1890.] The Theory of Free Stream Lines. 129 



January 16, 1890. 



Sir G. GABRIEL STOKES, Bart., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — 



I. " On the Chief Line in the Spectrum of the Nebulae." By 

 J. Norman Lockyer, F.R.S. Received December 9, 1889. 



[Publication deferred.] 



II. " Observations regarding the Excretion and Uses of Bile." 

 By A. W. Mayo Robson, F.R.C.S. Communicated by 

 Dr. Clifford Allbutt, F.R.S. Received December 24, 

 1889. 



III. " The Theory ot Free Stream Lines." By J. H. MiCHELL, 

 Trim Coll. Cam. Communicated by Professor J. J. 

 Thomson, F.R.S. Received January 3, 1890. 



(Abstract.) 



The chief object of the paper is to give a general method for the 

 problem of free stream lines in two-dimensional motion of liquids 

 when the boundaries are plane. The method rests on the trans- 

 formation from one diagram to another by means of functions of 

 complex variables, and, so far, is. similar to that given by Kirchhofr 

 in his ' Vorlesungen,' which is, however, of very limited application. 



The first part is devoted to general theorems of transformation. 



If x + iyEEz, x—iyzEz', 



+ ^ EEE w, (p—ity EE tv', 



and z is a function of w, then the transformation theorems are obtained 

 by considering the function 



dz dz' 



