632 
Mr. C. E. Van Orstrand : Liver 
the derivatives from the formulas of either Newton or Bessel r 
preferably the latter for arguments other than at the beginning 
or end of a series of tabular values. 
As an application of formula (4) let it be required to find 
the interpolation interval (n) from the following tabular 
values of the function and its differences, when the logarithm 
of Mercury's distance from the Earth equals F„ = 9*7968280. 
Date 
Log. Dist. of 
1898. 
£ from 0. 
May 8 
9-7560706 
+91669 
10 
97652375 
+24839 
116508 
-474S 
12 
9-7768883 
20091 
+382 
136599 
4366 
+ 75 
14 
9-7905482 
15725 
457 
152324 
3909 
+135 
16 
9-8057806 
11816 
+ 592 
164140 
-3317 
18 
9-8221946 
+ 172639 
+ 8499 
20 
9-8394585 
We take from the table, 
F = 9-7905482, 
a — \ {a x + a_i) 
= + 144461-5 
^0 
= + 15725 
c =i(c 1 + c 1 ) 
= - 4137-5 
do 
= + 457 
e = 2 ( e l + *-l) 
= + 105-0 
and then 
compute, 
- 
7/ h d 
2 24 
= + 7843-5 
3-894510 
^'=+0-233773 
c' = C -~- 
= - 693-9 
2-84130» 
? V= -0-0020681 
6 24 
d' = *h 
= + 19-0 
1-2788 
rd'= +0-0000566 
24 
e'=-*- 
= + 0-9 
9-954_ 10 
^=+0-0000027 
120 
AF = Y n -F (y 
= + 62798-0 
4-7979458 
/i= -0-0223441 
a'=a -^ +4h =+145154-6 
b 
5-1618308 
/ 2 = +0-0018500 
n^AF-f-a' 
= 
9-6361150_ 10 
/ 3 = +0-0000359 
r = ?? 1 -Ha' 
= 
4-4742842_ 10 
/ 4= -0-0000027. 
