SURVEY OF THE BRITISH ISLES FOR THE EPOCH JANUARY 1, 1886. 
24‘J 
1-7 — 11 = 0-036854 c, 
I - 53-514 = - m{\ — 5) + V 
m = -151 + -07 sin (45 c), 
all that can be desired in this respect is attained. 
These equations do not, however, give the forces at the central stations with the 
accuracy attained in the southern districts. Far better results are obtained if we 
assume that the lines are parallel to the 1'7 line and are at equal distances from each 
other. In this case m is constant, and, in addition to the first of the above equations, 
we have only 
I — 53-514 = — 0-151 (\ - 5) + c. 
The values obtained from the central stations l)y botii formulm are given in the 
following Table :— 
Distl'ict. 
Horizontal Force at central stations in northern 
districts deduced from 
Mean of all 
stations in district. 
Formula 
with m variable. 
Formula 
with m constant. 
I. 
1-5580 
1-5583 
1-5582 ■ 
II. 
1-6363 
1-6390 
1-6358 
V. 
] -6650 
1-6608 
1-6658 
VI. 
1-6979 
I-697I 
1 -6972 
We have, therefore, to choose between two formula}. The simpler represents the 
lines throughout Scotland as practically parallel, both with those wdiich in the south 
extend right across the kingdom without considerable curvature and with those 
found by the district equations for the north of Scotland, and also reproduces the 
values of the Horizontal Force at the central stations with great accuracy. The more 
complex expression represents the mean directions of the lines in the centre of Scot¬ 
land and north of Ireland more satisfactorily, though these are obviously tillected by 
some widespread disturbance, but it fails when tried by the test of the reproduction of 
the forces at the central stations. We think there can be no question that, under 
these circumstances, the simpler formula, which assigns directions to the lines in 
harmony with those obtained in other parts of the kingdom, must be that selected ; 
and we have therefore employed it. 
In the following Table the values of the Horizontal Forces at the central stations 
are compared with the calculated values given by the foi'mul8e— 
MDCCCXC —A. 2 K 
