166 E. LANCASTER JONES 
TABLE I 
Adja- 
A d cent m' 3m" me gm ON nN sie a 
As 
pal i 2+s5 1.667] 5 1.667|—3'.333|—1-111| 0.7411) sOn2d gies 
2 | +10 1+3 3-333|—1.666|/—0.556| 0.556] 0.185|—1.481]—0.494... 
3] —10] 2+4 |—3-333|—3-334]/—I-111|—0.110|—0.370|—1.111|—0.370... 
4| —20| 3+5 |—6.667|/—1.666|/—-0.556|/—3.889|—1.296] 0.186} 0.062... 
5|+ 5 j1+4+6| 1.667)/—8.333)—2.778] 1.667] 0.556/—3.333|/—1I-II1... 
67 |) —x0 5 —=3.333| 1-667] ©.556|—2.778|—0-926] 0-556)" 1osraseee 
The values for m obtained by summing the first four elements m’ 
to miv are within 1.0 of the correct values, and would be quite near 
enough in practice for obtaining the values of gravity at the stations 
and drawing up the isogam chart. The original link-increments from 
ay 
FIG. 2. 
which the d’s were calculated were of the order of 50 units, so that 
the final values adjusted on the basis of this fourth approximation 
would be correct within 2 per cent, which is the limit for gravity work 
of this type. The final values, obtained by putting m equal to 
m' +m" +m!" + mi¥ are m= 2.47, M2= 2.47, M3= — 5.19, m4= —8.46, 
ms; = —1.67, mgs= — 3.52, which should be compared with the values 
obtained in the next section. 
A more rapid approximation in the solution of the set of correlate 
equations 
n,m, — Um, = d, 
can be obtained by solving partially for those which involve m,, as 
follows. 
We have, say, 
N;M, — Mz — Me — My — mM, = a,, 
N2M2— M,— Ma— My, — +-- = dz, 
NM, — My — M, — My — = d,, 
mymy — M, — M, — ME — dy, 
n.m, — Mm, — My — mM, — = d, 
826 
