Flow of Viscous Liquids. 



363 



shown in fig. 3. The external circle AB corresponds to 

 i/r = ; AC, AO, AD correspond respectively to — 27r\|r = ^, 

 1, 2. As appears from (31), the highest value of — 27n/r is 4, 

 and gives a curve at A of infinitely small area. 



Fig-. 3. 



In the neighbourhood of A (fig. 1), (30) reduces to a simpler 

 form. Thus 



(1-OP 2 ) 2 

 ^'^ 2AP 2 =1+ COs2( k 



(330 



where <£> = PAO. The second term here satisfies the funda- 

 mental equation as being derived by multiplication with AP 2 

 from a solution, AP -2 cos 2(f), of V 2 i/r = 0. 



Equations (19), (30) give the means of expressing the 



2B 2 



