FINITE DIFFERENCES 



407 



- -{8 -|- 12n -f 9n a - 9n + 2n 8 - 6n a -f- 

 8 



Using this relation for u 

 tained for the 10th term. 



+7w+8} 



as a means of verifying the result ob- 



W 9 = 5(2 x 9 3 + 3 x 9 2 + 7 x 9 + 3} 

 8 



1767 



3 

 = 589 



199. In the preceding work it should be noticed that u repre- 

 sents the first of the given values, and therefore the work can only 

 be done by using the values of the successive differences which 

 occur at the top of the table. It is possible to work with the 

 differences lying on a diagonal line in any part of the table by 

 altering the position of M O . 



Thus if M is taken to be situated somewhere in the middle of 

 the table, then we have to distinguish between the values of u, 

 which occur on either side of w . Those values going downwards 

 from M are denoted, as before, by u lf u 2 , M 3 , etc., while those 

 working upwards from M O are denoted by M-J, M_ 2 , M_ 3 , etc. 



u 



A 2 u 



A 3 M 



A 4 M 



A r- M 



A 6 M 



-A 5 M f 





