Deobmbeb 2S, 1883.] 



SCIENCE. 



827 



that a clear and delinite presentation of chemi- 

 cal tlieories is quite essential to their proper 

 coinpreliension. While it is manifestly highlj- 

 important that the student should not onl\' be 

 ae()uainted with the facts upon which chemical 

 theories rest, but should also appreciate i'nWy 

 the nature of conclusions reached by inductive 

 reasoning, still a constant reiteration of the 

 doubts, uncertainties, or conflicting evidence, 

 wliieh surround the various hypotheses, seems 

 to us ill advised iu an elementary text-book. 



Although structural chemistry in a certain 

 sense is independent of the valence hypothesis, 

 still this hypothesis was one of the earliest 

 and most natural inductions resulting from the 

 study of the constitution of chemical com- 

 pounds, and is so interwoven with the present 

 theories, that any attempt to exclude it rigor- 

 ously from a discussion of the subject merely 

 adds an unnecessary complication. We con- 

 fess that we do not think the ordinary student 

 will read with much interest the pages devoted 

 to structural formulae, or ' proofs ' of their cor- 

 rectness, if he chances to see beforehand the 

 opening sentence of the retrospect which fol- 

 lows (p. -232). 



" A study of the preceilingohapters on constitution 

 will show that no .ibsolute meaning is to be altaclied 

 to the word. Constitutional formulas are those which 

 suggest certain reactions, and recall analogies. The 

 formula CH3 — OH does not mean that liydroxyl 

 (OH) is necessarily present in the compound, or that 

 C H , is present, but that the different parts of the 

 ciimpound bear such relations to each other that 

 when the compound is decomposed, it acts as if the 

 parts were united as the formula indicates. The 

 formula suggests possibilities ; it may not represent 

 realities." 



If the author be correct, and " it cannot be 

 denied that we are now in a period of chemis- 

 try which may fairly be called one of formula 

 worship" (p. 100), it is very certain that 

 formula worship has been of vasth" greater ser- 

 vice to chemistry than agnosticism is ever 

 likely to be. 



We fail to see that any advantage is gained 

 by the introduction of new conventional signs 

 in place of those already in common use, to 

 represent the linkage of the carbon atoms in 

 the olefinct and acetylen series (])p. 202, 20G) ; 

 nor can we understand whj- the double linkage 

 of the nitrogen atoms, which the author ap- 



parently accepts, since he uses the old sign 

 ( = ) in his formulae for the azo- and the diazo- 

 compounds (p. 222), stands upon any more 

 trustworth\- experimental basis. Furthermore, 

 we cannot help expressing our surprise that 

 the author should have ventured the statement, 

 "Of the substitution products of benzene, 

 which contain three substituting groups, more 

 than tiiree varieties have been observed " (p. 

 208) , which seems a bit of rashness hardly con- 

 sistent with the caution elsewhere displayed. 



THE CORNELL MATHEMATICAL 

 LIBRARY. 



Cornell universili/ lilirari/. Special lists. No. 1. Math- 

 ematics. Ithaca, X.Y., 1883. 92 p. 8°. 

 This classified list of works, with index, in- 

 cludes some twenty-five hundred titles relating 

 to mathematics, and such allied subjects as 

 astronomy, engineering, and physics. These 

 books form what is known, from tlie name of the 

 donor, as the ' Kelly mathematical collection.' 

 An examination of the list shows that it con- 

 sists of books actually jjurchased within the 

 past few years, with good judgment, and a con- 

 scientious endeavor to cover, so far as practica- 

 ble, the immense field of mathematical research, 

 past and present, as evenly as possible. 



It comprises, besides many rare and valuable 

 works not readily accessible to American stu- 

 dents, the collected works of the great masters 

 of analysis, and the more important mathemati- 

 cal journals. 



The mathematical capabilities of American 

 youth are quite equal to those of Germany or 

 England ; but the facilities ottered them by our 

 universities for the study of this grandest of 

 sciences are in general far behind those found 

 abroad. When the professors and teachers of 

 mathematics in this country shall themselves 

 become lifelong cultivators of mathematical 

 pursuits, and shall have the same average 

 proficiency- as those abroad, there will be no 

 difficulty in accomplishing results in llie mathe- 

 matical training of college students fully equal 

 to any attained elsewhere. But such professors 

 and such students cannot be without libraries 

 such as this is the beginning of. We can but 

 express our deep satisfaction with this good 

 work in the interest of sound learning. 



WEEKLY SUMMARY OF TEE PROGRESS OF SCIENCE. 



MATHEMATICS. 

 Kummer's surface. — Professor Cay ley, in a brief 

 note ' on the sixteeii-nodal ijuartic surface,' remarks, 



that Riemann's theory of the bitangents of a plane 

 quartic leads at once to a very simple form of the 

 equation of the sixteen-uodal quartic surface; viz., 



