BRITISH ISLES FOR THE EPOCH JANUARY 1, 1915. 
27 
Next, to get the best potential solution we combine the four equations of condition 
for N and W. Thus 
SjAN = ai2( + Ax) + 6i2 Al 
SgAN = rq2 A\ + />i2( + A0 
— Wq sin XyZ ( + AX)+ cos XqSiAW = — ?>i2 ( + AX) + 622 A^ 
— WosinXo2AX+ cos X^SgAW = — 6,2 AX + 62 ^ ( + A/) 
and we solve for a^, b^, b.^ by least squares. In practice it is very easy to calculate 
how much these coefficients differ from those obtained in the independent reduction 
of N and W. 
The results are entered on Table V. 
The values of V obtained in the first instance by the same method do not of course 
require adjustment to fit a potential function. 
The lines thus obtained for the districts were drawn on a large scale O.S. map, and 
although they did not join at the boundaries, the discrepancies were a good deal less 
than might have been expected, thus justifying the tentative division into non-over- 
lapping districts. 
The next step was to obtain forms for the general representation of the British 
Isles. I proceeded by the humble method of meaning the district potential solutions. 
A slight adjustment of constants proved necessary to reduce the discrepancies between 
the means for different districts. These were adjusted by least squares. The 
discrepancies tabulated in Table IV. may appear in some cases large, but they follow 
no simple law, as far as I can ascertain, and I prefer to attribute them (as the known 
iron mines suggest) to district causes. 
Table IV.—Mean Values of Geographical Components for the Districts compared 
with the Values Calculated from the best Potential Solution. 
District. 
North. 
West. 
Vertical. 
Xfl. 
k. 
0 . 
C. 
0 
1 
P 
0 . 
C. 
i 
1 1 
P 
0 . 
C. 
0-C. 
I. 
II. 
57 2l'-8 
-3 44-8 
15,106 
1.5,099 
-f 7 
5041 
5046 
- 5 
46,279 
46,315 
-36 
III. 
55 2-1 
-2 45-6 
16,157 
16,156 
+ 1 
5025 
5012 
+ 13 
45,284 
45,199 
+ 85 
IV. 
54 42-9 
-6 48-6 
15,906 
15,890 
+ 16 
5582 
5581 
+ 1 
45,406 
45,456 
-50 
V. 
52 44-8 
-0 4-4 
17,330 
17,361 
-31 
4760 
4743 
+ 17 
43,925 
43,933 
- 8 
VI. 
52 54-0 
-2 40-2 
17,011 
17,043 
-32 
5070 
5093 
-23 
44,251 
44,255 
- 4 
VII. 
52 53-1 
-8 14-9 
16,506 
16,-503 
+ 3 
5862 
5858 
+ 4 
44,882 
44,795 
+ 87 
VIII. 
51 22-3 
4-0 3-2 
17,943 
17,940 
+ 3 
4803 
4786 
+ 17 
43,262 
43,319 
-57 
IX. 
51 13-2 
-2 51-2 
17,751 
17,717 
+ 34 
5163 
5191 
-28 
43,518 
43,538 
- 20 
E 2 
