ISO' 



SCIENCE. 



[N. S Vol. XVI. No. 395. 



organic union of the entire mathematical 

 field. On the whole, the indications are 

 that the separation Avhieh AA'as so deplored 

 ten years ago is now being arrested.* 



Besides the discovery of new functions 

 a useful work might also be done in the 

 tabulation of old ones. Our sister Associa- 

 tion in England has set us a good example 

 in this respect. The tables of elliptic in- 

 tegrals given by Legendre ought to be ex- 

 tended; and tables for the elliptic func- 

 tions would be Avelcomed. The Neumann 

 function needs tabulation, and several oth- 

 ers might be mentioned. The familiar 

 functions ought also to be tabiilated on the 

 complex plane. The labor could easily be 

 divided up. I have myself made a begin- 

 ning of this kind of work by computing the 

 trigonometric and hyperbolic sine and co- 

 sine oi x-\-iy for values of x and y ranging 

 sepai-ately from to ^ 5^ at intervals of .1 ; 

 it Avas published in Merriman and Wood- 

 ward's 'Higher Mathematics,' 1896, and I 

 have already had my reward in the fact 

 that one electrical engineer has told me that 

 he has used this complex table in the appli- 

 cation of vector-theory to alternating cur- 

 rents. In connection with the chart al- 

 ready referred to. Dr. Harris has given a 

 convenient method of computing snz, cnz, 

 dm. My friend. Dr. Virgil Snyder, has 

 tabulated, under Professor Klein's direc- 

 tion, the "VVeierstrass sigma and zeta func- 

 tions for the case gs=0. The tables ex- 

 tend over nine parallelograms in the com- 

 plex plane at intervals of one twenty-fourth 

 of each period. They are now being pub- 

 lished in Martin Schilling's ' Modell Ver- 

 lag' (Halle). The case flfo^O will next be 

 treated. 



I have also dra^^Ti the attention of the 

 Section on former occasions to the impor- 

 tance of tabulating certain fundamental in- 



* This paragraph has been an:plified since the 

 address was read. 



tegrals, so as to increase our stock of what 

 are called ' known functions, ' in terms of 

 which many other integrals might be ex- 

 pressed. Among these were the two in- 

 tegrals 





log sin xdx, 

 Jfj{x)dx. 



In all that has been said I have confined 

 myself to things that have been forced 

 on my own attention. Many members of 

 this Section and of its esteemed affiliated 

 Society know of other standing problems. 

 Not to go beyond the list of past officers 

 that lies before me, I see the names of 

 Eddy, Woodward, Waldo and Ziwet, who 

 could tell us of the new problems in me- 

 chanics and dynamics; Gibbs, Hyde or 

 Macfarlane could speak for quarternions 

 and vector analysis; Bigelow for the me- 

 chanics of the atmosphere; Hayford for 

 geodetic and tidal problems; Story for in- 

 variant theory; Johnson for differential 

 equations; Moore for function theory; 

 Beman, Phillips or Strong for geometry 

 and analysis; Miller for group theory. 

 Then to speak for the various fields of 

 astronomical work we have a noble band 

 consisting of Newcomb, Young, Pickering, 

 Langley, Hall, Harkness, Hough, Van 

 Vleek, Eastman, Stone, Chandler, Doo- 

 little, Comstock, Paul, Upton, Holden, 

 Kershner, Frisby, Barnard, Hall, Frost 

 and Lord. 



It would seem that the work of the Sec- 

 tion not only advances science, but tends 

 to prolong life ; for I find only two starred 

 names in the list of officers since the Sec- 

 tion was reorganized on its present basis 

 twenty years ago. 



Rogers and Ferrel have entered into the 

 larger life ; and their works do follow them, 

 for they are being carried on to wider is- 

 sues. James McMahon. 



Cornell Universitt. 



