Abstract Single crystals of the cubic form of sodium chlorate are studied in growth from aqueous solution. An interferometric technique measures, via refractive index, concentrations and gradients of concentration contiguous to the crystal. The rates of advance of individual faces are measured and compared with predictions derived from the Nernst supposition, namely, that the concentration is saturation at a crystal face and that the facial rate of advance depends only on diffusion. It is found that faces sometimes grow at rates consistent with this supposition, but that on other occasions smaller rates of growth are observed, including instances of complete stoppage of growth. It is also found that individual faces can change discontinuously from one rate of growth to another. The observation of Berg, that concentration and normal concentration gradient are functions of position at the face, is developed, and empirical equations are obtained for the functions which connect the rate of growth with the concentration and gradient distribution along the face. To account for the advancing surface remaining plane, notwithstanding the non-uniformity of normal concentration gradient along it, it is necessary to suppose a transport of material along the face. Some observations on dissolution have been made, and a non-uniformity of concentration along a dissolving face is found and discussed.