NO. 8.] REMARKS ON THE EARTH'S CRUST. 77 



When the angle is reduced, the influence of the section becomes greater, 

 and with small values of 9, the influence increases very rapidly when 6 dimini- 

 shes. For = 3, which will give a radius of 330 km. for the limiting zone, the 

 increase in the acceleration will be 0'44 mm., and for 8 = 0.25 as much as 

 1'85 mm. The influence will still increase a little, if 6 decreases yet more; 

 but a decrease soon commences, and the influence then sinks with extreme 

 rapidity towards zero, when 9 approaches that value. 



By the aid of this curve, we can now easily obtain an idea of the 

 influence of the added masses here treated of, disregarding for the present 

 those that correspond to the incline of the continents towards the ocean 

 depths. We will consider a circular continent, say as large as South America, 

 with a radius equal to about 0'37 R a , or an angular radius of rather more 

 than 20 . 1 In the centre of the continent, or about 2200 km. from the coast, 

 the added masses, as we have seen, will produce an increase in the acceleration 

 of about 0'07 mm. When we approach the coast, the influence will at first 

 increase exceedingly slowly; at a point about 1000 km. from the nearest 

 coast, the increase in the acceleration will be only about 0'085 mm. 



If we divide the continent by a great circle through the point under con- 

 sideration parallel to the nearest portion of the coast-line, the influence of the 

 greater part will diminish quite slowly when the point approaches the coast- 

 line, and will produce an increase in the acceleration of about 0'03 mm. As 

 the angular radius of the continent is less than 90, the effect, however, of this 

 part will again increase a little, when the point comes very close to the coast- 

 margin, so that the acceleration in the coast-margin itself will have an in- 

 crease of about 0'06 mm. The influence of the other part, on the other hand, 

 will increase as the distance from the coast-line diminishes. In order to make 

 a more exact calculation of this influence, we may imagine the part divided 

 up into wedge-shaped sectors radiating from the point under consideration, and 

 so small that the angular radius of the sector may be regarded as constant. 

 The result given by this calculation is that at a distance of 3, or about 330 km., 

 from the coast, the influence will be about 0.17 mm., so that the added masses 

 for the whole continent at this point will produce an increase in the acceleration 

 of about 0'20 mm., or only 0'13 mm. more than in the middle of the continent; 

 at a distance of 0.5, or about 55 km., from the coast, the influence will be 



1 F. R. HELMERT Hohere Geodtisie. Bd. II, p. 313. 



