462 
CAPTAIN SABINE ON THE LENGTH OF THE SECONDS PENDULUM 
January 27, 
1830. Clock by Dent making 8631 1.0 Vibrations in 
a mean solar day. 
o *5 
o3 
tJO 
Times of 
Arcs of Vibration. 
Mean 
Mean 
Reductions 
1-3 
^ U 
(V 
H 
s 
o 
Disapp. 
Reapp. 
Coincidence. 
Temp. 
Gauge. 
Interval. 
to mean 
tem. 36°. 
to a Va- 
cuum. 
per diem. 
1 
o 
in. 
m s 
11 16 
m s 
11 27 
h m s 
10 11 21.5") 
10 23 37 > 
10 35 52 J 
O o 
o 
in. 
o 
3 
34.9 
0.86 
23 31 
35 45 
23 43 
35 59 
1.26x1.05=1.32 
1 35.1 
)> + 0.75 
1.275 
737.90 
-0.07 
+ 0.60 
86077.59 
15 
35.3 
1.69 
3 15 
3 44 
1 3 29.5 
0.70x 1.05 = 0.73 
J - — ■ 
Air pumped out to reduce the gauge. 
35.85 
16 
.'ll 
35.3 
35.4 
0.92 
1.53 
15 35 
21 06 
16 02 
21 47 
1 15 48.5 
4 21 26.5 
0.67 X 1.05=0.70 
0.40 x 1.05=0.42 
-) 35.35 
1,+ 0.75 
1.225 
742.53 
+ 0.04 
+ 0.58 
86079-14 
J 36.10 
31 
46 
35.4 
1.53 
21 06 
26 37 
38 55 
51 17 
21 47 
28 03 
4 21 26.5 
7 27 20 V 
7 39 40.5 > 
7 52 02.5 J 
0.40X1.05 = 0.42 
1 35.45 
l + 0.75 
1.725 
743.41 
+ 0.08 
+ 0.82 
86079-66 
47 
35.5 
1.92 
40 26 
52 48 
0.18X1.05 = 0.19 
48 
J 36.20 
Examining these observations we have 
I. 
II. 
III. 
Arcs 
1.32 to 6.73 
0.70 to 0.42 
6.42 to 6.19 
Vibrations per diem, uncor- ) 
rected for the arcs . ... J 
l 86077-59 
86079.14 
86079.66 
Compensation for the arcs by 1 
the formula J 
+ 1.67 
+0.50 
+0.14 
These numbers should agree if 'h 
the corrections for the arcs 1 
computed by the formula j 
wp.re a inst, rorrinen Ration J 
!> 86079.26 
86079.64 
86079.80 
From the differences that are here seen to exist, it appears that when the 
pendulum is vibrated with the weight above, the compensation for the arcs as 
computed by the customary formula is in defect ; and more in defect as the 
arcs are larger. To make the results agree, it is necessary to multiply the com- 
puted correction by 1.36. By the employment of this multiplier, the result 
obtained in the arcs of least magnitude (which as being the nearest to 
infinitely small arcs are presumed to be the most correct,) is not altered more 
than five-hundredths of a vibration ; whilst the results obtained in larger arcs 
