434 On Stresses caused in Interior of the Earth, §c. [June 16, 



if the excess or defect of ellipticity above or below the equilibrium 

 value were T oVo> then the stress-difference at the centre would be 

 8 tons per square inch ; and that, if the sphere were made of material 

 as strong as brass, it would be just on the point of rupture. Again, 

 if the homogeneous earth, with ellipticity were to stop rotating, 

 the central stress- difference would be 33 tons per square inch, and it 

 would rapture if made of any material excepting the finest steel. 



The stresses produced by harmonic inequalities of high orders are 

 next considered. This is in effect the case of a series of parallel 

 mountains and valleys, corrugating a mean level surface with an 

 infinite series of parallel ridges and furrows. 



It is found that the stress- difference depends only on the depth 

 below the mean surface, and is independent of the position of the 

 point considered with regard to ridge and furrow. 



Numerical calculation shows that if we take a series of mountains, 

 whose crests are 4,000 meters, or about 13,000 feet, above the inter- 

 mediate valley bottoms, formed of rock of specific gravity 2*8, then 

 the maximum stress-difference is 2*6 tons per square inch (about the 

 tenacity of cast tin) ; also if the mountain chains are 314 miles apart, 

 the maximum stress-difference is reached at 50 miles below the mean 

 surface. 



The solution shows that the stress -difference is nil at the sur- 

 face. It is, however, only an approximate solution, for it will not 

 give the stresses actually in the mountain masses, but it gives correct 

 results at some three or four miles below the mean surface. 



The cases of the harmonics of the 4th, 6th, 8th, 10th, and 12th 

 orders are then considered ; and it is shown that, if we suppose them 

 to exist on a sphere of the mean density and dimensions of the earth, 

 and that the height of the elevation at the equator is in each case 

 1,500 meters above the mean level of the sphere, then in each case the 

 maximum stress-difference is about 4 tons per square inch. This 

 maximum is reached in the case of the 4th harmonic at 1,150 miles, 

 and for the 12th at 350 miles, from the earth's surface. 



In the second part of the paper it is shown that the great terrestrial 

 inequalities, such as Africa, the Atlantic Ocean, and America, are 

 represented by an harmonic of the 4th order ; and that, having regard 

 to the mean density of the earth being about twice that of superficial 

 rocks, the height of the elevation is to be taken as about 1,500 meters. 



Four tons per square inch is the crushing stress-difference of 

 average granite, and accordingly it is concluded that at 1,000 miles 

 from the earth's surface the materials of the earth must be at least as 

 strong as granite. A very closely analogous result is also found from 

 the discussion of the case in which the continent has not the regular 

 wavy character of the zonal harmonics, but consists of an equatorial 

 elevation with the rest of the spheroid approximately spherical. 



