  We derive a formula for the connected $n$-point functions of a tau-function
of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue
of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679].
Moreover, we prove a simple relation between the KP-affine coordinates of a
tau-function $\tau(\mathbf{t})$ of the KdV hierarchy and the BKP-affine
coordinates of $\tau(\mathbf{t}/2)$. As applications, we present a new
algorithm to compute the free energies of the Witten-Kontsevich tau-function
and the Br\'ezin-Gross-Witten tau-function.
