The density rho of coexisting phases of the ternary system water+1,4-dioxane+potassium chloride was investigated along the liquid-liquid-solid coexistence curve near the critical end-point using a vibrating tube densimeter. By visual determination, this lower critical end-point was located at 311.026+/-0.010 K with a mole ratio dioxane (D) to water (W) r(c)=n(D)/n(W)=0.418+/-0.004. Density measurements were carried out in the range 0.01 K < (T-T-c)<31.5 K (i.e., 3x10(-5)10(-2) from a nonclassical (Ising) to a classical (mean field) exponent. In ancillary experiments, the critical salt concentration was determined. Reduced critical values were calculated and compared with those predicted by the simplest ionic model (RPM, Restricted Primitive Model). The relation between critical behavior and reduced critical parameters in the present and other non-Coulombic systems is discussed.