1004 



Dr. Dorothy Wrinch on the 



In the case when TJ*~l2/im = v* n the equation stands in 

 the form 



du d6 



W\/C0S a 



V cos 6 — cos a 



and we get 



COS a. 



\ogu/u 1 = — \/'2{'f--tyi). 



if u — u x when '^ = *»/r 1 , where 



sin 0/2 = sin a/2 sn (yjr, sin a/2) 



or 



sin 0/2 = sin a /2 sn —7-, log uJu + ^i 



y ' [_ v 2 cos a J 



/2 sn T^! + - log rjr . 



; T v/ 2 cos a J 



= Sin a. 



This curve oscillates between 0=±a, with r continually 

 increasing. As r->co is indeterminate, and instead 

 of tending to infinity along a certain line = 0o aiter a 

 finite number of contacts with the lines a and —-c, as in 

 the previous case when Ui 2 /2/a cos a > t'i 2 , this curve 

 oscillates between the rays ± a and has no direction at 

 infinity. A typical curve of this type is shown in fig. 2. 



Fiar. 2. 



The case when u 1 2 — TJ l 2 /2fjLm = u 2 2 >Q remains. 

 We have 



die d0 



vcosa s/u 2 — it 2 2 </cos6 — cos a 



Putting u = u 2 cosh f, we get 

 du 



= d%; 



V ii" — w 2 

 and consequently, if 



sin 0/2 == sin a/2 sn (yfr, sin a/2) 



