Motion of Viscous Liquids in Channels. 

 SA, the equation of the parabola will be 



f* COS \d — 7T, 



and that of the latus-rectum 6 2 = \ir 2 . 



31 



\£ 



Fig. 1. 

 S 



Ejr. 2. 



Let us take 



f=?4cosi^ 9 = rising, 



so that we have a conformal transformation if f, v be regarded 

 as Cartesian coordinates in another plane, the parabola Vans- 

 Eorming into f =7r, and the latus-rectum into £ 2 = v 2 . The 

 correspondence is shown in figs. 1 and 2, where corresponding 

 points are similarly lettered. ° 



Since 



m~ i <^ 



m 



the conditions to be satisfied by % become, with reference to 

 fig- 2, 



P+g = -«(f + r), .... (3) 



over the area L'SL ,, x =0 on £=*, d x / P=d r3 , ; on f 

 and dx/o?= —ox/9'; on ?=-?/. 



