It is possible to make some qualitative predictions about the way in which the space and time constants affect propagation velocity. If the space constant is large, a potential produced at one portion of an axon will spread greater distances along the axon. Because the potential will spread a greater distance along the axon, it will bring distant regions to threshold sooner. Thus, the greater the space constant, the greater will be the propagation velocity. The time constant is a reflection of the rate that a membrane can respond to an applied stimulus current. The smaller the time constant, the greater will be the ability of a membrane to respond rapidly to stimulus currents. Action potentials will be initiated sooner, and the propagation velocity will be greater. Therefore, the smaller the time constant, the greater will be the propagation velocity.
Thus, the propagation velocity is directly proportional to the space constant but inversely proportional to the time constant. Because relationships for both the space and time constants are known, it is possible to derive a new formula that describes the propagation velocity:
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