July 6, 1906.] 



SCIENCE. 



19 



for example, x + 2/ = os.^ xy ^h. Here it 

 would be of use to point out that x and y 

 are the roots of the quadratic X^ — aX + h 

 = 0, and similarly in the more general case. 

 The chapter on convergence of infinite series 

 leaves little to be desired. But the author 

 might have given Cauchy's condensation the- 

 orem that under certain conditions 



i /(n) and J rt«/(a») 



converge or diverge together. This has been 

 used to discuss the well-known case 



and is fundamental in the construction of 

 the De Morgan criteria. The result of § 953 

 may well be obtained by comparison with the 

 series 



and a more useful form is : The series con- 

 verges or diverges according as 



Li n \ 



nuroo \ Wn-J-1 



.)50. 



Dr. Fine has, unfortunately, been com- 

 pelled to leave the exponential theorem to the 

 last few pages of the book, and it would be 

 an advantage if more space could be given to 

 it in a later edition. Also the more logical 

 development in the indicial, binomial and ex- 

 ponential theorems, and that of De Moivre 

 would be to first prove that if f{x) is any 

 function of x which satisfies f{x) X fiv) = 

 f{,x-\-y), for all values of x and y, then 

 f{x) = [f(l)]'^ for all values of x; and then 

 to apply this in turn to each of the particular 

 theorems. 



The book as a whole is admirably complete, 

 and for this reason many parts might with 

 advantage be omitted on a first reading. 

 These parts could be indicated in some man- 

 ner, for example by means of asterisks. 



J. Edmund Wright. 



SOCIETIES AND ACADEMIES. 



THE AMERICAN CHEMICAL SOCIETY. NEW YORK 

 SECTION. 



The last regular meeting of the New York 

 Section of the American Chemical Society was 



held at the Chemists' Club, 108 West Fifty- 

 fifth Street, on Friday, June 8. The chair- 

 man. Dr. F. D. Dodge, presided. The follow- 

 ing papers were read: 



The Chemical Work of the Bureau of Stan- 

 dards: W. A. NOYES. 



The chemical laboratories of the bureau of 

 standards were ready for the beginning of 

 work in March, 1905. There are at present 

 five chemists working in these laboratories. 



Dr. Stokes and Mr. Cain have been working 

 upon the standards of purity for chemical re- 

 agents. Good progress has been made in se- 

 curing cooperation of the chemical manufac- 

 turers in this work, and some progress has 

 been made in the laboratory in the develop- 

 ment of methods for testing for impurities in 

 reagents, especially work of this character has 

 been done with methods for determining 

 traces of iron and work is being conducted 

 upon the common acids and alkalies. 



Dr. Waters has worked chiefly .with Dr. 

 Wolff upon the purification and testing of 

 materials for the preparation of standard elec- 

 trical cells. He also carried out last year the 

 analysis of the argillaceous limestone which 

 was distributed for the purpose of improving 

 the analytical methods taught in our colleges 

 and universities. 



Dr. Weber has analyzed a sample of sulphide 

 ore, a zinc ore, some agricultural samples for 

 sulphur and some samples of white metal. 

 These have been distributed chiefly among 

 technical or agricultural chemists by different 

 societies. 



The bureau has taken over the standard 

 samples of iron which heretofore have been 

 distributed by the American Foundrymen's 

 Association, and very careful analyses of these 

 samples were made at the bureau by Mr. Cain. 



Arrangements have been partially completed 

 with the American Steel Manufacturers' Asso- 

 ciation for the preparation of a series of 

 samples of standard steels of the three types, 

 Bessemer, basic open hearth and acid open 

 hearth. 



Dr. Noyes has been working on the ratio 

 between the atomic weights of oxygen and 

 hydrogen, and recently he has taken up, in 



