Mr Watts on the Elliptkity of the Eetrth, 29! 
the sum of all these quantities being divided by 7, and the ag- 
gregate result made equal to zero, we shall obtain 
— 25,9685258 + 0,66828595 . + 0,44301352 (2). 
This is the equation of minimum^ with respect to y ; and if we 
eliminate y from the equations (1) and (2), we shall find 
0,2058309 — 0,005251 32 . ^ = 0 ; whence we deduce 
^ = 39,0135648. 
This is the length of the seconds’ pendulum at the equa- 
tor ; and by substituting this value of x in the equation (2), 
we shall have, 
y = 0,20626348 ; 
therefore, in general, the absolute length of the seconds’ pendu- 
lum, as deduced from the preceding experiments of Captain 
Kater, will be 
I = 39,0135648 + 0,20626348 sin . 
This formula gives for the length of the seconds’ pendulum, in 
the latitude of London, 39,1399631 inches of Sir G. Shuck- 
burgh’s scale. 
Hence it follows, that the ratio ^ = 0,00528697, will ex- 
X 
press the total lengthening of the seconds’ pendulum from the 
equator to the pole, or which is all the same, the total increase 
of gravity. 
But Clair ault has demonstrated, in his excellent work on the 
Figure of the Earth, that, in every hypothesis relative to the 
interior nucleus covered by the ocean, the sum of the total in- 
crease of gravity, from the equator to the poles, determined as 
above, together with the earth’s ellipticity, is always the same, 
and equal to five halves of the ratio of the centrifugal force, to 
the force of gravity at the equator ; that is to say, this sum is 
equal to , or 0,0086505188. If, therefore, we call the 
lip j 
ellipticity C, we shall have 
G 4- 0,00528697 = 0,0086505188, 
C = 0,003635488 ; 
or, by reversing the fraction, 
C = required compression of the earth. 
