Figure 80 — Image of a line dipole in a 

 circular cylinder; see Section 52. 



rcos (6 

 = 4 -r 



cos(^j-a) a'^ cos(02+«) 



"72 ;; 



T rsin((9j-<») a^ sin ((92 +«)■] 

 , ^=-f. 



[52a,b] 



[52c,d] 



where the significance of r^, r^, 6^, and 6^ is as shown in Figure 80. The real constant pt 

 is the line-dipole moment of the given dipole. The dipole and its image have axes equally 

 but oppositely inclined to the line joining their positions. 



On the cylinder itself, since ^2/^, = a/b^ and r^ sin 6^ = r^ sin O2, expanding the 

 sines 



^cos 9^ a?- cos ^2 



But, also, on the cylinder 



/cos t)^ a" cos ^jX 

 ^/f = /x sina I ■•- — ) 



^ ^ ^\ ^2 ' 



Tj cos dy = (a^ -62 _ r\)/2h^ 



and 



Hence 



«.-i^f^-'i-i)-ii;(»;-«-'5) 



Vy = - 



/I sin« 



1 



[52e] 



and thus has a constant value, so that the cylinder forms part of a stream surface. 



120 



