inn/ lu'iiiininl Mniini-ti- />!.</ iir/xtnce*. 525 



itdcijuate representation of the actual state of things to assume that 

 the district has no magnetic matter to the north and south ; but it is 

 separated from other similar regions on the east and west by a non- 

 niMLMietic trench 36 miles wide. 



The difficulty in accounting fora high average diffei'ence of vertical 

 disturbing force increases with the size of the district, as has already 

 been explained. We are, therefore, choosing regions which afford 

 the most severe test of the theory that the disturbing forces are due 

 to the magnetism induced in iron-bearing rocks. If we confine our 

 attention to a line crossing the two trenches and the plateau half- 

 way between their northern and southern boundaries, no important 

 error will be introduced if we consider the length of the trenches and 

 plateau to be indefinitely extended north and south. The values 

 obtained are, however, affected by the assumptions we make as to the 

 magnetic character of the ground east and west of the district un del- 

 consideration. The first hypothesis made is that the external 

 boundaries of the trench are narrow plateaux, and that beyond them 

 t ! iere is no magnetic matter. Afterwards, we will suppose that they 

 extend to infinity at a uniform height above the magnetic floor. We 

 may also, at first, assume that the edges of the magnetic masses are 

 vertical, and that they are magnetised by the vertical component of 

 the earth's field only. It will be convenient to express all distances 

 iu kilometres, and, as above stated, all disturbing forces in terms of 

 O'OOOOl C.G.S. or O'OOOl metric unit. 



The mean values of all the positive and all the negative vertical 

 force disturbances in England and Wales, recorded by Dr. Thorpe 

 and myself, are + 59 and 80 respectively, giving an average range 

 of about 140. 



A difference of this order can be obtained if we suppose that the 

 slabs of magnetic matter are 16 kilom. (or about 10 miles) thick, and 

 that thus the upper surfaces are 4 kilom. (or about 2^ miles) from the 

 surface of the earth: 



The components of the attraction exerted on a point by a plane 

 rectangular plate consisting of an uniform layer of attracting matter 

 of density a may be expi'essed as follows : 



Let planes be drawn through the point perpendicular to the plate 

 and parallel to its edges. Let the points in which these meet the 

 edges or edges produced of the rectangle be joined to the point, and 

 let these make angles 2 and 0j, 0. 2 and t with the normal. 



Then the components perpendicular to the plate and parallel to it 

 and to the plane of the 0's are 



^{sin" 1 (sin 0j sin 3 ) sin" 1 (sin 2 sin t ) sin" 1 (sin 0j sin 0.,) 



+ siu~ 1 (sin0 1 sin j)}, 



