SCIENCE. 



[N. S. Vol. XXII. No. 574. 



fundamental ease mentioned above, and that 

 they introduce a slightly more general form 

 of notation, which is necessary in the last 

 analysis for the solution of certain problems. 

 An adequate account of these chapters can be 

 omitted here with more grace since the writer 

 has shown his appreciation of them in a man- 

 ner more befitting their real importance in a 

 review of a more technical character in the 

 Bulletin of the American Mathematical So- 

 ciety (November, 1905), which will be acces- 

 sible to a reader whose interest is professional. 



It would be misleading to leave an impres- 

 sion that Bolza's book is elementary or that 

 it can be read without special mathematical 

 training. It is highly technical even in com- 

 parison with most of the extant English works 

 on mathematics. Its standards are not higher 

 than they should be, however; they are un- 

 usual in a book printed in English; they are 

 not higher than the average standard of the 

 classical foreign mathematical treatises; they 

 are beyond question a step in the right direc- 

 tion. 



This book is not primarily a text-book; 

 it will not share the speedy oblivion of that 

 class; and there are many evidences that this 

 and a few other extremely recent mathemat- 

 ical books published in America are merely 

 the first of a considerable volume of mathe- 

 matical productions of like grade, which, if 

 the average standards remain equal to those 

 set by this book, will indeed deserve to be 

 called an American mathematical literature. 



E. R. Hedrick. 



Columbia, Mo., 

 December 1, 1905. 



SOCIETIES AWD ACADEMIES. 



THE WASHINGTON ACADEMY OP SCIENCES. 



At a meeting of the academy on November 

 28, Professor Wilhelm Ostwald, of Leipzig, 

 who is now lecturing at Harvard University, 

 gave an interesting address upon the proposed 

 * Universal Auxiliary Langiiage.' The sub- 

 stance of his address was as follows : 



In our time, when international congresses 

 of all kinds, scientific, commercial, political, 

 etc., are gathering almost every day, the neces- 

 sity of a general means of mutual understand- 



ing is felt more keenly than at any former 

 time. Small wonder therefore, that at one 

 of these congresses, that of philosophy, held at 

 Paris, 1900, the question was earnestly dis- 

 cussed, whether it was possible to overcome 

 this insufferable obstacle to the common work 

 of mankind. As a result, an international 

 committee was elected to consider the matter 

 and to propagate the general idea. This com- 

 mittee came to the conclusion that the selec- 

 tion or creation of a general auxiliary lan- 

 guage was necessary, which should not sup- 

 plant the existing languages, but should be 

 learned by everybody besides his native speech 

 for the purpose of international intercourse. 

 This language must satisfy the following three 

 conditions : 



1. It must fulfill the needs ■ of ordinary in- 

 tercourse of social life, of commercial com- 

 munications and of scientific and philosophic 

 relations. 



2. It must be easily acquired by every per- 

 son of average elementary education, and espe- 

 cially by persons of European (and American) 

 civilization. 



3. It must not be one of the national lan- 

 guages. 



Upon this program a widespread and effect- 

 ive propaganda has been developed. About 

 800 scientists of various countries, all univer- 

 sity professors or members of scientific acad- 

 emies, and besides these about 200 societies of 

 the most various kinds: scientific societies, 

 chambers of commerce, touring clubs, etc., 

 representing many thousand members, have 

 joined the general movement. The purpose 

 is, to ask after due time the Association des 

 Academies, which represents the most impor- 

 tant academies all over the world and is, 

 therefore, the highest scientific corporation 

 existing in our days, to take over this work 

 of the international auxiliary language as its 

 own, to appoint a working committee for the 

 selection and introduction of such a language 

 and to form a lasting and effective center for 

 its culture and development. In case the 

 association should decline this noble and im- 

 portant task, such a working committee will 

 be selected by the above named international 

 committee, formed by the representatives of 



