86 smitiisoxiax MISCELLANEOUS COLLECTIONS VOL. 5 i 



sidered corresponds indeed, according to what has been above said 

 only approximately to the velocity potential. 



(p = a { x — 6j cos m l x.e~ n i v — b 3 cos 3 m x x .e~ n , y 



— b 5 cos 5 m v x . e~ n i V j , j 



■ .(11) 



as determined by the above coefficients, b h , but we can easily 

 demonstrate that in the present example the differences could 

 scarcely be observed in fig. i. 



FIG. I 



From the preceding value of <p we derive the following values for 

 the components of the velocities of the current : 



u = a I 1 + ^ b h m h e " y sin m h x \ 



{ 2 k 



= a < 1 + -_ (b x e V sin m, x + Sb 3 e V sin 3 m, x 



+ 5 6 5 e~ n * y sin 5 ra t x) > , 



> . 



(12) 



v = a X ^P 6,, « A e n * v cos w A a? 

 = a X .1152 > ^ e~V cos m, x + % e~ n * v cos 3 m x x 



i — » 1/ 



JL_ *? A 



+ To * * COS ^ m i X 



(13) 



