C 4 X 9 ] 
the compofition of forces, the angle NAM (whofe 
tangent, to the radius O A, is expreffed by O A x 
X—) will be the change of the direction of the 
ncf m l a 
rotation, at the end of the aforefaid time (m). But, 
this angle being exceeding fmall, the tangent may be 
taken to reprelent the meafure of the angle itfelf; 
and, if Z be a (fumed to reprefent the arch defcribed 
by A, in the fame time ( m ) about the center O, we 
(hall alfo have ~ and confequently 
O A x — r X — = Z x — r . From whence it appears, 
ncf m ncf r r » 
that the angle expreffing the change of the direction 
of the rotation, during any fmall particle of time, 
will be in proportion to the angle defcribed about 
p 
the axe of rotation in the fame time, as — > is to 
1 ncf 
unity . E. /. 
Altho’, in the preceding propofition, the body ig 
fuppofed to be a perfedl fphere, the folution, never- 
thelefs, holds equally true in every other fpecies of 
figures, as is manifeft from the inveftigation. It is 
true, indeed, that the value of n will not be the 
fame in thefe cafes, even fuppofing thofe of c, f 
and F to remain unchanged ; except in the fphe- 
roid only, where, as well as in the fphere, n will 
be = j- i the momentum of any fpheroid about its 
axis being 2-5ths of the momentum of an equal 
quantity of matter placed in the circumference of 
the equator, as is very eafy to demonftrate. 
But to (hew now the ufe and application of the 
general proportion here derived, in determining the 
regrefs of the equinodtial points of the terredrial 
H h h 2 fpheroid, 
