168 E. LANCASTER JONES 
In Table III, where V,=n?—7n,’, the approximations are shown 
worked out to m’, at which stage the residues are well below o.1 and 
the values obtained for the m’s are within 0.02 of the correct values. 
This would be an over-elaborate refinement in practice, but illustrates 
the rapidity of approximation obtainable by the method. 

TABLE III 
N A m’ A” +m” +m!" +m — +mvY — 
rea tees 3 5-714 | 0.374 0.421 0.020 4-347 
4 9.286 | 0.676 0.683 0.019 | —2.7 
6 Bares 0.625 0.239 0.078 
18.125 | 0.425 1.343 0.117 
4.286 | m —2.589 | 0.061 —0.192 | —0.017 1.549 
7\2 4 9.286 | 0.676 0. 683 0.019 3-617 
5 1.667 0.357 0.1909 0.063 | —1.703 
10.953 | 0.319 0.882 0.082 
3.571 | m —1.565 | 0.046 —o.126 | —o.012 1.914 
ales I | 4.286 2.589 | 0.061 0.192 0.374 
5 1.667 0.357 c.199 o.c63 | —6.191 
2.619 2.946 0.138 0.255 
—5.714 | m| 0.374 —0.421 —0.020 | —0.036 | —5.817 
VEAL ZI r | 4.286 2.589 | 0.061 0.192 
2 | 3-571 1.565 | 0.046 0.126 0.676 
6 2.825 0.625 0.230 0.078 |—10.045 
4-732 4-779 0.132 0.396 
—9.286 | m| 0.676 —o.683 —o.019 | —0.059 | —9.369 
6/5 2 | 3.571 1.565 | 0.046 0.126 
3 5-714 | 0.374 0.421 0.020 
2.143 I.IQr 0.375 0.146 
—1.667 | m —0.357 —o.199 —o.063 | —0.024 | —2.310 
8 | 6 I | 4.286 2.589 | 0.061 0.192 
4 9.286 | 0.676 0.683 0.019 
5.000 1.933 0.622 0.211 
—3.125 | m —0o.625 —0.239 —o0.078 | —o0.026 | —4.093 
The final values obtained are 
M, = 1.55, M2 = 1.91, m3 = — 5.82, 
Ws =" —1053)]'5) 7b ae 2-o ly 26 = = 4-0 
§5. RECTANGULAR NETWORKS 
The case of a rectangular network has a particular importance, 
since it corresponds to an ideal arrangement of stations often used in 
practical geophysical surveys on suitable terrain. 
Referring to equations (9) and (10) of §4, we have 
n= 4 and n,’ = 1, 2, 3 or 4 generally. 
° N, = n? — n,’ = 12, 13, 14 OF 15, 
and we can solve by successive approximation, as in the case of tri- 
angles, using the formulae 
828 
