THE BEST VALUE OF 415 





where 8w 3 , S 2 !^, 8 3 w,,, S 4 ^ represent the successive differences 

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



Thus the best value of -^ for a given value of x is given by 

 dx 



du cs. l c\ 1 1 1 1 

 or h-r- = ow, + -8 2 w a + 7ro 3 u,. + TOT*- + . . . 



dx 234 



where h is the increment in the value of x. 



As an example, from the given values of x and y it is required 



to find the value of -^- when x = 6. 

 dx 



7-5 39-15 



Here the increment in the value of x is 0-5 and h = 0-5. 

 Working upwards from x = 6 



= 4.47 + 1 x 0-66 +- x 0-06 

 2 o 



= 4-82 



Or, working downwards from x = 6, 



= 5-19 - ^ x 0-78 f|x 0-06 

 2 <3 



- 4-82 



