68 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
Table A. 
a 
_o 
’■4J 
First 
Second 
Differ- 
i 
Successive 
Successive 
O 
Sum. 
Sums and Differences. 
Differences and Sums. 
ence. 
10 
14 
10 + 14 
10-14 
(10+14) 
+ (12 + 16) 
(10 + 14)1 . 
-(12 + 16)/ -"1 
(10- 14) = C4 
(12-16) = d4 
12 
16 
50 
12 + 16 
12-16 
50 + 54 
50-54 
(50 + 54) 
i 
(50 + 54)1 , 
(50-54) = C5 
(52-56) = d5 
54 
+ (52 + 56) 
f- 
^5 
-(52 + 56)/ 
(7i + (75 = [5]i 
52 
52 + 56 
52-56 
^1 + ^5 = 
m, 
+ = 
ci + c, = [3], 
56 
n. 
Ci-C5 = [4L 
^1 — 
11 
11 + 15 
11-15 
(11 + 15)' 
\ 
(11 + 15)1 -f 
-(13 + 17)i -•'1 
(11-15)^ 
15 
+ (13 + 17). 
\ 
+ (13-17)/ "^1 
-(13-17) ) 
13 
17 
51 
55 
13 + 17 
13-17 
51 + 55 
51-55 
(51+55) 
+ (53 + 57) 
h 
^5 
(51 + 55)1 , 
-(53 + 57)/ 
(51-55) ( _ 
+ (53-57) ( 
(51-55)) ^ 
-(53-57) ) 
53 
53 + 57 
53-57 
^1 + ^5 = 
Pi 
A +/,=[+ 
9i+9^ = [^]i 
hi + h^ = [ll]i 
K-h=mi 
57 
2 m 
/.-A = [8]i 
9i-95 = [^0\ 
mi+^i = [13Ji 
mi-j?i = [15] 
1 
ni + gi-[14Ji 
20 
24 
20+24 
20-24 
(20 + 24)' 
+ (22 + 26). 
:«2 
(20 + 24) 1 
-(22 + 26) J ~ 2 
(20-24)-C2 
(22-26) = d2 
22 
22 + 26 
22-26 
26 
40 
44 
40 + 44 
40-44 
(40 + 44)' 
+ (42 + 46) 
■a^ 
(40 + 44)1 ^ 
-(42 + 46)/ 
(40_44) = C4 
(42-46) = d4 
42 
42 + 46 
42-46 
U 2 + = 
TUo 
{h2 + b,) = [ll 
(C2 + C4) = [3]2 
<^2 + < 74 = [5]2 
46 
(Xo - U 4 = 
( 62 - 64 ) = [ 2/2 
(Cg — C 4 ) = [4]2 
<^2-^4 = W 2 
21 
21 + 25 
21-25 
(21+25) 
- P 
(21+25)'! 
(21-25) ) _ 
(21-25)) , 
25 
+ (23 + 27), 
/ 
-H 
-(23 + 27)/ -^2 
+ (23-27)) 
-(23-27) i 2 
23 
27 
41 
45 
23 + 27 
23-27 
41 + 45 
41 -45 
(41+45) 
+ (43 + 47) 
(41+45)1 
-(43 + 45 )) -^4 
+ ( 43 - 47 )) ^4 
(41-45)) 
- (43 - 47) ) 4 
43 
47 
43 + 47 
43-47 
e-2 + ^4 = 
e.2-e^ = 
■-P 2 
■Pi 
/2+/4 = m 2 
/2-/4 = [8]-2 
92 + 9iH^]2 
5'2-S'4 = [ 10 J 2 
h2+h=[n\ 
^2 - ^4~[l^]2 
^2 + 7^2== 
'13' 
2 
d5“ 
2 
+ ^2 = 
d4' 
2 
30 
30 + 34 
30-34 
(30 + 34)\ 
(30 + 34)1 
(30-34) = C 3 
(32-36) = dg 
34 
+ (32 + 36) ) ~ 
-(32 + 36) 1 “3 
32 
32 + 36 
32-36 
36 
31 
31+35 
31 - 35 
(31+35)\ 
(31 + 35)/ . 
-(33 + 37 ) ) “-^3 
(31-35) ( _ 
+ ( 33 - 37 ) ) ^3 
(31-35)) ^ 
-(33-37) i “^^3 
35 
+ (33 + 37) J " 
33 
33 + 37 
33-37 
^3 + ^3 = [ 
3 
^3 = PL 
^3 ~ [^]3 
^3 ~ [ 5 Is 
37 
^3 ~ ^3 ~ [ 
Is 
y 3 =[p 3 
93 — 
A -3 = [ 10]3 
