No. 5.] TABLES OF EXPONENTIAL FUNCTION— VAN ORSTRAND. 11 



A comparison of the present values with those mentioned in the first part of this paper 

 shows some interesting results. The values given by Schulzo are generally incorrect in the 

 last or the next to the last decimal. Newman's 18-place table of the descending exponential 

 is correct to 16 decimals when the last two decimals are taken into account. His values for 

 x= —3.5, —26.1, —26.4, and —26.9 contain misprints. The values of f~"-' by Burgess is in 

 error by approximately one unit in the tliirtieth decimal. Glaisher's value of e"'" computed 

 from formula (1) is correct. His table of the reciprocals of the factorials contain errors shghtly 

 in excess of 5 units in the next succeeding decimal for n = 20, 27, 41, and 50. All of Bret- 

 Schneider's values are correct and the values of e* given by Gram to 24 decimals are correct. 

 The value of e^P given by Gauss is incorrect in the twenty-third and following decimals. 



The present paper was completed before the 1916 report ' of the British Association for the 

 Advancement of Science was received. The report of the committee on the calculation of 

 mathematical tables (pp. 59-126) contains the following tables of sin x and cos x to radian 

 argument : 



Table I: Values of sin x and cos x to 11 places of decimals at intervals of 0.001 from 0.000 

 to 1.600. 



Table II: Values of x— sin x and 1 —cos x to 11 places of decimals at intervals of 0.00001 

 from 0.00001 to 0.00100. 



Table III: Values of sin x and cos x to 15 places of decimals at intervals of 0.1 from 0.1 

 to 10.0. 



In one value only, does the tabular error of Tables I and III exceed 10 units in the next 

 succeeding decimal; the value of sin 9.1 should read 52 instead of 53 in the last two tabular 

 digits. 



Nearly all of the numerical computations were made by A. G. Seiler, piece work computer, 

 and R. Weinstein and A. T. Harris, aids in the physical laboratory of the Geological Survey. I 

 am indebted to F. A. Wolff, of the United States Bureau of Standards, Washington, D. C, for 

 valuable suggestions in regard to the contents of Table IX, and to E, B. Escott, who kindly called 

 my attention to the omission of several important references which had been overlooked in my 

 prehminary pubUcations in the Journal of the Washington Academy of Sciences (1912-13). The 

 values given by Gram and Bretschneider were especially useful as a partial check on certain 

 values which I had previously carried to a slightly greater number of decimals. No errors were 

 discovered in my computations. 



' The same report, pp. 123-126, contains the following: 



10 place values ol the loRarithmic gamma function at i ntervals of 0. 005 from 0. 005 to 1. 000. 



10 place values of the integral of the loKarithmic gamma function at intervals of 0. 01 from 0.01 to 1.00, 



13 place values of the logarithmic derivate of the gamma function at intervals of unity from 1 to 101, and from 0.5 to 100.5. 



