532 Prof. Riicker. On the Magnetic Permeability of 



cone, of which the vertex is in the surface, the vertical angle is 

 2 tan" 1 \/2, and the upper and lower faces are y Q and y kilom. from 

 the surface respectively, the force exerted at the vertex is 



2xO-8871og 10 (y/y ) 



where a is the density on the horizontal surface. 



If y = 20 and y = O5 kilom., this gives a vertical disturbing 

 force of 1110. By thus assuming a favourable form for the rock 

 mass, it is possible to account for the force by means of ordinary 

 basalt, which nowhere approaches the surface nearer than a depth of 

 500 metres, or about 1600 feet. 



Some difficulty may be felt about Ireland, over a large part of 

 which the vertical force disturbance is negative. 



If this be regarded as a real upward force, it could only (on the 

 hypothesis under consideration) exist in the neighbourhood of mag- 

 netic matter, which would probably cause more widespread positive 

 disturbance than has been registered. 



I am inclined to account for this by a shift in the datum from 

 which the disturbances are measured. If the calculated vertical 

 forces are all O'OOIOO C.G.S. unit too large in Ireland, the vertical 

 disturbance would be nearly everywhere positive. An error of this 

 sort would be accounted for by an error of 0'00040 C.G.S. unit in the 

 horizontal force, and this again would correspond to a displacement of 

 the lines of equal horizontal force through 6 miles. If, however, the 

 error was due to an unfavourable combination of inaccuracies, both 

 in the lines of equal dip and equal horizontal force, this displacement 

 of the lines might be reduced, so that, on the whole, it is not impos- 

 sible that the datum in Ireland may be 100 units of vertical force 

 disturbance different from that in England. If this is so, and if the 

 change is gradual across England, the difference between the means 

 of the negative and positive vertical disturbance would be diminished, 

 and the calculated would be brought into closer accord with the 

 observed range of vertical forces. 



As the Malvern Hills have been so carefully studied, it seemed 

 worth while to see whether the observed deflections of the needle 

 towards the hills could be accounted for by their magnetic nature. 



It is, however, at once evident that the problem is beset with diffi- 

 culties. The permeability of the range appears to be different in 

 different parts, and a mean value will not give accurate results. 

 The visible mass of igneous rock, supposed to be of mean perme- 

 ability, is certainly insufficient to account for the observed effects, 

 and if we attempt to base calculations on assumed underground 

 extensions of the mass, they are of course founded on pure hypo- 

 thesis. 



The easiest way of attacking the problem is to calculate the sum of 



