316 
MR, airy’s account OF THE BARTON EXPERIMENT 
Next, it is necessary to determine experimentally the law, or rather the numerical 
succession of values, in the diminution of the arc of vibration. For this purpose, 
observations were made at Greenwich on the extent of the whole arc in successive 
half-hours. The following Table contains (with sufficient approximation) the range 
of arc through each half-hour, the middle arc on which the correction may be sup- 
posed to depend, and the logarithmic correction as taken from the last table. 
; Range of Arc 
j through half-hour. 
Middle 
Arc. 
Log. 
Correction. 
Range of Arc 
through half-hour. 
Middle 
Arc. 
Log- 
Correction. 
Range of Arc 
through half-hour. 
Middle 
Arc. 
Log. 
Correction. 
f 2-35— 1-97 
2-14 
831 
0-71— 0-59 
0-64 
81 
0-22— 0*19 
0*20 
7 
' 1-97— 1-64 
1-79 
579 
0-59— 0-49 
0-34 
52 
0-19— 0-16 
0*17 
6 
1-64— ] -38 
1-50 
402 
0*49— 0-41 
0-45 
36 
0-16— 0-13 
0*14 
4 
1-38— M6 
1-26 
287 
0-41— 0-34 
0-37 
26 
0*13— 0-10 
0*11 
3 
M6— 0-98 
1-06 
205 
0-34— 0-29 
0-31 
18 
0-10—0*08 
0*09 
2 
0-98— 0*83 
0-90 
146 
0-29— 0-25 
0*27 
13 
0-83— 0-71 
0-76 
103 
0 - 25 — 0^22 
0-23 
10 
Suppose now that we wished to find the logarithmic correction for a Swing whose 
first arc was T97 and whose last arc was 0‘98. This Swing extends over four equal 
intervals of time, for which the log. corrections are respectively 579, 402, 287, 205. 
The log. correction tlierefore applicable to the whole time will be the mean of these 
four corrections, or 368. In a similar manner, we may obtain the correction with 
any other beginning and concluding arcs among those in the table above, and thus 
the next table is formed. 
Logarithmic Correction for the whole Swing. 
Commencing Arc. 
2*35 
1 
1*97 
1*64 
1*38 
1*16 
00 
OS 
o 
0*83 
0*71 
0*59 
0*49 
0*41 
0*34 
0*29 
0*25 
0*22 
0*19 
0*16 
0*13 
0*10 
'1*97 
831 
1*64 
705 
579 
1*38 
604 
491 
402 
1*16 
525 
423 
345 
287 
0-98 
461 
368 
298 
246 
205 
0*83 
1 408 
324 
260 
213 
176 
146 
c3 
0*71 
365 
287 
229 
185 
131 
125 
103 
0*59 
j 329 
258 
204 
164 
134 
110 
92 
81 
fcc 
0*49 
' 298 
232 
182 
146 
117 
96 
78 
67 
52 
l-h 
0*41 
272 
210 
164 
130 
104 
84 
63 
56 
44 
36 
0-34 
’ 250 
192 
149 
117 
93 
74 
60 
49 
38 
31 
26 
o 
0*29 
^ 231 
176 
136 
106 
83 
66 
53 
43 
33 
27 
22 
18 
o 
Cj 
0*23 
214 
162 
124 
97 
76 
59 
47 
38 
29 
23 
19 
16 
13 
0*22 
i 199 
151 
115 
89 
69 
34 
42 
34 
26 
21 
17 
14 
12 
10 
0*19 
! 186 
140 
107 
82 
63 
49 
38 
30 
23 
18 
15 
12 
10 
9 
7 
0*16 
175 
131 
99 
76 
59 
45 
33 
28 
21 
17 
13 
11 
9 
8 
6 
6 
0*13: 165 
123 
93 
71 
54 
42 
32 
25 
19 
15 
12 
10 
8 
7 
6 
5 
4 
0*10 
!: 156 
116 
87 
66 
51 
38 
30 
23 
17 
14 
11 
9 
7 
6 
5 
4 
4 
3 
1^0*08 
148 
110 
82 
62 
48 
36 
28 
22 
16 
13 
10 
8 
6 
5 
4 
4 
3 
3 
2 
It was only necessaiy in fact to use so much of this table as is included between 
2'35 and T38 for Commencing Arc, and between 0'98 and 0'34 for Concluding Arc. 
Between these limits, a skeleton table was prepared for every O'Ol in each argu- 
