THE MECHANICS OF CILIARY MOVEMENT 217 



a'D' represent tlic force on D' due to the reaction of the hquid 

 to the motion of the cihum. This force is normal to the axis 

 of the ciUum and tangential to the cyHnder of rotation, and 

 may be divided into two components, one h'D' along the 

 axis of rotation, the other 6-'D' in a direction perpendicular 

 to the plane of this axis and O'D'. Similarly at any other 

 point D" the force may be split into the two components, 

 b"Yy" and c"D". 



The sum of the component forces ^'D', b"T)" , etc., for 

 every point on the cilium may be represented as BD, such that 



LbVi - BD. 



Similarly, the sum of the tangential components c'D', 

 c"D", etc., for every point on the cihum may be represented 

 as CD, such that 



UcD -- CD. 



The latter forces have a moment about the axis of rotation 

 which tends to produce rotation 

 of the body about this axis. 

 Their summation gives a re- 

 sultant couple F X MN (Fig. 61), 

 such that 



6-D X OD -^ F X MN. 



Consider the effect of these 

 two systems of forces on the 

 body of the spirillum (Fig. 62). Fig. 61. 



Fig. 62. 



The resultant OB represents the total effective force act- 

 ing upon the body from the water, probably through slight 

 pressures established by the motion given to the water as 

 a result of the whipping action of the cilium. The motion 



