458 Messrs. G. C. Foster and 0. J. Lodge on the Flow 



equipotential circle on each side of the middle line. The radius 

 of this circle is given in § 20 as 



__ 2afJL n 

 P ~fj? n -1' 

 solving* which we get 



*'= ~ p • 



The positive sign only is admissible, since /i is essentially posi- 

 tive ; whence the number of lines 



2n = -. log ^-. 



log p, p 



So, then, the resistance of a strip between two consecutive flow- 

 lines is 



1 u (ya + l)/cotan^a log p, ° p 



The number of flow-lines in the sheet is (§ 12) 



2tt 



therefore the resistance of the whole sheet is approximately 



27T x (/^+l)7r/co tan ^a log p, ° p 



Now, make the rectangles infinitely small (and therefore recti- 

 linear), by letting a approach and p, approach 1 ; then 



the same expression as that obtained at the end of § 22 for the 

 same case. 



The resistance of the segment contained between two flow- 

 lines intersecting each other with the angle y is, under the same 

 circumstances (§ 25), 



_, 2 , «+*/«« + />* 



R v=^ l0 S p ( 14 ) 



Any number of Poles in an Infinite Sheet. 



27. Lines of Flow. — The equation to the flow-lines for two 

 equal and opposite poles, A and B, in an unlimited sheet, was 



