308 



REPORTS ON THE STATE OF SCIENCE, ETC. 



Hypebbolic Sines and Cosines, Sinh ttx and Cosh tzx. 



The hyperbolic functions, Sinh tzx and Cosh ttx are required in the computation of the 

 Elliptic 6 functions with imaginary argument and the Gamma function with complex 

 argument. To construct the following tables, values of e+w^ were computed over the 

 range a;=0 to 4, first to intervals of 0'5, then 0-05, and finally to O'Ol. The short 

 table below of values of e^^ to twenty places of decimals when a; is a positive or 

 negative integer or half an odd integer formed the basis of the calculations. 



Tables of e'^" and e *'''' have been calculated by C. E. Van Orstrand * to twenty- 

 three places of decimals from a;=0 to x=360. Hayashi^ has published these tables 



to ten places and given the corresponding values of Sin — — and Cos — .^ over this 



range. Some values of the exponential function to powers of multiples of 7t are given 

 by Gauss.' 



1 C. E. Van Orstrand. Fifth Memoir of the National Academy of Sciences, 

 vol. xiv. Washington, 1921. 



* Hayashi. 'Tafeln der Kreis- und Hyperbel-funktionen.' Julius Springer. 

 Berlin, 1926. 



* Gauss. Werke. Band iii. ' De curva lemniscata.' 



* 



