272 
PROFESSOR K. PEARSOX OX THE MATHEMATICAL THEORY 
Table XY .—Frequency of Absolute and Relative Errors in Bright-line Series of 
Experiments. Number, 519 
Size of error. 
I 
(1) 
(2.) 
(3.) 
" (3-2.) 
ii 
: (1-3.) 
i 
(2-1.) 
7 ■ 755 
i 1 
- 1 
7 • 255 
_ 
— 
— 
1 
j _ 
6 • 755 
— 
— 
— 
— 
1 
_ 
6 • 255 
1 
— 
1 
— 
1 
— 
5 • 755 
— 
1 _ 
4 
2 
— 
5 • 255 
— 
] 
— 
1 
5 
! - 
4 • 755 
1 
— 
— 
4 
5 
4 • 255 
— 
-- 
— 
12 
17 
_ 
3 • 755 
1 
— 
1 
15 
18 
- 1 
3-255 
6 
1 - 
12 
19 
17 
1 
2 • 755 
4 
— 
19 
20 
29 
1 i 
2-255 
12 
18 
26 
35 
8 
1 - 755 
22 
3 
26 
34 
41 
13 , 
1 - 255 
57 
8 
42 
49 
37 
19 j 
- 755 
71 
31 
48 
62 
41 
23 ' 
- 255 
97 
35 
44 
77 
60 
54 
- -245 
85 
73 
48 
90 
41 
72 ! 
- - 745 
69 
76 
46 
41 
56 
55 ! 
- 1-245 
56 
96 
60 
21 
35 
50 i 
- 1-745 
23 
79 
42 
19 
34 
59 
- 2-245 
l-r 
/ 
60 
36 
9 
21 
58 i 
- 2-745 
4 
30 
36 
5 
10 
38 
- 3-245 
1 
17 
20 
5 
6 
30 
- 3-745 
1 
5 
12 
1 
5 
15 1 
- 4-245 
— 
3 
5 
3 
2 
7 ! 
- 4-745 
1 
1 
2 
— 
— 
7 t 
- 5-245 
— 
— 
1 
— 
— 
3 i 
- 5-745 
— 
— 
— i 
— 
— 
2 i 
- 6-245 
— 
— 
1 
1 
— 
— 
2 
- 6-745 
— 
1 
— 
— 
— 
- 7-245 
— 
— 
— ! 
— 
— 
— 
- 7-745 
— 
— 
_ i 
-- 
— 
1 ! 
- 8-245 
— 
— 
- i 
_ 
— 
_ ' 
- 8-745 
— 
— 
— 
— 
— 
_ 
- 9-245 
— 1 
— 
— 
— 
— 
— 
- 9-745 
— 
— 
— 
_ 
_ 
- 10-245 
- 1 
_ i 
i 
— 
— 
— 
1 
present investigation \Ye have no less than twelve frequency distributions, six absolute 
distributions and six relative distiibiitions; the latter being of course of the type 
which will usually occur in astronomical or physical observations where the absolute 
errors cannot be measured. We have then material enough to discuss the problem : 
Is it suitable for the purpose ? It seems to me that there is nothing peculiar to our 
data which marks them off from other series of observational errors, except their 
rather extensive character, which was necessary if safe conclusions were to be drawn. 
There were four independent observers, three of whom at least had been long used to 
making observations and measurements ; the fourth, less accustomed, turned out in the 
sequel to have the steadiest judgment. Further, the investigations were begun with 
