422 Capt. Kater’s experiments for determining the variation 
If g, be the space a body falls through in one second of 
time at the Equator, L the length of the seconds pendulum, 
and c the circumference of a circle, the diameter being l, 
- g == \ L x c e . 
The length of the pendulum vibrating seconds at the equator, 
deduced from the observations at Unst and Dunnose, by the 
preceding formula, appears to be 39,00734 inches, and g , or 
gravitation at the Equator, to be equal to 16,0412 feet. Hence 
the centrifugal force at the equator is of gravitation, or 
of gravity ; which last being multiplied by j-, we have 
,0086501 for the sum of the fractions expressing the ellipti- 
city of the earth and the diminution of gravity, from the Pole 
to the Equator. 
In the following Table are given the diminution of gravity 
from the Pole to the Equator, and the resulting compression, 
deduced in the manner which has been described, by com- 
paring the observations at each station, successively with 
those at all the others. 
