172 CO-ORDINATION OF BEAT 



cilium (proportional to angular velocity x length) is inversely 

 proportional to the square of the cilium length. If each simple 

 cilium is capable of exerting about the same bending couple, there 

 is an optimum length for any type of cilium vv^hich depends on 

 its use and form of beat. If a cilium is short, it is unable to 

 sweep through a large body of water, but yet can beat very fast, 

 while a long cilium can move through a large volume of water 

 at a much slower speed; the optimum length is attained when 

 the cilium can move through a sufficiently large arc to perform 

 the required function, but yet is able to beat fast enough to 

 perform this function properly. 



On this basis Harris suggests that it would be valueless to the 

 animal if the body cilia of Paramecium or the cilia of the pharyngeal 

 epithelium of the frog were to be increased in length much 

 beyond 10 to 15 /x, since in both cases the cilia are used to move 

 fluids in the immediate neighbourhood of the surface; increase 

 in length would mean that the cilia would beat more slowly and 

 the movement of fluid would be reduced. Where a longer cilium 

 is required to move through a large volume of water, e.g. for the 

 movement of ctenophores or for the feeding current of Stentor 

 or MytiluSy then a high velocity of the beat can only be maintained 

 if a number of cilia beat together to increase the bending couple. 

 The effect of this is most easily seen in compound cilia, but it 

 may be used in cilia which are close together and beat synchro- 

 nously so that the effects of viscous drag may be minimized. 

 Compound cilia used as "legs", e.g. the cirri of hypotrich 

 ciliates, are also able to make use of the larger bending couple 

 that can be exerted when many cilia beat as one. 



A striking example of the effect of cilium length and com- 

 pounding on the rate of beat is provided by the comb -plates of 

 ctenophores. If a single cilium of such a comb -plate is 1 mm 

 long, and has a bending couple comparable with that of other 

 cilia, then according to the equation worked out by Harris, the 

 angular velocity of beat would be so slow that the cilium would 

 take several hours to complete a beat of the normal pattern. 

 However, in the normal comb-plates, some 10^ cilia are combined 

 together into a single structure, so that the bending couple that 

 can be exerted is large enough for the comb -plate to beat several 

 times per sec. Note that this is a hypothetical example, in the 



