188 Mr. F. Y. Edgeworth on a New Method of 



The rale and the exception may be illustrated by the fol- 

 lowing example*. Let the equations be 



x+y = a 1} x-ty = a 2 , x+y = a 3 , x + '6y = b x , x + '6y = b 3 

 Y 



represented by the annexed diagram. Beginning at the in- 

 tersection A we have, for movement in the direction Kp, 



and therefore 



For Kq we have 



and 



whence 



dU=dy {2-1-2); ds=J2dy 



dR = j8 

 ds ~ </2 



dR=-2dx + dy(3--(\), 

 dx + -C)dy = 0; 



dU 



3-6 



ds + n/1-36 



Again, for Ar we have 



dR 

 ds 



= ; and for AB, = ^. AB 



* This example also illustrates the possibility of the intersection be- 

 tween the Median loci being thoroughly indeterminate. The broken line 

 p A BC D« 1 is the locus of Median both for ordinatea and coordinates. 



