THE CASE WHEN A 7 w r o 



419 



differ slightly. Then the best value is taken as the mean of 

 the two, 



and * - A + * 2U ~ 



]O V "> ""/ ' 



204. The Case ichen A 7 M X = 0. Very often in dealing with tabular 

 values slight errors in the values themselves render the values 

 of the higher differences worthless for interpolation ; probably 

 the first three difference columns can be relied upon. Also in 

 many cases the actual number of tabular values given is not 

 sufficient to enable us to find all of the successive differences. 

 For example, if seven tabular values are given, the successive 

 differences corresponding to the middle of these values can be 

 found up to A 3 Mj., but the successive differences higher than this 

 are inaccessible. In order to provide for these cases, formulae 



have been established which give the values of h ~ and h 2 -^ in 



(I r dtE 



terms of the first three successive differences ; these formulae 

 have been based on the assumption that A'M.,. = 0. 



Wj| jf ^*X **^*X iA^Ujj -1 tijj 



blOa b ia 



