HIKKKI.AM). TI1K .XnKWKI.IA.N Al'KnKA I'OI.AkIS KXI'KI >ITI( ).N, tgO2 1903. 



By the substitution of this value in |C), we find the conditional equation, which, after some reduc 

 lions, assumes the form 



If then .v (l = is substituted, and we multiply by ". , we obtain 



11 it- ii'' J /. ' M ' 



If \ve now put 



" '-",]- ' = " antl ~ tfM* = ; '' 

 the conditional equation becomes 



2 it n- -f- ->i'(\ + 1 5 it 24 it- -f H ,r'| -f a 7 ;>- = ( I. 



On the other side we may eliminate .v ( , from (A) and |B), and then obtain an equation that gives 

 the connection between the ratlins of the boundary-circle and r (1 . 

 By multiplying (B| by .v and substituting 



we obtain 



.V .v.v, 



/.-M- L-M- I.-M- 



whence 



v - = ^7i-lw^ ' 



Bv substituting this in (B), we obtain the desired equation 



n- luir <--' \n'' 



~ 1PM* + )-M^ L+ /-M^ + )W " ' 



or, if we again introduce r instead ol .v , 



We shall now deal with the problem in a general way, that is to say with an arbitrary value 

 of the angle of expulsion or in other words the angle between the ratlins vector and the direction ot 

 motion at the initial moment. 



We then have, as will easily be seen, 



ar n -\- /.M _ r r sin n 



:t ' 



whence 



/..I/ 

 a = ,- V sin ,, - 



' 



By substituting this value in (IV), we obtain 



