422 PRACTICAL MATHEMATICS 



Example. Using the given tabular values of and p, find the 



best values of -? and -^ when = 95. 

 au atr 



80 85 90 95 100 105 110 



p 6-86 8-38 10-16 12-26 14-70 17-53 20-80 



In this case, as only seven tabular values are given, the first, 

 second, and third successive differences can be worked with, but 

 the higher differences are inaccessible. 



p Ap A 2 p 



80 6-86 



1-52 

 85 8-38 0-26 



1-78 



90 10-16 

 95 12-26^ 



0-32 



0-34 



100 14-70 

 105 17-53 



110 20-80 



2-44 



2-83 



3-27 



0-06' 



0-02 



0-05 



0-44 



Then 



and 



A 2 ]? - 



= 4-54 

 - 0*07 

 = 0-11 



But fc*- 



Also 



= _ (30 x 4-54 - 6 x 0-07 + 0-11} 



= 2-2648 



dp _ 2-2648 

 d0 5~ 



= 0-4550 



Ap 8p = 0-34 

 A 2 p + S 2 p = 0-71 

 A 3 - S 3 = - o-oi 



