6P REPORTS ON THE STATE OP SCIENCE. — 1916. 



those of Burran^ to six places, and those of Becker and Van Orstrand^ to 

 five places of decimals from f^=0 001 to 1-600 radians. 



The following tables to ten places of decimals were calculated to 

 thirteen places, first for the sixteen values 0"1 to 1*6, then from O'Ol 

 to 1"60, and finally from O'OOl to 1-600. From the values of the sine and 

 cosine of 0-1 to 1-6, intermediate values were obtained by employing the 

 sum and difference formulsB of these functions : the results were taken 

 from Q-GO to 0-05 and from Q-IO to 0*05 and thus furnished a check upon 

 the calculations. A similar procedure was followed in calculating the 

 sines and cosines when 6 is given to three places of decimals. In order 

 to ensure greater accuracy in the tenth place, the next figure is also 

 given. In very few cases will the error reach a unit in. the eleventh 

 place. The subsidiary table of sines and cosines of 6 from 6=0-00001 

 to 9=000100 can be employed in conjunction with the first table. 



Table I. 

 Tables of Sines and Cosines {6 in radians). 



' Burrau, Tafeln der Funktionen Cosimis vnd Sinvs, 1907. 

 -' Becker and Van Orstrand, Smithsonian Mathematical Tables, Hyperbolic 

 Functions, pp. 171-223. 



