THE BEST VALUE OF 417 



ax 1 - 



Working along the diagonal lines indicated, it is evident that 

 account can only be taken of the first three successive differences, 

 the values of the following successive differences are clearly 

 inaccessible. 



//, the increment in the value of #, is 1. 



Now $u x -i- AM Z = 0-34762 + 0-82185 



= 0-66947 

 8X - A 2 t* x -- 0-08026 + 0-02222 



- 0-00804 



8 3 w x + A 3 M^ = 0-00579 + 0-00288 

 - 0-000867 



Then h * = \ (8u. + AwJ + \ (Vu, - A 2 w z ) + \ (X + A 3 *,) 

 = \ x 0-66947 - i x 0-00804 + 1 x 0-00867 



M 4 O 



= 0-33417 



Hence when x = 3, -^ = 0-33417 

 ax 



d 2 v 

 203. T^e Be5< Value of -r-^ /^a/ can be obtained from Tabular 



Values of x and y. 



It has already been shown that 



fcA= A-^A 2 + iA 3 -iA 4 +iA 8 - . . . 



11 c 1 oir 



Then /> 2 A 2 - A 2 - A 3 + A 4 - A 5 -f A 6 - ... 



' 



or h g - AX - AH., + jlAX - |A%. + ^AX - ... 



where A 2 w z , A 3 w.,., A 4 w z , etc., represent the successive differences 

 running downwards in a diagonal direction from the term u x . 



Also fcA=S + 



2 



1 12 6 180 



where 8 u x , 8 3 M Z , 8 4 w z , etc., represent the successive differences 

 running upwards in a diagonal direction from the term u x . 



2 D 



