{x,<o) 



Figure 205 — A line distribution ab of point 

 sources. See Section 123. 



The components of velocity are, using Equation [123f,g] with a= -a, b = 0, r^^r^, ''6=''' 



On the positive a;-axis t = x, r^ = x + a\ and it is obvious from symmetry that q^= 0. 

 Hence a stagnation point Q occurs where, to make q^ = 0, 



On the positive a;-axis ijj ^ aa\ also, lA = a a on the surface of revolution S defined by 



'w = — (a+ t-tA 



[124f] 



By expanding r and t^ in powers of 27^, it is readily shown that S crosses the a;-axis perpendic- 

 ularly at Q. Since everywhere on S 



c?Sr a / ^ x+ a \ a 

 ST — = — ( 1= — (cos^- cos d,) < 



the surface S is broadest at a; = - ■'o, where, since ST cannot increase without limit on S, r-r^ 

 -. a and To -* 2\/ a a/U . For the definition of 6 and 6^ see Figure 206. Thus, if R is the 

 maximum radius of S, 



R = 2 l/y^ ' ^(? = 7 (y^^^ - «) H24g,h] 



At the middle of the line of sources or at a; = - a/2, where r = r^, on S 



~ l/ 2 «a R 



[124i] 



313 



