THE FUNCTIONS OF THE PARTS OF CILIA 147 



couple required to overcome the external resistance to movement, 

 and takes no account of internal resistance. 



Substitution of known values for Paramecium cilia in this equation 

 gave Harris a value for C of 5 x 10~^" dyn cm. It is also interesting 

 to compare the value found by substitution of figures measured for 

 Stentor membranelles, which we have seen to be compound cilia 

 built from 60 to 75 simple cilia. Such substitution gives a value for 

 C of 3 X 10~^ dyn cm. Since Harris suggested that the bending 

 couple of a compound cilium composed of n simple cilia should be 

 nC, the couple due to each component cilium of the Stentor membra- 

 nelle works out at 5 x 10~^" dyn cm or a little under — a remarkable 

 agreement for a much larger structure with a faster beat. 



Further calculation led Harris to conclude that if a bending couple 

 of 5 X 10~^° dyn cm is required to bend a length of the cilium into 

 an arc of radius 6/x, and if the central fibrils were responsible for 

 maintaining stiffness, they would have to have a Young's modulus 

 of 3 X 10^^ dyn/cm^ (that of biological fibrils is unlikely to exceed 

 about 10* dyn/cm-). If, on the other hand, it is assumed that turgor 

 pressure is acting against the ciliary membrane to maintain the 

 required rigidity, the Young's modulus for the membrane need be 

 only 5 X 10* dyn/cm^, and the internal turgor pressure required 

 would be about 7-6 x 10~' dyn, which could be provided by the 

 osmotic pressure due to a concentration difference across the membrane 

 of about 0-03 mol (assuming a non-dissociating molecule); all of 

 these last three values are thought reasonable. 



Additional evidence may be used to support the idea that 

 internal pressure maintains rigidity. For example, Bradfield 

 (1955) mentioned that the ciliary membrane nearly always appears 

 wrinkled in fixed and dehydrated specimens whether the fixitive 

 is hypotonic or hypertonic, and it is interesting that a large increase 

 or a large decrease in the external osmotic pressure will stop the 

 activity of lamellibranch gill cilia (p. 94). Also, where additional 

 contractile material is present, as in mammalian sperm, the shaft 

 is strengthened by a thickening of the outer layer of the ciliary 

 cylinder; this could maintain the stiffness of the shaft both by 

 increasing the tension the ciliary membrane can exert, and by 

 acting as a spring by virtue of its spiral construction. The sheath 

 of the sperm tail is especially well developed in the bandicoot 

 sperm where the outer contractile fibrils are very thick. 



Evidence which may count against this idea comes from the 

 undulating membrane of some flagellates (p. 38), where the axial 

 bundle of fibrils lies near one side of a greatly expanded flagellar 

 membrane. In these cases, however, some additional material is 



