ADJUSTMENT BY LEAST SQUARES 173 
194ms — Ms_4 — Msy4 = 56ds + 15(ds_1 + ds41) 
+ 4(ds—2 + dsy2) + (ds_s + dsis), (16) 
which gives a very rapid approximation for any central cell S. 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 S+2, the above equation still holds for ms 
if the term —ms,4 on the left is replaced by +ms42 and dgy3 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, gage La 
where 
br = 4Pr-1 — Pra; (17) 
for any positive integral value of 7, and 
Pile Sys P24 
§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 go°, 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 
 ZSISISTISD 
FIG. 5 
The table of correlate equations with cell 5 as center is shown in 
Table VI. 
833 
