126 Proceedings of the Boyal Society of Edinburgh. [Sess. 
Table III. — Graduation of the Reciprocals of Numbers by Spencer’s Formula 
and the Least-Square Formula k=l, m = 10. 
No. 
X. 
u:> 
05 
05 
05 
05 . 
Os'hD 
^ II 
o 
Forced Value of 
U = u. 
Graduated Value 
of u—u'. 
Difference between Un- 
graduated and Graduated 
and True Values x 10 2 . 
"5 s CO 
bl 
(U- 
u') 2 . 
By Least- 
Square 
Formula 
* = 1, 
m = 10. 
B y 
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 ) 
( 5 ) 
(6) 
(7) 
(8) 
(9) 
(10) 
(11) 
201 
9751 29 
9751 
202 
9505-00 
9505 
203 
9261-13 
9261 
204 
9019-66 
9020 
205 
8780-54 
8781 
206 
8543-74 
8544 
207 
8309-23 
8309 
208 
8076-97 
8077 
209 
7846-94 
7847 
210 
7619*10 
7619 
211 
7393-41 
7393 
7393-36 
7393-29 
41 
5 
12 
1681 
25 
144 
212 
7169-86 
7170 
7169-80 
7169-73 
-14 
6 
13 
196 
36 
169 
213 
6948*41 
6948 
6948-34 
6948-26 
41 
7 
15 
1681 
49 
225 
214 
6729-02 
6729 
6728-93 
6728-94 
2 
9 
8 
4 
81 
64 
215 
6511-68 
6512 
6511-63 
6511-64 
-32 
5 
4 
1024 
25 
16 
216 
6296-35 
6296 
6296-31 
6296-36 
35 
4 
-1 
1225 
16 
1 
217 
6083-00 
6083 
6082-99 
6083*05 
0 
1 
-5 
0 
1 
25 
218 
5871-61 
5872 
5871-58 
5871-69 
-39 
3 
-8 
1521 
9 
64 
219 
5662T5 
5662 
5662-15 
5662-23 
15 
0 
-8 
225 
0 
64 
220 
5454-60 
5455 
5454-64 
5454-67 
-40 
-4 
-7 
1600 
16 
49 
221 
5248-92 
5249 
5248-97 
5248-97 
- 8 
-5 
-5 
64 
25 
25 
222 
5045-10 
5045 
5045-14 
5245T1 
10 
-4 
-1 
100 
16 
1 
223 
4843-10 
4843 
4843-10 
4843-09 
10 
0 
1 
100 
0 
1 
224 
4642-91 
4643 
4642-88 
4642-88 
- 9 
3 
3 
81 
9 
9 
225 
4444-49 
4444 
4444-46 
4444-46 
49 
3 
3 
2401 
9 
9 
226 
4247-84 
4248 
4247-80 
4247-79 
-16 
4 
5 
256 
16 
25 
227 
4052-91 
4053 
4052-84 
4052-86 
- 9 
7 
5 
81 
49 
25 
228 
3859 70 
3860 
3859*59 
3859-64 
-30 
11 
6 
900 
121 
36 
229 
3668-17 
3668 
3668-08 
3668-10 
17 
9 
7 
289 
81 
49 
230 
3478-31 
3478 
3478-19 
3478-23 
31 
12 
8 
961 
144 
64 
231 
329009 
3290 
3289*99 
3290-00 
9 
10 
9 
81 
100 
81 
232 
3103-50 
3103 
3103-44 
3103-40 
50 
6 
10 
2500 
36 
100 
233 
2918-50 
2919 
2918*47 
2918-41 
-50 
3 
9 
2500 
9 
81 
234 
2735-09 
2735 
235 
2553-24 
2553 
236 
2372-93 
2373 
237 
2194-14 
2194 
238 
2016-86 
2017 
239 
1841-05 
1841 
. . . 
240 
1666-72 
1667 
... 
... 
241 
1493-83 
1494 
242 
1322-36 
1322 
243 
1152-31 
1152 
Total for columns 9, 
, 10, and 11 
19471 
873 
1327 
