Figure 229 - Streamlines due to translation 



of a prolate spheroid in the direction of 



its axis. The foci are shown by dots. 



See Section 137, Case 1. 



Now, for any number f, 



•■nH'-'rH-i\F7.-it? 



hence, expanding, for |fl > 1, 

 ^+11 1 



In 



1 J_ _1_ 



^-1 ^ 2^2 3^3 4^ "" 5^5 



J_ _1_ J_ 



1 1 



4^ 5^' 



2 2 2 



^ 3^2 5^^ 



[137y] 



^ 1 1 



^2_i ^ ^3 ^5 



[137z] 



Hence, if e -» and thus C^ ^ «, e^^j = ^^/^q = (2/3 + ••••) ^ -> 3/2. Again, as 

 e - 1 and C -» 1, both In (1 + e) and In (1 - e) become numerically negligible in comparisc 

 with e/(l - e^y, hence g^ -* 0, g^/{l - e^) -> 1. 



Toward infinity C -> ~ and, from Equation [137v], since ^ -» r/k and A; = ea, 



= ^i^f^A'(7^ + ••••) = Y<^'^i«' 



cos 



approximately. 



349 



