  In this paper, we prove Thomae's formula for a triple covering of $\bold P^1$
with arbitrary index. This formula gives a relation between theta constants,
determinants of period integrals and the difference products of branch points.
To specify a symplectic basis of the curve, we use the combinatorics of binary
trees on $\bold P^1$. This symplectic basis behaves so well for degenerations
that we obtain the absolute constant in this formula and reduce it to a special
case treated in [Bershadsky-Radul], [Nakayashiki].
