324 
MR. AIRY’S ACCOUNT OF THE HARTON EXPERIMENT 
Fii'St Series. Log-. Rate of Pendulum 8 below on Pendulum 1821 above. 
No. of 
Swing. 
Log. 
Lower Pendulum 
No. of 
Swing. 
Log. 
Rite Pendulum 
No. of 
Swung. 
Log. 
Lower Pendulum 
No. of 
Swing. 
Log. 
Lower Pendulum 
Upper Pendulum 
Upper Pendulum 
Upper Pendulum 
Upper Pendulum 
1 
9-99928067 
8 
9*99928485 
15 
9*99929623 
22 
9*99927705 
2 
9045 
9 
7284 
16 
8478 
23 
7793 
3 
9005 
10 
8116 
17 
8501 
24 
9783 
4 
8261 
11 
8683 
18 
8381 
25 
8385 
f) 
9458 
12 
8278 
19 
7723 
26 
8582 
6 
9014 
13 
9524 
20 
8724 
7 
8281 
14 
8135 
21 
9083 
1 
Second Series. Log. Rate of Pendulum 1821 below on Pendul 
um 8 above. 
27 
0*00073466 
34 
0*00074088 
41 
0*00073841 
48 
0*00073718 
28 
4199 
35 
3471 
42 
3720 
49 
3371 
29 
3602 
36 
351 1 
43 
3714 
50 
3941 
30 
3684 
37 
3628 
44 
3727 
51 
3518 
31 
3868 
38 
4004 
45 
3382 
52 
3580 
32 
3919 
39 
3903 
46 
3709 
33 
3319 
40 
3232 
47 
3852 
Third Series. Log. Rate of Pendulum 8 below on Pendu 
lum 1821 above. 
53 
9-99928138 
57 
9*99928427 
61 
9*99928297 
65 
9*99928865 
54 
8078 
58 
8440 
62 
9319 
66 
8366 
55 
9635 
59 
8661 
63 
8406 
67 
8900 
56 
7957 
60 
8786 
64 
8243 
Fourth Series. Log. Rate of Pendulum 1821 below on Pendulum 8 above. 
68 
0*00073376 
72 
0*00074105 
76 
0-00073941 
80 
0*00073541 
69 
4097 
73 
3691 
77 
3929 
81 
3827 
70 
3162 
74 
3381 
78 
3549 
82 
2831 
71 
3748 
75 
3732 
79 
3997 
39. On tracing the irregularities in these numbers to their sources, it will be 
seen that they arise almost entirely from the irregularities in the comparisons of 
the clocks. The rate of each pendulum upon its clock is either so constant, or 
changes by such uniform degrees in the same direction, that there is every reason 
to presume on the extreme steadiness both of the detached pendulums and of the 
clocks. 
Remarking then that, when a large variable error is combined with a small 
variable error, the magnitude of the probable error in the combination is scarcely 
affected by the small error, we may treat these irregularities of result as if they 
were entirely due to irregularities of comparison; and we have now to investigate 
the rule to be followed in combining the special results, supposed to be erroneous 
from that cause only, in order to obtain a final result whose probable error shall be 
the smallest possible. It is evident that we are not to give equal weights to the 
