Using results of Agler, Aleksandrov and Doubtsov we study Clark measures determined by rational inner functions $\Phi(Z),$ of degree $(n,1)$ on the two torus $T^2= \partial D^2.$ In particular in considering the Clark measure $\sigma_a$ arising from the equation

$$Re((a+\Phi(Z))/ (a- \Phi(Z)) \equiv \int_{T^2} P(Z,\zeta) d \sigma_a(\zeta),$$

where , $Z\in D^2, \zeta \in T^2, a \in T,$ we obtain functions $B_a,$ and $W_a$ , defined on $T$ for which the following equation holds for $f \in L^2(d \sigma_a),$

$$\int_{T^2} f(\zeta)d \sigma(\zeta) = \int_T f((\zeta, \overline{B_a}(\zeta)) W_a(\zeta) d m(\zeta) + \sum_{k=1}^m C_k^a \int_T f(\tau_k,\zeta) d m(\zeta). $$

$1.$ Doug Clark; J. Analyse Math, $25$, ($1972$)

$2.$ Cima, Matheson, Ross; Math. Surveys and Monographs, Vol. $125$ , AMS

$3.$ Bickel, Cima, Sola,(Arxiv)

$4.$ Rudin, Two Books on SCV

$5.$ E.Saksman, Notes, Malaga U.

$6.$ Doubtsov,( Arxiv)