1919-20.] On a Class of Graduation Formulse. 
125 
Table II. — Graduation of the Cubes of Numbers by Spencer’s Formula and 
the Least-Square Formula k = l , m=10. 
No. 
X . 
II 
CO 
6 
+ 
e k 
o 
'o 
CD 
0 
Is S 
l> II 
o 
o 
Graduated Value 
of u = v ! . 
Difference between Un- 
graduated and Graduated 
Values, and True 
Values x 10 2 . 
<M ’ 
liTco 
(U- 
u ') 2 . 
By Least- 
Square 
Formula 
k = 1, 
m = 10. 
By 
Spencer’s 
Formula. 
Col. 2- 
Col. 3. 
Col. 2- 
Col. 4. 
Col. 2- 
Col. 5. 
(Col. 7) 2 . 
(Col. 8) 2 . 
(1) 
(2) 
(3) 
(4) 
G) 
G) 
(7) 
(8) 
(9) 
(10) 
(11) 
60 
2160T3 
2160 
61 
2269-94 
2270 
62 
2383-41 
2383 
63 
2500-60 
2501 
64 
2621-57 
2622 
65 
2746-38 
2746 
66 
2875-09 
2875 
67 
3007-76 
3008 
68 
3144-45 
3144 
69 
3285-22 
3285 
• . • 
70 
3430*13 
3430 
3430-03 
3429-99 
13 
10 
14 
169 
100 
196 
71 
3579-24 
3579 
3579-11 
3579-10 
24 
13 
14 
576 
169 
196 
72 
3732-61 
3733 
3732-50 
3732-48 
-39 
11 
13 
1521 
121 
169 
73 
3890-30 
3890 
3890-19 
3890-19 
30 
11 
11 
900 
121 
121 
74 
4052-37 
4052 
4052-32 
4052-29 
37 
5 
8 
1369 
25 
64 
75 
4218-88 
4219 
4218-91 
4218-84 
-12 
-3 
4 
144 
9 
16 
76 
4389-89 
4390 
4389-90 
4389-90 
-11 
-1 
- 1 
121 
1 
1 
77 
4565-46 
4565 
4565-50 
4565-52 
46 
-4 
- 6 
2116 
16 
36 
78 
4745-65 
4746 
4745-73 
4745-76 
-35 
-8 
-11 
1225 
64 
121 
79 
4930-52 
4931 
4930-58 
4930 66 
-48 
-6 
-14 
2304 
36 
196 
80 
5120T3 
5120 
5120*21- 
5120-28 
13 
-8 
-15 
169 
64 
225 
81 
5314-54 
5315 
5314-61 
5314-68 
-36 
-7 
-14 
1296 
49 
196 
82 
5513-81 
5514 
5513-87 
5513-91 
-19 
-6 
-10 
361 
36 
100 
83 
5718-00 
5718 
5718-08 
5718-06 
0 
-8 
- 6 
0 
64 
36 
84 
5927-17 
5927 
5927-25 
5927T9 
17 
-8 
- 2 
289 
64 
4 
85 
6141-38 
6141 
6141-43 
6141-37 
38 
-5 
1 
1444 
25 
1 
86 
6360-69 
6361 
6360-77 
6360-67 
-31 
-8 
2 
961 
64 
4 
87 
6585-16 
6585 
6585-23 
6585-15 
16 
-7 
1 
256 
49 
1 
88 
6814-85 
6815 
6814-86 
6814-87 
-15 
-1 
_ £ 
225 
1 
4 
89 
7049-82 
7050 
7049-84 
7049-87 
-18 
-2 
- 5 
324 
4 
25 
90 
7290-13 
7290 
91 
7535-84 
7536 
92 
7787-01 
7787 
93 
8043-70 
8044 
94 
8305-97 
8306 
95 
8573-88 
8574 
96 
8847-49 
8847 
• . • 
97 
9126-86 
9127 
98 
9412-05 
9412 
99 
9703-12 
9703 
1 
Total for columns 9, 10, and 11 
15770 
1082 
1712 
