EE PRESENT ATI OX OE THE MOTION OF A FREE RIGID BODY. 
7 
plane may be zero, the forces acting on the body will become absolutely identical with 
those acting on the particle G, — that is, we shall have F'=G^I -^2 —n 2 ujj, and F, as 
before, =2G_p^. — February 1870.] 
It may be worth while to point out that the correlated and contrarelated bodies 
treated of in the latter part of Professor Sylvester’s paper include, as a particular case, 
Poinsot’s “rolling and sliding cone;” for the equation of that cone is 
X- y 
, "T~ 
d 2 — p ' 2 ~ b 2 — p 2 ' c 2 — p 
„5=0, 
which is asymptotic to the two following surfaces : 
/y>2 n ,2 ,v2 
. i -JL | z 
d 2 — p 2 ' U 2 — p 2 c 2 — p 2 
2 
the former of which is confocal, the latter contrafocal, to the momental elli soid of the 
free body. Hence, since the difference between the squares on corresponding semiaxes 
is in this case ]f, each of these hyperboloids will roll on the invariable plane through 
the fixed point, which will be asymptotic to it, while the plane itself rotates with uniform 
angular velocity X. Hence the asymptotic cone will move in exactly the same manner. 
