A linear relationship between the sea floor depth and the square root of age has been found for ocean lithosphere spreading from mid-ocean ridges. The asymptotic solution of depth as a function of age for the thermally contracting lithosphere predicts a linear dependence of depth ontwith a proportionality involving the initial lithosphere temperature, the thermal diffusivity, and the isostatic expansion coefficient averaged to include any temperature dependent phase changes. Empirical depth observations, when plotted as a function of the square root of age, bear out this prediction well, but there is a variation in the gradient,ht, along the ridge on a fine scale (up to 20% over 200 km). This implies a fundamental variation of the contraction parameter over the same scale, most probably of compositional origin. Details of a more complete cooling model near the ridge crest, including a crust of different thermal parameters than those of the mantle, predict a crestal height about 0.2 km below that of the simplified model. Individual profiles from the southeast Pacific show no such crestal deviation, and it is concluded that by quickly cooling the new crust, hydrothermal circulation may remove any effects of the crust which would be seen in the topography of a lithosphere cooled totally by conduction. The straightness of depth versust for older ocean data (to 80 m.y.) precludes any basal isothermal boundary shallower than 100 km.