18 
NOTE ON THE DEMONSTRATION OF CLAIRAUT’s THEOREM. 
[635 
which is of the form 
g = G jl 4- u 2 -f (i - cos 2 0) + 2u 3 + ...|. 
Taking the Earth to be the spheroid of revolution 
then 
and the equation is 
or say 
r = a {1 + e ( J — cos 2 #)}, 
u 2 = e — cos 2 0), u 3 = 0, &c., 
S^ejl -(f^-e)(i-cos»0)j, 
g = G{l- (I m - e) (J - cos 2 0)}, 
where 
œ 2 a 
m ’ ~~G~ 
, is the ratio of the centrifugal force at the equator 
gravity, which is the theorem in question. The expression “ it follows ! 
used as meaning it follows as a mere analytical consequence, in the 
approximation, the steps of the deduction being purposely omitted. 
to the force of 
has been twice 
proper degree of