Interpolation by Means of a Reversed Series. 637 
and another is 
+ $! + 6j + &I+&4+ . 
+&Lpi+a»+&i+....] I , 
+ Vpl + ^2 + ^3+....] | 
+ &i 3 [&i + 6 a + &3 + . • ..]+.... &s[6r+6g+. . . .] 
The elements have been selected firstly with respect to 
the verticals, and secondly with respect to the diagonals. 
Of other approximately homogeneous and symmetrical com- 
binations there are none. Group (1) has been used in 
equation (3). Group (2) gives the formula 
+ © v [- 5 - 21 ^---"] 
/6V 
4- ( 7 ) -I 1 [+14+.:..], 
or 
»-«.+/i S)«i'+/.(?)V+/.©V+/QV. • (6) 
As in equation (3), symmetry fails in the term b 2 2 n 1 5 . The 
functions within the brackets are not dependent upon a single 
quantity as in the other formula, but their evaluation involves 
only a summation of simple functions of the same variables. 
The distribution of algebraic signs is unique. 
Computing again the interpolation interval (n) from the 
data of the first problem, there results : 
log(^W = 8-004909_io n 1= + 0*4326284 
log (pW-8-58290,-10 f\ (-?)»i'= -0-0097313 
log (^V= 7-16580_io f% (j)V= +0-0004293 
log(^Vi 2 = 6-6565_io / 3 /^V= -0-0000232 
log (^W = 4-967_ 10 / 4 (^,)V = +0-0000018 
W = S = +0-423305, 
the value obtained by the first method. 
