ADJUSTMENT BY LEAST SQUARES 169 
mM, a (4d, ar Zd;)/N, 
m,!' = Dm! /N; 
ie (x1) 
ml” eel =m." /N, 
which give approximations approaching the complete solution m, 
with rapidity rather greater than in the case of triangles. 
It should be carefully noted that, throughout the above reasoning, 
we have assumed that each first-remove and second-remove polygon 
is independent. If any polygon occurs as a common second-remove to 
two first-remove polygons, it must be counted twice in the sums 
Dm, 2m’, - - 
§6. SOLUTIONS OF INCREASING PRECISION. 
RECTANGULAR NETWORKS 
In networks which have a regular pattern, whether of triangles or 
rectangles, formulae can be developed for expressing the correlate of 
any particular figure (polygon) in terms of the excesses of its surround- 
ing figures, to any degree of remoteness. 
Previously we have only considered the elimination of the first- 
remove polygons, leaving the second-remove ones as first residuals. 
We next consider how to eliminate polygons of second and greater 
remoteness. 
Figure 3 shows a rectangular network in which the rectangles are 
numbered from one corner oo in rows and columns. 
00 ol 02 03 04 
10 II 12 13 14 
20 21 22 23 24 
30 31 32 33 34 
Fic. 3 
Any rectangle has a number of first-remove rectangles varying 
trom 2 to 4 according to its position at a corner of the complete net- 
work, on the outer run or in the interior of the network. 
From the geometry, each first-remove rectangle may have contact 
with a second-remove rectangle which is common to ‘another first 
remove. For instance, 11 is common to o1 and 10, both first removes of 
00. 
We shall first find expressions for the correlate of any rectangle, 
eliminating both the first-remove and the common second-remove 
829 
