636 
MR. B. STEWART ON THE NATURE OF THE FORCES 
But this is not often the case ; and although generally both elements are on the same 
side of their normals, yet it happens -occasionally that the one element is above while 
the other is below ; while on such occasions there is nothing in the behaviour of the 
peaks and hollows to indicate the action of any other than the ordinai 7 disturbing 
force. 
33. This may perhaps be explained by supposing two antagonistic forces to be in 
operation at once, the one tending to elevate, and the other to depress the curve, the 
absolute values of these forces bearing a somewhat large proportion to their differences, 
and the one force affecting the elements in a slightly different manner from the other. 
Suppose, for instance, that + 1 and — 1 denote the position of the horizontal and the 
vertical-force curves at the same moment, the former being elevated above its normal, 
and the latter depressed below it. 
Conceive this result due to the action of an elevating force represented by +40 +20 
opposed by a depressing one represented by — 39 —21, and we have a sufficient expla- 
nation of this anomalous circumstance, while at the same time both the antagonistic 
forces sufficiently present the normal type. 
34. The same style of reasoning will apply in comparing the declination curve with 
that of either force ; only here we must suppose that the one force affects the declination 
in a somewhat different manner from its antagonist, so that the proportion between a 
declination peak and one of either force is not so constant as that between peaks of the 
two forces. The idea of two antagonistic forces, the difference of which represents the 
visible action, seems also to give the simplest explanation of the fact, that sometimes a 
force which depresses one of the elements will change in the course of a few hours to 
one which elevates it — since otherwise we must suppose the disturbing force to have 
changed its character. 
This also is the view of disturbing forces which General Sabine, who has studied the 
subject so long and so successfully, has lately been disposed to adopt on other grounds; 
and I am happy to think that the idea herein advocated is that of one whose judgment 
is so mature and whose information is so extensive. 
35. Adopting this view of the subject, it is worthy of remark that the same element 
of the disturbing forces (the declination) which changes so much its comparative value 
from one disturbance to another, changes also the most of the three when we pass from 
the one to the other of the antagonistic forces concerned in the same disturbance. 
In conclusion, I may be allowed to state that this paper is submitted to the Royal 
Society rather as indicating a method of analysis than as embodying the results of an 
investigation. 
