i 66 Mr. Goldingham’s observations for ascertaining 
Thermometer 88°, barometer 30,064 inches, specific gra- 
vity of the pendulum 8,1085. Hence the specific gravity of 
the pendulum for the mean of the first series of observations, 
the thermometer being 83°, 48, and barometer 30,121, was 
8,02096, and the correction for the buoyancy of the atmo- 
sphere is +6,2075 vibrations. For the second series, the 
thermometer having been 85°, 49, and barometer 30,258 in- 
ches, this correction is 6,220 vibrations. These corrections 
being applied to the number of vibrations before found, will 
give the true number of vibrations of the pendulum in 24 
hours in vacuo at the level of the sea, the thermometer being 
70°, and are as follow : — 
By the first series of observations, 86172,3 755. By the 
second series, 86172,328. The mean being 86172,352. 
The length of the seconds pendulum in London, (latitude 
51 0 3T 8", 4 N.) at the temperature of 70°, according to Cap- 
tain Kater, is 39,142213 inches. Now, the pendulum of 
experiment used at Madras, made 86293,44 vibrations in 24 
hours in London, latitude as before, and 83 feet above the 
level of the sea, the mean height of the thermometer being 
67°, 6, of the barometer 29,97 inches (vide Appendix). The 
correction for the height above the sea is 0,22, and that for 
the buoyancy of the atmosphere 6,566, both to be added : 
these corrections being applied, will give 86300,226 for the 
number of vibrations of the pendulum of experiment in 24 
hours in vacuo at the level of the sea, the temperature being 
70°. Now, 86300,226 s : 86400 2 : : 39,142213 : 39,232772 
the length of the pendulum of experiment. 
Then 86172,375" : 86400 2 : : 39,232772 ; 39,02632308 7, 
the length of the seconds pendulum at Madras by the first 
series of observations. 
