. The London, Edinburgh and Dublin philosophical magazine and journal of science . e coefficient of x,i. e. equally. This is evidently the broken line A B C D E F;for an ordinate drawn through any point of it cuts the systemof five lines in five points, one of which is on the locusA B C D E F and two others are on either side. It is obviously very easy todraw this locus when once wehave any portion of it; for we simply traverse the network,changing our line at every corner. The second median locus is obtained by weighting theequations, or lines according to the coefficients of y. Thefirst two
. The London, Edinburgh and Dublin philosophical magazine and journal of science . e coefficient of x,i. e. equally. This is evidently the broken line A B C D E F;for an ordinate drawn through any point of it cuts the systemof five lines in five points, one of which is on the locusA B C D E F and two others are on either side. It is obviously very easy todraw this locus when once wehave any portion of it; for we simply traverse the network,changing our line at every corner. The second median locus is obtained by weighting theequations, or lines according to the coefficients of y. Thefirst two count for very little, and the last three again countequally. The median is thus the line K L throughout, for thecrossing of the slightly weighted lines does not disturb thebalance of weights. We are now to take the point of intersection of these loci2 12 468 Mr. H. H. Turner on Mr. Edgeworths Method of as the final solution of the equations. It will be noticed thatthis leaves the solution somewhat indeterminate; for anypoint of the portion C D satisfies the required & H This special case is in many respects an unfavourableexample of the method under consideration; but it illustratessufficiently well the following points :— (1) The two median loci are broken lines which follow thelines of the network formed by the separate observation-lines(except in one very special instance mentioned below), andformed according to the following rule. Suppose the linesall labelled with the coefficients of x in the equations repre-senting them. At any point of the locus let A be the sum ofall the labels to the left (looking along the locus), and B thesum of all those to the right; / the label of the line withwhich the locus coincides. Then A +1> B and B +1> A. The locus continues to coincide with the line I until it iscrossed by another, say from the right, weight m. Then ifthe locus is to change to this new line, the sum of labels onthe left is still A, but on the right is
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