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APPENDIX. 
briefly described, to consist in ascertaining with the utmost possible accu- 
racy, at different stations the latitudes of which are correctly known, the 
number of vibrations which would be made by a certain pendulum in a given 
time, were it placed at the level of the sea, in vacuo, and at a certain tem- 
perature. This purpose is effected by setting up a clock containing the pen- 
dulum in a convenient and protected situation, and by observing the number 
of vibrations which it makes on an average of several intervals of 24 hours 
each, accurately determined ; the actual circumstances of the temperature, 
pressure of the atmosphere, arcs in which the vibrations are performed, and 
the elevation above the sea, being carefully noted, and their effects in 
retarding or accelerating the vibrations calculated and allowed for. 
This operation, which is sufficiently simple in description, proves less so 
in the performance, by reason of the extreme accuracy which is required in 
the results, and of the many causes whereby slight errors may be intro- 
duced, which demand the utmost precaution and watchfulness to guard 
against. 
The squares of the number of vibrations in 24 hours in the different lati- 
tudes, are to each other, as the force of gravitation in such latitudes ; 
and the difference between the Polar and Equatorial diameters is de- 
duced from the acceleration, obtained by comparing the observations at eacli 
station successively with those at all the others. 
Two clocks were used in these experiments, being the property of the 
Royal Society, and the same which accompanied Captain Cook round the 
world. 
The pendulums were prepared by Captain Kater ; being each cast in one 
piece of solid brass, and vibrating on a knife-edge of hard steel, on agate 
plates ground into portions of hollow cylinders. 
The experiments were made in the present Voyage, and in the preceding 
one in 1818; one only of the clocks was employed in the first voyage, 
but both in the second. 
The stations at which the experiments in 1818 were made, were as 
follow : **.. 
At Brassa, one of the Shetland Islands . . Lat. 60° 09' 42" N, 
At Hare, or Waygat Island, in Davis Strait, Lat. 70° 26' 15" N, 
And in London Lat. 51° 3T 08". 4 N; 
