ADJUSTMENT BY LEAST SQUARES ' 175 



Similarly, in the network of figure 6h, we should get 



i2mo = 7^0 + 3(<^ii + dii + diz) + dii + </22 + ^23 



+ <^24 + <^5 + <^26. (21) 



The coefl&cient of wo is always 21 — 3«i, where «i is the number of 

 first-remove cells. 



Fig. 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, W32, • • • , 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 



Fig. 6h 



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 21 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 



24W0 = 15^0 + 7(^11 + di2 + dis) -f- 3(^21 + • • • + dis) 



-{- 2{d3i -f d32 + dsz)' (22) 



§8. GENERAL NETWORK. PROCeDITRE 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 



