JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. Ill JUNE 19, 1913 No. 12 



MATHEMATICS.— Ta6?es of the exponential function.' C. E. 

 Van Orstrand. U. S. Geological Survey. 



The most important tables of extended values of the expo- 

 nential function have been constructed by Schulze, Newman, 

 Glaisher and Burgess.- 



Schulze gives values of the ascending exponential at intervals 

 of unity between the limits 1 and 24 inclusive to 28 or 29 signi- 

 ficant figures, and for the special arguments 25, 30 and 60 his 

 values include 32 or 33 figures. In so far ias I have been able 

 to ascertain, Schulze gives no information regarding methods of 

 computation or accuracy of results. Glaisher verified the first 

 15 figures of Schulze's value of e'^ by direct substitution in the 

 series; the first 23 decimals of e'° with his table of factorials;^ 

 also the first 13 powers of e were verified to 22 places of deci- 

 mals, and the values of e'\ e'^, . . . e-^ to 15 places of decimals 

 by means of the relation 



e— 1 



' Published with the permission of the Director of the U. S. Geological Survey. 



2 Schulze, Sammlung logarithmischer trigonometrischer .... Tafeln 



(Berlin 1778). F. W. Newman, table of the descending exponential function 



to twelve or fourteen places of decimals. Camb. Phil. Soc. Trans. 13. 1883. 



J. W. L. Glaisher, Tables of the exponential function. Camb. Phil. Soc, Trans. 



2 f _,, 

 13. 1883. James Burgess, On the definite integral —j= \ e dt, with extended 



V^Jo 



tables of values. Trans. Roy. Soc. Edinburgh 39. 1900. 



' Glaisher, 1. c. 



345 



