"26 Proceedings of the Royal Irish Academy. 



a field of flow with a number of infinities in the boundary. For the sub- 

 stituted obstacle is polygonal, and gives rise to a field in which the velocity 

 is infinite at every convex corner. No matter how numerous the corners, it 

 is difficult to regard such a Held as constituting an approximation to the How 

 past a smooth obstacle. It is not. therefore, as aids to approximation that, 

 the formulae are considered : but it i< hoped to show that they are useful in 

 tl xacl theory. 



I IKTK.I.MINATION OF TDK PODSTS "1 DEPARTURE OF FREE StREAM-UNES 



from a Curved Obstacle. 



13. In cases of liquid Bow pasl a rectilineal polygonal obstacle it is usual 

 t.. take for granted that th" stream-line which follows the contour of the 



forward pari of the obstacl i either Bide breaks away as a Free stream-line 



;u .1 comer of the obstacle. Bui the considerations which support this 



tmption do nol apply to a - thl\ curved obstacle, and the important 



ilem of the determination of the points of departure in such a case calls 

 foi attention. 



The question may be approached by considering the rate of change "i the 

 direction of the tangent to the free stream hue just at the point of departure. 

 >.. far a- the previous analytical formulation is concerned any points on the 



obstacle maj I to be the points of departure of the tree Btream-lines. 



But it aftei such an assumption has been made, the curve of the etream-line 

 I..- traced and it lie found that at the verj outset it enters into space occupied 

 by the solid obstacle, clearly the specified motion i- physically impossible. 

 Thus there - __•-'- itself a rule to the effect that unless tin' inward 

 curvature •■! the free stream-line at the point of departure i- less than that 

 of the obst icle, the specified motion is impossible. This rule may, in a sense, 

 stand; nut it> wording may prove misleading unless it is known and 

 remembered that generally the free stream-line his not 'u>\ a definite 

 curvatun lius of curvature at it~ point of departure. This fact will 



be proved in the following article For the sake both of practical utility 

 and of keeping the main argument as free as possible from analytical 

 complication, it i- proposed to consider in the first instance the case ol 

 symmetrical Bow. 



14. In dealing with a configuration "i the kind typified in figure \, 



1 flow can In- specified by <i: - < (£)'/£. where i i- expressible 



in the form set out in formula (:'.!'). 



