IS Proceedings of the Royal Irish Academy. 



If, therefore, a succession of values k, be taken for k, all Mug between 

 - a and a, and if to C(Z) be assigned the form 



S) = -K'n{^(Kn?)/(?-«r)) A ' 3 (9) 



where X' is a complex constant, the relation (7) will represent upon the 

 relevant half-plane of Z the region bounded internally partly by an open 

 rectilineal polvgon having corners at k . k : . etc. and c, and partly by curved 

 lines extending to infinity : and when the field relation is employed it specifies 

 a field of How in which the polygon represents the obstacle, and the curved 

 boundary the free stream-lines. 



Sin ;> is a pure curve factor, that is such as would if employed 



singly give a boundary free from corners, the corner-factors in t (£) are simply 



se which appear explicitly in formula 9 : to these, in formula l7), must 

 be added the comer-factor X,- B ngles of the polygon; measured 



on the side of the moving liquid, ai 2* t £ = e, (1-A,)a- at £ = ci, 

 (1 - Xt)ir at _ = «.. etc.. as indicated in figure •">. It is. of course, permissible 





to tab the vain- 1 if this be i with a power 



k' the ansrle at the vertex will 



The form of that pari ••(" the 1 »< which is in dead 



water is, at ' Hit 



An obstacle ..f the type gure 1 may be regarded as the 



limit . the type jure 5, a.< the sides 



of the i become indefinitely numerous and indefinitely small. If the 



stacle is to be ! th everywhen angle "f the 



tl and I index A. with the sole 



exception h infinitesin may ben 



vertical ai . _ - it is necessary to put 



