718 



SCIENCE 



[N. S. Vol. XXXIV. No. 882 



Series Prima, Opera Mathematica, Volumen 



Primum. Leipzig und Berlin, B. G. Teub- 



ner. 1911. Pp. xcv + 651. 



Leonhard Euler (1707-1783) has been the 

 most prolific mathematical writer of all past 

 times. The great extent of his writings de- 

 layed the appearance of his complete works 

 until the day when big scientific projects can 

 be carried through by international coopera- 

 tion. The mathematical world had never be- 

 fore witnessed such extensive international 

 collaboration in a financial way, as when the 

 means for publishing the forty-five large vol- 

 umes of Euler's complete work were secured. 

 While Euler's native country, Switzerland, did 

 the most in proportion to her means, by con- 

 tributing more than one hundred thousand 

 francs towards the expense of this publication, 

 many other countries, especially Germany, 

 Russia and France, aided very liberally. 



In our own country, the American Mathe- 

 matical Society contributed five thousand 

 francs and our libraries, doubtless, contributed 

 much more in the form of subscriptions. The 

 great academies of Paris, Berlin and St. 

 Petersburg, of which Euler was a member, 

 each subscribed for forty copies of the com- 

 plete works, and thus aided the project not 

 only financially, but still more by their great 

 scientific influence. The last of these three 

 academies contributed also five thousand 

 francs in money. The total amount of sub- 

 scriptions and money collected before the pub- 

 lication began amounted to over four hundred 

 and fifty thousand francs. 



The volume before us is in German, with 

 the exception of a paper by J. L. Lagrange 

 entitled, " Additions a I'analyse indeterminee," 

 which appeared for the first time in the French 

 translation of Euler's algebra in 1774. In 

 addition to an extensive eulogy on Euler by 

 Nikolaus Fuss, and a few introductory notes 

 in reference to the publication of Euler's com- 

 plete works, the present volume is devoted to 

 a very elementary introduction to algebra 

 under the title " Vollstandige Anleitung zur 

 Algebra mit den zusatzen von Joseph Louis 

 Lagrange, herausgegeben von Heinrich Weber." 

 This algebra was prepared for publication 



after Euler had become totally blind. Euler 

 desired to prepare a work which could be 

 understood by every one and which would be 

 complete in every particular. He dictated it 

 to a servant who had been a tailor and knew 

 nothing about mathematics beyond the cal- 

 culations involved in elementary arithmetic. 

 It is said that this tailor understood it com- 

 pletely, and, by the time the more difficult sub- 

 jects were reached, he could work out th« 

 details with ease. 



The work was soon translated into Eussian 

 and into French, and it exercised a greater 

 influence on the development of algebra during 

 the eighteenth century than other work. It 

 was translated into English in 1797 and a very 

 large number of editions in various languages 

 have appeared. While the greater part of it 

 is devoted to very elementary questions in 

 algebra, it proceeds gradually to such matters 

 as the general solution of the cubic and the 

 biquadratic equations, and especially to inde- 

 terminate analysis. In the latter part it is 

 proved that the sum of the cubes of two ra- 

 tional numbers can not be the cube of such a 

 number. This is a special case of the noted 

 Fermat's theorem, for the complete proof of 

 which a prize of twenty-five thousand dollars 

 is now offered through the Konigliche Gessell- 

 schaft der Wissenschaften in Gottingen. 



The complete works of Euler are to appear 

 in three series. The first of these is devoted 

 to pure mathematics and wiU probably consist 

 of 18 volumes. The second series, composed 

 of 16 volumes, is devoted to mechanics and 

 astronomy; while the third series, composed of 

 11 volumes, is devoted to physics, works of 

 various contents and letters. The different 

 memoirs will be republished in the same lan- 

 guage in which they first appeared. 



G. A. Miller 



Applied Electrochemistry. By M. de Kay 

 Thompson, Ph.D., Assistant Professor of 

 Electrochemistry in the Massachusetts In- 

 stitute of Technology. New York, The 

 Macmillan Company. 1911. 

 The subject of applied electrochemistry has 



now become so large and important that a 



