NO. 8.] REMARKS ON THE EARTH'S CRUST. 79 



point under consideration advances quite up to the coast-margin, so that instead 

 of becoming normal again along the coast-margin, the acceleration will show 

 somewhat of an increase. The increase will depend upon the steepness of 

 the incline, there being thus a maximum for a certain slope, the increase 

 becoming less both for steeper and gentler inclines. 



It is easy to see that the effect resulting from these added masses upon 

 a point on the coast-margin itself will be an attraction. If we imagine a 

 sphere with the surface passing through the centre of the earth, and the 

 earth's radius as diameter, this, as already mentioned, will cut off from the 

 added masses a portion whose influence upon that point on the surface through 

 which this sphere passes, will be the half of the influence of an entire 

 spherical shell with thickness and density like those of the added masses. If 

 a sphere such as this is made to pass through a point in the coast-margin, 

 it will cut the spherical surface going through the ocean-bed in a small circle 

 with a radius of about 200 km. If the slope of the continent is 1 in 60 

 - which is not unusual (see page 73) - - the base of the continent will lie at a 

 distance of about 210 km. from the coast-line, assuming the depth of the 

 ocean to be 3'5 km. It will then be seen that the incline encloses almost 

 completely that part of the sphere which falls within the outermost shell 

 of the earth, which has a thickness of 3'5 km. The added masses on the 

 incline will consequently, at one point in the coast-line, exert an influence 

 about equal to a fourth part of that of a spherical shell having a thickness 

 of 3'5 km., and the same density as that of the added masses, and will thus 

 effect an increase of about 1'2 mm. in the acceleration. The subjacent nega- 

 tive added masses will not nearly be able to compensate this influence, as 

 they only contain a portion of the masses that the spherical surface in 

 question would cut off from a spherical shell of the same thickness (fe, fo 2 ) 

 as theirs. A more minute determination of the effect of these added masses 

 upon a point on the surface requires a somewhat complicated calculation, 

 as the integrations can only be approximately performed. I have obtained at 

 one point in the coast-line the following expression for the attraction, assum- 

 ing that the slope is constant. 





