68 0. E. SCHI0TZ. [NORW. POL. EXP. 



We thus find that the difference ^/ between the pressures exerted by 

 the external shell upon the internal nucleus beneath the oceans and beneath 

 the continents, cannot be greater under the conditions we have considered, 

 than the pressure that a volume of water of a depth of 120 m., or a slab of 

 rock of 48 m., with specific gravity 2'5, will exert upon their substratum. 



A slab of rock such as this, by its attraction, will only alter the accele- 

 ration at one point on its surface by 0'05 mm. If it be considered that the 

 various points on the lowlands where the force of gravity has been determined, 

 are not on the sea-level, but at a greater or less, though slight, height above 

 it, making it necessary to reduce the observations to sea-level, it will be seen 

 that the observations in the lowlands could be as well satisfied by assuming 

 that equally large areas of the surface of the internal nucleus are exposed on 

 the average to an equal pressure from the external shell, as by supposing 

 that the quantities of mass above it are on an average equally large. 



In the calculation of the flux of force above, we have started with the 

 supposition that the lines of force follow the normals of the limiting spherical 

 surface. Strictly speaking we cannot generally assume this to be the case, 

 on account of the uneven distribution of the masses in the external shell. 

 As experience shows, the deviation of the vertical line in the lowlands is slight 

 on the whole, and this deviation will not therefore produce any change in the 

 general result at which we have arrived. 



Before proceeding further, however, we will consider what conclusion may 

 be drawn, with regard to the acceleration, from the fact that the lines of force 

 are deflected from their normal straight course, supposing that this is not 

 due to any special accumulation or deficiency of masses in the depths. We 

 will imagine a tube of force passing through the boundary of a surface-element, 

 E\ du, upon the surface of the inner nucleus. Owing to local irregularities 

 in the distribution of matter, the walls of the tube, during its passage through 

 the earth's crust, will not follow the normals through the boundary of the 

 element, and the tube will cut off from the free surface of the earth a surface- 

 element, Rl dca', which will generally differ somewhat from the normal, 

 R* da>, which would have been cut off if the lines of force had had a normal, 

 straight course, dw and dio' are, as above, the solid angle under which the 

 elements are seen from the centre. 



