REVIEWS 679 



The Science of Mechanics : a Critical and Historical Account of its Develop- 

 ment. By ERNST Mach. Supplement to the Third English Edition, 

 containing the Author's Additions to the Seventh German Edition. Trans- 

 lated and Annotated by PHILIP E. B. JOURDAIN, M.A. (Cantab). [Pp. 

 xiv + 106.] (Chicago and London : The Open Court Publishing Co., 1915. 

 Price 2s. bd. net.) 

 This book is in its essence a complement to Mach's Mechanics, the English 

 translation of which by Mr. McCormack was published in 1895. ^ consists of 57 

 pages of additions and alterations made by the author in the seventh German 

 edition, two pages of corrections to be made in the Mechanics, and 38 pages of 

 notes on the original text made by Mr. Philip E. B. Jourdain ; there is also a very 

 full index. From the publishers' preface we learn that this rather ambiguous plan 

 of supplementing the English translation has been adopted by them after much 

 thought and consultation with Prof. Mach ; while in a preface by Mr. Jourdain 

 to his notes he states that " the author's wish that no changes shall be made in 

 the original text is binding, not only for personal reasons, but also because the 

 work is now a classic." The notes which follow the preface have been approved 

 by Prof. Mach. It is in hearty sympathy with the publishers and with Mr. 

 Jourdain that we express our regret that the present form has been adopted. We 

 cannot think that it is wise in a living author to stereotype his work ; apparently 

 if the literal interpretation is to be taken of the words quoted above, even 

 " Leibniz " is to remain " Leibnitz," and " Appelt " must retain the double p. The 

 result is either that students of the English translation are to read the work in Mr. 

 McCormack's translation with their eyes wandering over the three sections of this 

 book, or that they must mark down in their copy corrections, additions, and 

 alterations, an unsatisfactory process to a bibliophile. To Prof. Mach every 

 student of mechanics owes a deep debt of gratitude ; it would have been increased 

 if he had allowed a new edition to incorporate the additions and alterations made 

 in the seventh German edition. In mathematics there is a sense in which it may 

 be said there are no classics. Euclid's Elements would not have influenced 

 mathematical thought for two thousand years if the author and his editors had 

 regarded the text as inviolable. 



The various parts of the book, whether due to Prof. Mach or to Mr. Jourdain, 

 contain excellent matter, interesting historical facts, and acute philosophical 

 criticism. The printing of the book is admirable. 



A Treatise on the Theory of Invariants. By Oliver E. Glenn, Ph.D., 

 Professor of Mathematics in the University of Pennsylvania. [Pp. x + 245.] 

 (Boston, New York, and London : Ginn & Co., 191 5. Price 10*. bd. net.) 

 The object of this book is, firstly, to present in a volume of medium size the 

 fundamental principles and processes and a few applications of invariant-theory 

 with emphasis upon both the non-symbolical and the symbolical methods ; and, 

 secondly, to emphasise a logical development of the theory as a whole and to 

 amalgamate the methods of British and continental mathematicians. Although 

 the original memoirs have been consulted extensively, the author has considered 

 it expedient to give only a few references in the text, and the well-known Report 

 of Meyer and his article in the Encyklopadie are referred to for other references 

 and fuller details of the historical development. The present reviewer has not 

 seen a more stimulating introduction to the theory. It is seldom that writers of 

 text-books have found it possible to awake the student's interest in a branch of 



