The fundamental problem of not exceeding the critical saturation of nitrogen in a diver's body requires both physics and physiology in its solution. The basic differential equations of nitrogen saturation and desaturation in a specific tissue are integrated over an idealized dive. Constants determined through physiological research can be substituted and a time-depth ascent curve for any tissue established. A stepwise method is outlined whereby critical tissues at each portion of the ascent can fix the proper ascent curve for the entire body. The advantage of pure oxygen breathing is demonstrated numerically and the failure of helium-oxygen mixtures to shorten ascents is explained by use of the derived equations.