  We prove a general formula for the intersection form of two arbitrary
monomials in boundary divisors. Furthermore we present a tree basis of the
cohomology of $\overline {M}_{0,n}$. With the help of the intersection form we
determine the Gram matrix for this basis and give a formula for its inverse.
This enables us to calculate the tensor product of the higher order
multiplications arising in quantum cohomology and formal Frobenius manifolds.
In the context of quantum cohomology this establishes the explicit K\"unneth
formula.
