Like those for n, the kinetic reaction schemes for both m and h are simply those describing the back-and-forth movement of these charge groups between one state and another.

The rates at which these movements take place are set by the rate constants shown here in the figure. For both m and h, the rate constants are not constant but depend on the potential across the membrane.

The Na activation variable m is small but finite at rest and increases upon depolarization.

For depolarizations, "alpha m" is larger than "beta m," causing the steady value of m to build up.

For hyperpolarizations, rest, and repolarizations, "beta m" is much larger than "alpha m," causing the steady value of m to become smaller and ultimately approach zero.

The inactivation variable h is large at rest and decreases upon depolarization.

The onset, decay, and reset time courses of the sodium conductance data had to be fitted with the time course of m^3 * h. In those days, the fitting was often done by making transparent template curves with a range of parameter values to overlay data traces. Interpolations and iterations were used to improve the resolution in the data values. In this figure the conductance data points (circles) overlay the m^3 *h curve fairly well for a strong depolarization (88 mV from rest).

Hodgkin and Huxley then, in their fourth 1952 paper, carried out the following: fitting of their records of sodium conductances, as shown here, over a wide range of voltages. tabulating and plotting the values of the alphas and betas for each voltage finding analytical expressions for alpha and beta versus the voltage

They were then ready to use the analytical expressions for alpha and beta as a function of the membrane potential in their equations for the membrane current. Numerical integration of their equation was to be used to calculate an action potential.