418 PRACTICAL MATHEMATICS 



As an example, take the set of values of x and y given in para- 



d 2 ti 



graph 201, and find the value of -^ when x = 6. Thus working 



dx" 



diagonally downwards, AH = 0-78, AH =0-06, and AH = 0. 



Then h^z = AH - AH + ^AH- - - . 



= 0-78 - 0-06 

 = 0-72 



&y__ 0-72 

 dx*~~W 



= 2-88 



Working diagonally upwards, 8H = 0-66, H = 0-06, and 

 SX - o. 

 Then * = SH + 3 Wa; + ^ Ux + . . . 



= 0-66 + 0-06 

 = 0-72 



% - 2-88 

 dx 2 



Now the law from which the values of x and y have been calcu- 

 lated is : 



y = 0-08a? 3 + a? - 2-1 



= 

 ax 



=0,8* 



= 2-88 when x = 6 

 The expressions 



7 o^ 2 V 11 A 5 . . 137 . , 



*1I - A W ^ A ^ + 12 A% ^ - 6 A U + 180 A U * ~ ' ' 



and h^ = Vu x + Vu x +lVu x + ^u x + ^u x . . . 



d?u 



will give exact results for h 2 -^ if ultimately some difference 



ctx 



column contains equal terms throughout or in the next column 

 all of the terms are zero. But when dealing with experimental 

 values, or tabular values calculated correct to a certain number 



d 2 u 

 of significant figures, this is not the case, the two values of ^ 2 -r^ 



