  For a given dimension d $\ge$ 2 and a finite measure $\nu$ on (0, +$\infty$),
we consider $\xi$ a Poisson point process on R d x (0, +$\infty$) with
intensity measure dc $\otimes$ $\nu$ where dc denotes the Lebesgue measure on R
d. We consider the Boolean model $\Sigma$ = $\cup$ (c,r)$\in$$\xi$ B(c, r)
where B(c, r) denotes the open ball centered at c with radius r. For every x, y
$\in$ R d we define T (x, y) as the minimum time needed to travel from x to y
by a traveler that walks at speed 1 outside $\Sigma$ and at infinite speed
inside $\Sigma$. By a standard application of Kingman sub-additive theorem, one
easily shows that T (0, x) behaves like $\mu$ x when x goes to infinity, where
$\mu$ is a constant named the time constant in classical first passage
percolation. In this paper we investigate the regularity of $\mu$ as a function
of the measure $\nu$ associated with the underlying Boolean model.
