D.— ZOOLOGY. 73 



APPENDIX B. 



Some Numerical Data of Flagellar Motion. 



In the active flagellum of Grantia compressa the longitudinal extension 

 of the convex side as compared with the concave side must be in the ratio 

 x y° to produce the observed radius of curvature (about 3-5[x) 40 . Assuming 

 the length of the concave side constant, this would mean an average 

 extension approximately in the ratio if. If this were the passive result 

 of an increase in volume, as in the elementary theory suggested in the 

 text, and if the diametral expansions were in the same ratio, then the 

 indicated increase in volume would be in the ratio |. 



But it was pointed out to me by a biologist at Plymouth, working on 

 spermatozoa, that their right-handedness of motion indicates that the 

 molecules of the flagellum are orientated with length parallel to its axis. 

 It seems possible, therefore, that the unstable molecular strain which 

 causes the flexion may be accompanied by an addition only to length of 

 the molecules. It is' impossible to assert definitely that a change of 

 width from -4[A to -44p. would be recognisable in the retinal image, but my 

 own belief is that in a slowly moving flagellum such a change in width 

 would have an appreciable optic effect, and that in the flagella which 

 I watched there was no increase in width of 10 per cent. ; though as to 

 5 per cent, one would have no strong opinion, and as to 2 per cent, none 



at all. 



It will be noted that the diameter of the flagellum can only contain 

 some 40 to 80 protein molecules, and that of the flagellum of a minute 

 flagellate cannot contain more than a quarter of this number, so that the 

 true theory of flagellar movement must be simple. 



The conception of one meridian of the flagellar skin being importantly 

 more or less extensible than the rest was suggested to me by Sir W. B. 

 Hardy ; but he has no responsibility for the treatment of his suggestion. 



The wave of contraction generally passes up the flagellum of Grantia 

 with a velocity of 25fA ± 5 [A per second, but was observed with velocity 

 over 100[A s. " I concluded from other data that it is probably 200 to 

 500\i s. in healthy life, and that about 2b\i s. is a minimum, so that if this 

 cannot be attained, transmission does not take place. I computed the 

 work done on the water per double stroke to be of the order of 1 xlO -10 

 C.G.S. units, with 5 vibrations per second. Healthy frequency {Q.J. M.S. 

 1895, p. 17) is probably nearer 20 vibrations per second. 



40 Internal radius. 



