252 Captain Hall's details of experiments 
Thus we have obtained 86119,01 vibrations by the rates deduced from the 
transits of stars, and 86119,02 by the sun’s transits. But the sums of the factors 
being respectively 285 and 112, the former determination, or 86119,01, may be 
taken for the final mean number of vibrations in 24 hours. 
The height of the bail of the pendulum was found by levelling, agreeing with a 
trigonometrical measurement, to be 115 feet; the correction due to which is 
v 
0,47 Xio= 0 > 2 ^; this together with that for the buoyancy of the atmosphere, 
V V 
viz. 5,74, gives 6,02 to be added to the mean number of vibrations ; and we have 
86125,03 for the final number of vibrations which would be made by this pendulum 
in vacuo at the temperature of 68°, at the level of the sea, in a mean solar day at 
San Bias, in latitude 21 0 32' 24" N. and longitude 105° 15' W. 
From the above data, and the number of vibrations made by the same pen- 
dulum in London, after returning to England,* viz. 86236,95, together with the 
known length of the second’s pendulum in London, the length of the second’s pen- 
dulum at San Bias is found to be 39,03776 inches ; and comparing this with the 
lengths of the second’s pendulum determined by Captain Kater at the principal 
British stations, we obtain the following expressions for the diminution of gravity 
from the pole to the equator, and ellipticity of the earth, together with the lengths 
of the equatorial pendulum by each comparison. 
Stations compared with San Bias, 
in Lat. 21 0 32' 24" N. 
Unst - in Lat. 60 45 28 N. 
Portsoy - - - 57 4 ° 59 
Leith - - - 
Clifton - - 
Arbury Hill - 
London - 
55 5 8 4 i 
52 27 43 
52 12 55 
5 1 3 i 8 
Shanklin Farm - 50 37 24 
Mean 
Diminution of 
Gravity from 1’ole 
to Equator. 
,0054703 
,0054789 
,0054683 
,0054328 
,0054819 
,0054452 
,0054505 
,005461 1 
Ellipticity. 
3 I 4>44 
1 
1 
3i4»25 
1 
310,78 
1 
315,60 
1 
3 n>9 8 
1 
312,50 
3i3*55 
Length of 
Equat. Pendul. 
39,00899 
,00895 
,00901 
,00920 
,00893 
,00912 
,00910 
39,00904 
* See the Remarks after the Experiment given in the Appendix. 
