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1. Strength—duration curves for excitation in long point-stimulated sheep cardiac Purkinje fibres, where the charge distribution varies along the length of the fibre, are characterized by (a) a time constant which is short relative to the membrane time constant, (b) an apparent fall in charge threshold for short duration stimuli, (c) an apparent rise in voltage threshold as measured by an electrode at the point of current passage (see Dominguez & Fozzard, 1970).
2. Strength—duration curves obtained from shortened segments of Purkinje fibres, where the charge distribution along the segment is fairly uniform after 2-3 msec, have much larger time constants.
3. For stimulus durations longer than the 2-3 msec necessary to establish charge uniformity, strength—duration curves obtained from shortened segments of Purkinje fibres were well fitted by the Lapicque—Hill equation, I/Irh = [1 — exp (—t/
)]-1.
4. The differences in the time constants and apparent voltage thresholds for point-stimulated long fibres and uniformly charged short fibre segments could be explained by the liminal length concept of Rushton (1937). The liminal length concept, in its simplest form, states that a liminal length of fibre must be raised above a given voltage threshold in order for a propagated action potential to be generated.
5. This concept predicts that the shorter the liminal length, the shorter the time constant of strength—duration curves in point-stimulated long fibres.
6. Another conclusion of the model is that only those point-stimulated long fibres with longer liminal lengths would have a constant charge threshold for stimuli of the order of 0·2 .
7. Liminal length was found by experiment and calculation to be about 0·1-0·2 
m in cardiac Purkinje fibres.
8. The differences in behaviour with regards to excitation between the point-stimulated theoretical squid axon and the point-stimulated Purkinje fibre may be explained by assuming that the liminal length of the theoretical squid axon is several times larger than that of the Purkinje fibre.
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