  The forward elastic scattering of light on light, {\em i.e.,} the reaction
$\gamma+\gamma \to \gamma+\gamma$ in the forward direction, is analyzed
utilizing real analytic amplitudes. We calculate $\rho_{\gamma \gamma}$, the
ratio of the real to the imaginary portion of the forward scattering amplitude,
by fitting the total $\gamma \gamma$ cross section data in the high energy
region $5 GeV \le \sqrt s \le 130 $ GeV, assuming a cross section that rises
asymptotically as $\ln^2 s$. We then compare $\rho_{\gamma\gamma}$ to
$\rho_{nn}$, the ratio of the even portions of the $pp$ and $\pbar p$ forward
scattering amplitudes, as well as to $\rho_{\gamma p}$, the $\rho$ value for
Compton scattering. Within errors, we find that the three $\rho$-values in the
c.m.s. energy region $5 GeV \le \sqrt s \le 130$ GeV are the same, as predicted
by a factorization theorem of Block and Kadailov.
