144 Prof. P. J. Daniell on the 



Then 



f l««fax=( AWw+ f 1 B(l-<sr 2 )««far + ( V^l-^ 2 )- 1 ^^, 

 Jo Jo Jo Jo 



1 = A IB 3C 



2 2 2 2 2 2 



or o = ^+os- + ; 1 o» 



or 1=A+jB + |g. 



Let *B=B', 1 0=0', 



then 1 = A + B' + C (iv.) 



Substitute these values into equation (iii.) and then, since 

 2-V3r(§)= 1*0743, 

 «-~f V^iS=iL + B /2 C04104)-2B'C'(-021Gl) + C ,2 C01442). 



Substitute them also into equation (ii.), then 



lfv|^cffl=^rA»+2AB'H+B'^.|+2AC\/5-i 



27TJ! dn 37rl 15 15 7 V 49 F 2 



_i_9TVP' 40 /^ X ^n/2 2?r X l 

 + -* U 39V49F 2 + O^FJ' 



where F denotes 



Fg,|,l,?-^- 3 ) = 1-01741. j 



§ 3. Then 



~ f V |- dS =- ^ [A 2 + 2AB'(1 + -06667) + B' 2 (l + '21905) 



+ 2A0 / (1 --04383) + 2B'C (1 - -01932) + C /2 (l + -06150)] J 

 and 



i-f Y IJ^ S =^ L +^:[ B/2 ( , 09670)---2B'C , C05091) + C ,2 (-03398)]. 



Then the required D is the minimum value of 



JL [a 2 + 2AB'(1 + -06667) + B' 2 (l + -31575) + 2AC'(1 - -04383) 

 + C ,8 (l-'02752) + 2B'C'(l-'07023)]. 



