The.a;-axis is a line of symmetry. The components of velocity are 



o = V 





Compare [123f,g]. 



On the positive a:-axis r= x, r, = x+a, and 





Thus a stagnation point Q^ occurs on the a;-axis at a; = l^ where 



Again, where x < - a, r = - x, t = - x - a, 

 and 



/ «^ \ 

 7 = - t' ( 1 + — 



Thus a second stagnation point Q^ occurs at >r = - ^2 where ^9 '" '^ 

 and 



[125d] 



[125e] 



[125f] 



[125g] 



[125h] 



[125i] 



On the dJ-axis, except on the segment from - a to 0, lA = 0. Furthermore, = on the 

 surface S whose equation is 



262 



\ a T I 



a'^-{T^-rY 



[125j] 



By expanding r. and t^ in powers of oT, using the binomial theorem, and then dividing through 

 byoT^, it can be verified that S has rounded ends at Q^ and Q^. Its shape depends only on the 

 value of 6/a, while its size is proportional to 6, since the equation remains satisfied when h 

 and all linear dimensions including a are changed in the same ratio. The outline becomes 

 more slender, especially toward the rear, as h/a is diminished. 



316 



