ON THE CALCULATION OF MATHEMATICAL TABLES. fW 



^^ h] 2(sin 18)^ ^ siD345(8inl8 )^ 



^^^^ ^~ 1 rn,^\2_Qx~\ ~ ^^^ 72-sin 30 sin 89 sin 21 



= . . . =al 1-9702 =cos21°=cos^(18). 



So also for C(36) and C(72). 



C(27-)»=a;' *"i"^ V2 ^ ■'' ^^ +^' 



12 



-'#^-«) 



1 



=a;^v/2(sin72 + sin30) 



1 



=2^2 0;^ sin 51 sin 69 



C(2r)=al 0-0507 . . . =M24 . . . =C(36) 

 C(4r)2= 2n/2x" ^' sin 39 sin 21 



C(4r)=ai 0-00775 . . .=1-018 . . . =C(72) 



zstL = 



10v/(si-S3) iOa;7(2 gin 18)^ 



_— 3a; + l _ -3x+l 

 10>/(si-S3) i0a;%sinl8)^ 



2zs|L-zsfL=2A^^^/ 

 (2 sin 18)^ 



zs|L + 2zsiL=^A^^^ / 



(2 sin 18)* 



9. Table II for K=2K', k'=(V2— l)^ is derived from the Lemniscate 

 Table I by an application of the Quadric Transformation, using the 

 formulas in Report 1913, p. 88, and so may be considered of equal 

 accuracy. 

 1919. « 



