1890.] 



Presents. 



133 



where in both lies between and and cos -1 a is the inclination 

 of the stream to the plane. 



In the second part of the paper, some general transformation 

 theorems are obtained, which are applicable to problems of electric 

 condensers, forms of hollow vortices, &c. 



If two polygons lie one within the other, the transformation of the 

 area between them which makes the boundaries ^ curve is 



dz lL-i 

 -g— = n r {e[a(iv — w,)]H[a(ft>— iiv)]} * , 



where ot r is the internal angle of the polygon at w = w r) and 0, H are 

 the elliptic functions usually so indicated. 



A similar transformation is given for the case in which one polygon 

 lies outside the other. The method is then applied to find the form 

 of hollow vortices in certain cases. The transformation which gives 

 the motion due to a stationary hollow vortex between two parallel 

 planes is 



z = A log tn (iv—^iK 1 ). 



Presents, January 16, 1890. 



Transactions. 



Briinn : — Naturforschender Verein. Verhandlungen. Bd. XXVI. 

 8vo. Briinn 1888 ; Bericht der Meteorologischen Commis- 

 sion des Natarforschenden Vereines. 188G. 8vo. Briinn 

 1888. The Verein. 



Brussels : — Societe Royale Malacologique de Belgique. Annales. 

 Tome XXIII. 8vo. Bruxelles [1889] ; Proces-Verbal. 1888, 

 Juillet — Decembre. 1889, Janvier — Jnillet. 8vo. Bruxelles. 



The Society. 



Liege : — Societe Geologique de Belgique. Annales. Tome XIV. 

 Livr 2. Tome XVI. Livr. 1. 8vo. Liege 1889. 



The Society. 



London: — Photographic Society of Great Britain. Journal and 

 Transactions. June to December, 11389. 8vo. London. 



The Society. 



Boyal Institution. Reports of the Weekly Meetings. January 



to June, 1889. 8vo. London. The Institution. 



Royal Medical and Chirurgical Society. Proceedings. Ser. 3. 



Vol. 1. 8vo. London [1889]. The Society. 



Royal Meteorological Society. Quarterly Journal. Vol. XV. 



Nos. 70-72. 8vo. London 1889. The Society. 



Royal Microscopical Society. Journal. 1889. Parts 4 — 6. 



8vo. London. The Society. 



l 2 



