**2.1 Escape Speed for a Simple Spherical Model**

We can tie in local observations of high velocity stars with
the notion of the escape speed (cf.
Binney & Tremaine 1987).
For a simple spherical model we have :

(1)

The corresponding escape speed is

(2)

Substituting *V*_{c} = 220 km s^{-1}, *r* =
*R*_{} = 8.5 kpc
and an estimate for the escape speed of 500 km s^{-1}, we find
*r*_{*} = 4.9 *R*_{} 41 kpc, and
*M (r = r*_{*}) = 4.6 10^{11}
*M*_{}. Note that
Olling and Merrifield
(1998)
advocate lower values for the distance of the Sun to the Galactic Center and
for the rotation velocity at the distance of the Sun. Recent
estimates of the escape speed from HIPPARCOS data are discussed
in Meillon et al. (1997),
and fall within a range of 400 to 550 km s^{-1}.