82 



If this undulating membrane be examined with a very high 

 power of the microscope, waves are seen to travel continually over 

 its surface, passing from the front to the back. "These," as 

 Hensen explains, " are caused by each successive transverse 

 portion passing one after the other from one 

 extreme position (Fig. 47) to the other. For 

 instance, if at the initial period a portion of 

 the edge, which is seen from above, occupies 

 position 1 to J 1 (Fig. 47), it is seen at the 

 end of the first quarter of the period to have 

 assumed position II to II 1 , or, which amounts 

 to the same thing, position II x to II 2 . At 

 the end of the second quarter the portion 

 II 1 to 71 2 is in the position III to III 1 or, 

 which is the same, III 1 to III 2 . At the end 

 of the third quarter III 1 to III 2 has passed 

 into the position IF to IV 1 , whilst, at the end 

 of the whole period it has again taken up 

 position I to I 1 . The movements follow after 

 each other with a certain degree of force and 

 speed ; it remains now to be seen how a for- 

 ward motion results from them. Any one 

 point on the surface of the undulating border 

 (Fig. 47) moves, as is indicated by the arrow, 

 from 8 to y with the force x = ay. This force 

 can be resolved into its two components aft 

 and fty. The force aft is exerted in the direc- 

 tion of the border, compressing it, and ap- 

 parently producing no further effect. Force 

 fty may be again split up into yS and ye. 

 ye exerts a direct backward pressui-e on the 

 water, and hence, in consequence of the re- 

 sistance of the water, propels the body in a 

 forward direction. Force 78 would cause the 

 body to rotate on its own axis ; but opposed 

 to it is the opposite force, which is developed 

 at all the places where the arrows point in an 

 opposite direction (as for instance over D). Further the same 

 force ye is present in Fig. D as in Fig. C, only the shaded por- 

 tions of Fig. A develop the forces which are opposed to ye. It is 

 seen, however, that the size of the surfaces in question, and hence 



FIG. 46. Spermato- 

 zoon of Salamandra 

 maculatn : k head ; w 

 middle portion ; ef tail ; 

 xp anterior end ; u un- 

 dulating membrane. 



