BEITISH ISLES FOE THE EPOCH JANUAEY 1, 1915. 
55 
be significant. There is no obvious reason why linear formulae should apply to the 
British Isles, but on the other hand there is a well-founded distrust in the present 
methods of measuring vertical force. In view of the highly important discriminating 
value of good vertical component values in theoretical work, our results emphasize 
the urgency of improved methods of observation of this component. 
We have now to consider the Disturbing Forces indicated by our analysis of this 
survey, and to compare them with those found by UtiCKBR and Thorpe. But before 
we enter on a detailed comparison it is desirable to emphasize the theoretical principles 
involved. 
Stated in general terms our problem is to abstract the features common to a large 
number of observations. This problem is common to the investigation of all natural 
phenomena ; but whereas in laboratory observations the conditions can be controlled, 
so that a definite solution can be obtained, the magnetic observations in a survey are 
made under uncontrolled conditions and a determinate solution is not possible. Our 
only test is the closeness with which we can represent the observations by an 
empirical formula. When the formula ceases to be simple, or to admit of easy 
interpretation, we must stop. The residuals are the disturbing forces for which 
causes must be assigned within the region surveyed. 
In their survey Bucker and Thorpe aimed at making the residuals as small as 
possible, by using overlapping districts, and formulae proceeding to squares of the 
geographical co-ordinates ; but in the present survey, the districts did not overlap, 
the formulae used were linear in the geographical co-ordinates, and moreover 
conformed to a magnetic potential. 
Since the surveys differ in epoch by 29 years and the main parts of the magnetic 
forces have changed considerably in the interval, this is equivalent to a change of 
the uncontrolled conditions. Thus a comparison of the disturbing forces is very 
instructive. 
In the Tables IX. and X. the disturbing forces for 1886 were computed from the 
values given by Bucker and Thorpe, ‘Phil. Trans,,’ A, vol. 181, p. 270, and it must 
be remembered that the new stations are not identical with the old ones. 
As regards the horizontal components, the agreement is in most cases remarkably 
close and supports the view that these disturbing forces are not mere errors of 
experiment, but are due to real local or regional causes. In a few cases (e.g'., Portree) 
the discrepancies may reasonably be attributed to the change of observing point 
in a highly disturbed region. There are, however, a number of discrepancies that 
cannot well be accounted for by change of observing point, and they imply either 
error of observation or change of the local conditions. 
When we compare the vertical components of disturbance the results do not 
appear so concordant, and this is brought out in Table X., which gives the district 
disturbing forces. It might have been expected that Bucker and Thorpe’s formulae 
would give lower residuals for the districts, but the table shows little if any superior 
