SURVEY OF THE BRITISH ISLES FOR THE EPOCH JANUARY I, 1886. 293 
The following are a priori probable consequences of the hypothesis that each 
district, bounded by two valley lines, is subject to an attraction tending towards the 
centre 
(1.) Since the regional forces are weak near a valley line it is in such a position that 
we should expect the effects of such local forces as might exist to predominate, and 
discrepancies to occur more frequently than elsewhere. 
(2.) The centre of a district, in the neighbourhood of the ridge line, should be a 
region of relatively high Vertical Force. It will be remembered that the ridge line is 
drawn by means of the disturbances of the Declination and Horizontal Force only, 
and, therefore, an agreement between its position and that of a region of high Vertical 
Force is an independent confirmation of the accuracy of the theory that the forces in 
play in the district form a connected system, that is, they are regional and not merely 
local. 
(3.) The directions of the Horizontal Forces at points of maximum or minimum 
Vertical Force may be indeterminate in the sense that they cannot be deduced from 
the distribution of the Vertical Forces. This point has already been insisted on. 
(4.) In crossing a valley line both sets of attractions in the region which it separates 
tend to produce a maximum and minimum of the Horizontal Force (see fig. 10, p. 263). 
If the southerly attraction were alone in play both of these would have values less 
than the normal. If the northerly acted alone both values would be greater than 
the normal. Hence, since the maximum will be to the north of the minimum it is 
probable that in producing it the effect of the northern attraction will predominate 
and the values will be greater than the normal, while in the case of the minimum 
they will probably be less. 
Comp)arison ivitli Mr. Welsh’s Survey of Scotland. 
No more severe test of the physical reality of the disturbing forces deduced by 
us from our observations can be applied than by the enquiry whether similar methods 
applied to Mr. Welsh’s survey lead to similar results. In part, the severity of the 
test lies in the fact that the methods cannot be precisely similar. As England was so 
imperfectly surveyed in 1857, we are compelled to assume a linear function to express 
the isomagnetics in Scotland at that date. The isogonals and isoclinals were calculated 
by Balfour Stewart, who used the geographical mile system of co-ordinates. Unfor¬ 
tunately the third element selected by him for calculation was the Total Force, which 
throws but little light upon problems such as those we are now investigating. We 
have, therefore, calculated the lines of equal Horizontal Force, using, as in our other 
calculations, the differences between the latitudes and longitudes and those of the 
central station as co-ordinates, and by combining these with Balfour Stewart’s 
calculated values we have found the disturbing forces at the various stations. 
o 
Again, Mr. Welsh omitted the determination of one or more of the elements 
