English universities. ... In nine short, extremely readable, and truly informing chapters it gives the reader a very vivid account at once of the origin and development of the University of Cambridge, of the rise and gradual supremacy of the colleges, . . . and the subsequent fortunes of the premier coUege of Cambridge. The subject is treated . . . under four great periods— namely, that during the Middle Ages, that during the Ecnaissaiice, that under the Ehzabethan statutes, and that during the last half-century. No one who begins Mr. Ball's book will lay it down till he has read it from beginning to end. — The Glasgoio Herald.
It is a sign of the times, and a very satisfactory one, when ... a tutor . . . takes the trouble to make the history of his college known to his pupils. Considering the lack of good books about the Universities, we may thank Mv. Ball that he has been good enough to print for a larger circle. Though he modestly calls his book only "Notes," yet it is eminently readable, and there is plenty of information, as well as abundance of good stories, m its poges. — The Oxford Magazine.
Mr. Ball has put not only the pupils for whom he compiled these notes, but the large world of Trinity men, under a great obligation by tliis compendious but lucid and interesting history of the society to whose service lie is devoted. The value of his contribution to our knowledge is increased by the extreme simplicity with which he tells his story, and the very suggestive details which, without much comment, he has selected, with admirable discernment, out of the wealth of materials at his disposal. His hiitial account of the develop- ment of the University is brief but extremely clear, presenting us with facts rather than theories, but establishing, with much distinctness, the essential difference between the hostels, out of which the more modern colleges grew, and that monastic life which poorer students were often tempted to join. — The Guardian.
An interestuig and valuable book. ... It is described by its author as "little more than an orderly transcript" of what, as a Fellow and Tutor of the College, he has been accustomed to tell his pupils. But while it does not
506
pretend either to the form or to the exhaustiveness of a set history, it i*- scholarly enough to rnnk as an authority, and far more interesting and read- able than most academic histories are. It gives an instructive sketch of the development of the University and of the particular history of Trmity, noting its rise and policy in the earlier centuiies of its existence, until, under the misrule of Bentley, it came into a state of disorder which nearly resulted in its dissolution. The subsequent rise of the College and its position iu what Mr. Ball calls the Victorian renaissance, are drawn in lines no less suggestive ; and the hook, as a whole, cannot fail to be welcome to every one who is closely interested in the progress of the College. — T'he Scotsman.
Mr. Ball has succeeded very well in giAring in this little volume just what an intelligent undergraduate ought and probably often does desu-e to know about the buildings and the history of his College. . . . The debt of the "royal and religious foundation" to Henry VIII. is explained with fulness, and there is much interesting matter as to the manner of Ufe and the expenses of students in the sixteenth century. — The Manchester Guardian.
TRINITY COLLEGE, CAMBRIDGE
By W. W. rouse BALL. [Pp. xiv + 107. Price 2s. net.]
J. M. DENT AND CO., LONDON.
This booklet contains a somewhat more popular sketch of the history, external and internal, of the College, with notes on some of its famous past members. It is intended to supply such information as all those in any way interested in the matter would desire to have. It is illustrated by Mr. Edmund H. New.
Mr. Rouse Ball is a sound antiquary and an accomplished writer. He is also in close touch with the actual life of the great home of learnmg through which he guides us in his skilful pages. His topographical descriptions are clear and concise, his historical sketches, both of the external and the internal life of the College are interesting and Uvely, while the occasional light which he throws upon the habits and ways of collegians, ancient as well as modern, is extremely valuable.— T/fe Guardian.
The skill with which the . . . subjects have been treated will be recognised and appreciated by all readers. Not less adequate are the author's description of the College buildings, his account of Trinity life, customs and traditions, and his references to the many eminent men who have added lustre to the great College in successive generations. — The World.
A charming book . . . which tells just what every Trinity man should wish to know about his College, its buildings and its famous sous.— The Oxford Magazine.
In his account of the College, Mr. Eouse Ball is equally at home in dealing with the history, the architecture, the collegiate life, and the personal associa- tions which gather so closely around the College. His anecdotes and tales are chosen with judgment, and told with a vivacity and humour which add materially to the dehghtfulness of the book.— T^e Bookseller.
This book is pleasant, it is anecdntical, it is practical, fui-nishing just the details that one wants, with the relief of the agreeable and entertammg.— The Spectator,
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