23G 
MR. A. W. RRCKER AND DR. T. E. THORPE ON A MAGNETIC 
These results prove that in this case, at all events, the differences between the 
results of the two methods of calculation are not greater than those produced in the 
numbers given by the method of least squares according as stations affected with 
considerable disturbances (23' and 76' respectively), and amounting to 4 percent, only 
of the total number, are included or excluded. 
We do not think, therefore, that it is in general advisable to use so cumbrous a 
juethod as that of least squares, when the addition of a station or two may modify the 
results to an extent far exceeding the error with which numbers obtained by the 
equations of condition are likely to be affected. If, however, the district under 
investigation is of such a shape that the effects of change of latitude and longitude 
respectively cannot be easily separated, it may be desirable either to modify the rule 
for obtaining the equations, or to employ least squares. 
In the case of a district so large as Scotland there is another objection to the use 
of least squares, viz., that the fundamental assumption on which that method is 
leased is almost certainly not true when applied to it. We shall show hereafter, as is 
indeed already known for other districts, that the errors are not irregularly distributed 
over the entire area, but that large fractions of the whole are affected with errors of 
a particidar kind. We cannot, therefore, regard the employment of least squares as 
theoretically better, while it is certainly practically more inconvenient than the 
method of equations of condition. The following Table contains the boundaries of 
the nine districts, the latitudes and the longitudes of the central stations, the values 
of tlie Declination at the central stations {^q), and of the change in Declination per 
degree of latitude and longitude {tIB'/dl and dS'/dk) both expressed in minutes of arc. 
Table V. 
District. 
Rouiidaries. 
Central Station. 
_ (W 
* (U' 
cU’ 
Lat. N. 
Lon 
c? * 
Lat. N. 
Lon 
g. W. 
o 
0 / 
0 
o 
o 
o 
Q 
/ ! 
T. 
All Sc otland 
56 
48-0 
4 
19-0 
21 
38-8 
14-5 
40T 
II. 
.54 to 57 
0 to 
G W. 
55 
27-3 
3 
41-6 
20 
55‘6 
16-7 
36-4 i 
III. 
52 
55 
0 
5 W. 
53 
26-7 
2 
26-0 
19 
39-0 
L5-5 
33-6 ! 
IV. 
50 
53 
2E. 
3 W. 
51 
47-7 
0 
17-5 
18 
6-6 
17-4 
28-9 1 
V. 
53 
55 30 
5 W. 
10 W. 
54 
2-9 
7 
36-5 
22 
41-3 
17-2 
32-5 ' 
VI. 
52 
55 
3W. 
8 W. 
53 
290 
5 
43-0 
21 
25-6 
20-9 
31-6 ' 
VII. 
49 
52 
I W. 
6 W. 
50 
47-0 
3 
IT 
19 
6 2 
17-8 
28-9 
I VIIJ. 
51 
54 
5 W. 
II W. 
52 
57T 
8 
I3T 
22 
85'0 
27-3 
80T 
i IX. 
50 
53 
3W. 
8W. 
51 
49-5 
4 
47-4 
20 
19-7 
22-4 
29-2 
. 
In District I., on account of its irregular form, the method of equations of condition is 
not very suitafile, and the method of least squares has been used. In order to compare 
tliis with the formula obtained by Balfour Stewart from W^elsh’s observation the 
