ON THE CALCULATION OF MATHEMATICAL TABLES. 49 



And in a Quadric Transformation, with 

 (20) 



(21) 

 (22) 



X, — 

 as in Table II. 



Jv/(i . l + 6a;2 + a;^). 

 , ^=v/k' tn Um^K, k' = (s/^-1\\ K=2K', 



Lemniscate Bisection : r = 45. 

 2. These are given page 72, Report 1911, for the general case, 



E(45) -^(1-K') = tav mod. angle=|^l--L^ =0-1464466094. 



Introducing the angle a=^(45), cot a-^\/ k', 



A(45)=sin 45 (sin 2a)J, D(45)=A(45)sec a, 



A(45) / k' 1„ 



cosa=:^^^,, { = . / ^ ,=cn-K. 



D(45) V IfK' 2 



sin 2a=?^'''=2V2(v^2-l) 2=al 0-30102 99957 



1 +K 



V 2=al 0-07525 74989 



>/2-l=ali;61722 43147 



sin 2a=al 19935^80 93 



Vsin 2a=al 1-99837 79523 



sin 45 = all -84948 50022 



A(45)=al 1-84786 29545 



A(45)=0-70447 07318 



A(45) = al 1-84786 29545 



sec a=al 0-19138 78426 



D(45)=al 0-03925 07971 



D(45) = l-09458 82886 

 sliL=v'(2-s/2), cliL=V(v/2-l), dliL = ^-^-, tl|L=V2. 



