Coefficient of Static Fraction

[poonintoon]

Please could somebody explain how the coefficient of static friction can be quoted as a constant in tables etc?
$\mu_s = F_s/ R$
In most cases the reaction force is constant but as I push the box harder the friction force increases.

Is $$\mu_s$$ actually the coefficient of limiting friction? Or am I totally misunderstanding?

 

[A.T.]

Is $$\mu_s$$ actually the coefficient of limiting friction?

Yes.