32 Proceedings of the Royal Irish Academy. 



Points of Depasture of Free Stream-Lines in Asymmetrical Flow. 



19. It has been shown above article 10 thai every rase of asymmetrical 

 Bow can \f ilealt with by the relation 



| -a-; -<>:/■• :, ■-- Exp -i-| |'_ * J' | \ogF 1;]^], 



where (50) 



?(&&)-(&- Z)\Z* («'-?) •./ l: l(a- -?)*{£„* -a*)*), 



51 

 and \ i? a function of £. It follows that if \ be the vector-angle of >l: <C 

 corresponding to a real value £, of £, and ii ; 



» O-W-s , ■- \ 



41 :: " - - ; : .:^> 



nil in the Bqnare hrackel omitted when £. a, bul retained 



when t < - ". 



f a 



1 | f C) - £i|'| . 



r »J I I ',< g <,,M 



t 



If the theorem ol the i pplied t" the sobjecl of integration, regarded 



inction Foi q zero, the in t • _ — n to be 



equivalent to 



2, . f | 



where , t ,, 0. Thia latl gral ten. Is to a definite limit f"i ij -> 0, 



namely the form L'"t by omitting >»'. Also, when >/ is small, the Brel 

 term pproximab 'if. So, if q* = t and is very 



small, formula S3) yields I ition 



, .. - : 



+ i_ ( [ + f j | 





- a 



