Refractive indices n and salt concentrations m(s) of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10(-3) < t = (T - T-c)/T-c < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10(-3) < t < 8.07 x 10(-2). From these experimental results, compositions f(D) (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, m(s), f(D), and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, m(s), and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable f(D) requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.