ADJUSTMENT BY LEAST SQUARES 173 



194WS — nis-4 — ms+4 =" 56^3 + is(<^s-i + ds+i) 



+ 4{ds-2 + ds+2) + {ds-3 + <^s+3), (16) 



which gives a very rapid approximation for any central cell 5. For 

 cells near and at the ends of the chain the same multipliers are valid, 

 but the residual m's have slightly different coefficients. For example, 

 if the chain terminates in 5+2, the above equation still holds for ms 

 if the term —ms+i on the left is replaced by -\-ms+2 and ds+s is 

 omitted on the right. 



The series of multipliers available for such a single chain of rec- 

 tangular cells is the series 



I, 4, 15, 56, • • • Pr, 

 where 



pr = 4pr-l — pr-2, (l?) 



for any positive integral value of r, and 



pi = 1, p2 = 4. 



§7. TRIANGULAR NETWORKS. MORE RAPID APPROXIMATIONS 



As in the case of the rectangular networks just considered, so in 

 triangular networks can more rapid approximations for the correlate 

 of any cell be obtained by eliminating the correlates for second- as 

 well as first-remove triangles. 



As the triangles will normally be restricted to those in which no 

 angle is less than 45° and none greater than 90°, we can assume that 

 only rare instances will occur of common second-remove cells. The 

 normal case will be one in which each triangular cell has from one to 

 three first-remove triangles touching it, and each of these has one or 

 two independent second-remove triangles in external contact with it. 



Single chain of triangles. Consider the case of Figure 5, which relates 

 to triangular cells in the same way that Figure 4 relates to rectangular 

 ceUs. 



Fig. 5 



The table of correlate equations with cell 5 as center is shown in 

 Table VI. 



833 



