June 9, 1899. ] 



SCIENCE. 



817 



In Science for September 24, 1897, I men- 

 tioned these treasures as ' extended researches 

 anticipating the discoveries of Cayley and 

 Klein.' Engel now says of them, p. 393 : "J. 

 Bolyai had also commenced to work out a great 

 and consecutive presentation of geometry, but 

 what he had written down remained entombed 

 in his papers and has never been published. 



' ' Staeckel will before long make generally ac- 

 cessible so much of it as is suitable for publication, 

 and it will then appear that J. Bolyai in his 

 exposition set to work according to principles 

 similar to those Lobach6vski actually followed. ' ' 

 But though Lobachevski has given his complete 

 message to the ages, yet is perceptible a touch 

 more masterful in even the brief two dozen 

 pages of the young Magyar. 



Through a given point to draw a parallel to 

 a given straight ; to draw to one side of an 

 acute angle the perpendicular parallel to the 

 other side ; to square the circle — these problems 

 would be sought in vain in the two quarto vol- 

 umes of Lobachevski. 



Bolyai Janos gives solutions of them startling 

 in their elegance. For example (Halsted's 

 Bolyai § 34), " Through D we may Draw DM || 

 AN in the following manner : From D drop 

 DBiAN ; from any point A of the straight AB 

 erect AClAN (in DBA), and let fall DCj_AC. 

 A quadrant described from the center A in 

 BAG, with a radius = DC, will have a point B 

 or O in common with ray BD. In the first case 

 the angle of parallelism manifestly is right, but 

 in the second case it equals AOB. If, therefore, 

 we make BDM = AOB, then DM will be || BN.'' 



About 100 pages of Eugel's book are devoted 

 to a life of Lobachevski, yet no word is said of 

 his wife, his children, his family life, his home 

 fortunes and misfortunes, nor is mentioned the 

 biography by E. F. Letvenov (St. Petersburg, 

 1894, pp. 79) containing romantic pictures of 

 these eternal interests. 



Geoege Bruce Halsted. 



Austin, Texas. 



The Spirit of Organic Chemistry. An Introduc- 

 tion to the Current Literature of the Subject. 

 By Arthur Lachman, B.S., Ph.D., Professor 

 of Chemistry in the University of Oregon. 

 With an Introduction by Paul C. Freer, 



M.D., Ph.D., Professor of General Chemistry 



in the University of Michigan. New York, 



The Macmillan Company. 1899. Pp. xviii 



+ 229. Price, $1.50. 



Under the above title an historical account of 

 the development of some of the most important 

 chapters is given. The subjects selected are 

 among those which have exercised the minds 

 and skill of the greatest chemists, and which 

 are to-day before the chemical world. Prob- 

 lems which have been solved in a single mas- 

 terly research are omitted. In the nine chap- 

 ters the following subjects are treated : The 

 constitution of rosaniline, Perkins's reaction, 

 the constitution of benzene, the constitution of 

 aceto-acetio ether, the uric-acid group, the 

 constitution of the sugars, the isomerism of 

 fumaric and male'ic acids, the isomerism of the 

 oximes, and the constitution of the diazo com- 

 pounds. 



The author has used excellent judgment in 

 condensing the literature, and has presented the 

 subject in a logical and clear manner. The 

 account is brought up to date, even the most 

 recent work receiving brief mention. The book 

 is, therefore, an introduction to the chemical 

 literature of to-day. On this account it is of 

 special value to the student who has just mas- 

 tered the text-books of organic chemistry and 

 who desires to go farther. The mass of litera- 

 ture which is summed up in but 225 pages is so 

 great aud complex that it is doubtful whether 

 the student would have the time and energy to 

 get as clear a conception of the subject by 

 searching through the journals as he can get by 

 a careful study of this book. After mastering 

 it he would be in a position to follow a paper on 

 any of the subjects treated. 



The literature of organic chemistry is so vast 

 that there is room for such critical reviews, for, 

 it seems to the writer, they tend to inspire 

 rather than pi'event reading. Professor Lach- 

 man's book will make the reading of the current 

 journals easier and is, therefore, helpful. It is 

 a contribution to chemical history, and supple- 

 ments Schlorlemmer'^ well-known " Rise and 

 Development of Organic Chemistry." 



James F. Noeris. 



Massachusetts Institute 

 OF Technology. 



