ADJUSTMENT BY LEAST SQUARES “E75 
Similarly, in the network of figure 6), we should get 
12m) = 7do + 3(dis + diz + diz) + doi + doe + doz 
+ dos + dos + doe. (21) 
The coefficient of mo is always 21—3m, where m, is the number of 
first-remove cells. 
Fic. 6a 
If in the network of triangles actually under consideration there 
are third-remove triangles, or triangles of still greater remoteness from 
the key triangle for which approximation is desired, there will be 
residual correlates, msi, m32,--- , introduced into equations of type 
(19) and (20). There is no difficulty in finding series of multipliers 
to carry the elimination to further stages, especially if the cells are 
To). 
[sI/ 
aes 
arranged symmetrically about the key cell. For example, the network 
of Figure 6b may be completed by the insertion of three triangles 31, 
32 and 33 between 22 and 23, and 24 and 25, and 26 and a1 respec- 
tively, giving three extra common third-removed triangles. The de- 
sired series of multipliers is then 2, 3, 7 and 15 and we get 
24mo = 15do + 7(dii + diz + diz) + 3(dei +--+ - + dee) 
ae 2(d31 + dz. + d33) . (22) 
§8. GENERAL NETWORK. PROCEDURE FOR ADJUSTMENT 
The foregoing analysis will have made quite clear the limitless 
possibilities of mathematical solution by means of correlate equations 
and multipliers suited to any cell of a network and its immediate sur- 
roundings. Interesting as such analysis is, its application to a practical 
835 
