468 Mr. H. H. Turner on Mr. Edgeworth's Method of 



as the final solution of the equations. It will be noticed that 

 this leaves the solution somewhat indeterminate; for any 

 point of the portion C D satisfies the required condition. 



& H 



This special case is in many respects an unfavourable 

 example of the method under consideration ; but it illustrates 

 sufficiently well the following points : — 



(1) The two median loci are broken lines which follow the 

 lines of the network formed by the separate observation-lines 

 (except in one very special instance mentioned below), and 

 formed according to the following rule. Suppose the lines 

 all labelled with the coefficients of x in the equations repre- 

 senting them. At any point of the locus let A be the sum of 

 all the labels to the left (looking along the locus), and B the 

 sum of all those to the right ; / the label of the line with 

 which the locus coincides. Then A + 1 > B and B + 1 > A. 



The locus continues to coincide with the line I until it is 

 crossed by another, say from the right, weight m. Then if 

 the locus is to change to this new line, the sum of labels on 

 the left is still A, but on the right is B — wi + 1 : thus we must 

 have 



A + m>(B— m+l), 

 and 



(B — m + l) + m>A. 



The second condition is the same as one of the former ; but 

 if the first is not fulfilled, the locus continues to travel along 

 the line /. By this rule the two loci can be traced with great 



