420 Capt. Kater’s experiments for determining the variation 
number of vibrations in 24 hours, in different latitudes, will 
be to each other as gravitation in such latitudes. 
But as experiments on the pendulum cannot be made at the 
Pole, it remains to describe the manner in which the diminu- 
tion of gravity from the Pole to the Equator, may be obtained 
by observations made at intermediate stations. 
I have remarked, that the centrifugal force varies as the 
distance from the axis of rotation ; that is as the cosine of the 
latitude ; thus at the Equator it is the greatest, at the Poles it 
is nothing. 
But the whole of the centrifugal force does not act in oppo- 
sition to gravity except at the Equator ; for let cd be the 
direction of gravity, jb that of centrifugal force, and let the 
centrifugal force for the latitude a , be expressed by the 
line ah ; if this be resolved into two forces ad and db, that 
portion which acts in opposition to gravity will be expressed 
by ad. But if ah be made the radius, 
ad is the cosine of the angle dab, = 
acr, the latitude of the point a. The 
effect then of the centrifugal force at 
a , in counteracting gravity, is still 
farther diminished in the proportion 
of the cosine of the latitude to the 
radius ; whence it follows, that the 
diminution of gravity from this cause, in proceeding from the 
Pole to the Equator, will be as the difference of the squares of 
the cosines of the latitudes. 
From the expression for the force of gravity at the surface 
of a spheroid,* we may readily perceive that that part of the 
0 j j, + L.. in which the sin z <p is the only variable quan- 
tity, <p being the angle of the terrestrial radius with the Equator. 
