34 Proceedings of the Royal Irish Academy. 



The third integral in H' depends ou 



1 <% - i r cos - r^-g)-s t ) r 



si (2a + £ )i (58) 



Therefore the smallness of H' makes formula i 56 i equivalent, when ** is 

 neglected, to 



a 

 , I" ' 'I 1 > \ 5 - \ <" • ,i- 



(o-c + I t ' I ("■-?•)-("-?) 



(59) 

 But 



•J . ^-[N«>-«HC-^r./[-r-HC-^* 



-a c 



and then I , when t- is neglected, reduces to 



•»-« >=[ 2 1! ;-!:' Hi 8N"»-<«* 



-« -• (60) 



This shows that, when the parameters arc Buch that the coefficient of tj is 

 zero, the angle of contingence of the free stream-line at its point of departure 

 is the same as that of the obstacle, so that the two curves osculate. 



Influence of the Shape of the Obstacle upon the Divergence of 

 the Free Streak-Lines, and thi Rbsis ance to Relative Flow. 



21. The theoretical considerations of the present paper have precise 

 bearing only upon flow which is everywhere irrotational, with discontinuity 

 at the free stream-lines. This may. for the moment, be called the 

 '• theoretical now " ; it is not realized in actual fact or experiment What 

 is realized generally to be a continuous flow which is not wholly 



irrotational, and this may be called the "actual Bow." In the theoretical 

 flow there is a dead-water or wake extending to infinity : in the 

 flow there is a wake of limited extent within which the motion of the 

 fluid is rotational. 



