1. The general theory of flagellar propulsion is discussed and an expression obtained whereby the propulsive speed of a spermatozoon can be expressed in terms of the amplitude, wave-length and frequency of the waves passing down the tail of a spermatozoon of Psammechinus miliaris.

2. The expression obtained is applicable to waves of relatively large amplitude, and allowance is made for the presence of an inert head.

3. The calculated propulsive speed is almost identical with that derived from observational data. Unless the head of a spermatozoon is very much larger than that of Psammechinus, its presence makes relatively little difference to the propulsive speed. Most of the energy of the cell is used up in overcoming the tangential drag of the tail.

4. Although the amplitude may change as a wave passes along the tail, the propulsive properties of the latter may be expected to be closely similar to those of a tail generating waves of the same average amplitude.

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